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Table of Contents
1. Probabilistic Design ................................................................................................................................	1
1.1. Understanding Probabilistic Design ..................................................................................................	1
1.1.1. Traditional (Deterministic) vs. Probabilistic Design Analysis Methods .........................................	2
1.1.2. Reliability and Quality Issues ....................................................................................................	3
1.2. Probabilistic Design Terminology ......................................................................................................	3
1.3. Using Probabilistic Design .................................................................................................................	8
1.3.1. Create the Analysis File .............................................................................................................	9
1.3.1.1. Example Problem Description ........................................................................................	10
1.3.1.2. Build the Model Parametrically .......................................................................................	10
1.3.1.3. Obtain the Solution .......................................................................................................	11
1.3.1.4. Retrieve Results and Assign as Output Parameters ..........................................................	11
1.3.1.5. Prepare the Analysis File ................................................................................................	12
1.3.2. Establish Parameters for Probabilistic Design Analysis .............................................................	12
1.3.3. Enter the PDS and Specify the Analysis File .............................................................................	13
1.3.4. Declare Random Input Variables .............................................................................................	14
1.3.5. Visualize Random Input Variables ...........................................................................................	20
1.3.6. Specify Correlations Between Random Variables .....................................................................	20
1.3.7. Specify Random Output Parameters .......................................................................................	23
1.3.8. Select a Probabilistic Design Method ......................................................................................	24
1.3.8.1. Probabilistic Method Determination Wizard ...................................................................	24
1.3.9. Execute Probabilistic Analysis Simulation Loops ......................................................................	25
1.3.9.1. Probabilistic Design Looping .........................................................................................	26
1.3.9.2. Serial Analysis Runs .......................................................................................................	27
1.3.9.3. PDS Parallel Analysis Runs ..............................................................................................	27
1.3.9.3.1. Machine Configurations ........................................................................................	29
1.3.9.3.1.1. Choosing Slave Machines .............................................................................	29
1.3.9.3.1.2. Using the Remote Shell Option .....................................................................	29
1.3.9.3.1.3. Using the Connection Port Option ................................................................	31
1.3.9.3.1.4. Configuring the Master Machine ...................................................................	33
1.3.9.3.1.5. Host setup using port option ........................................................................	35
1.3.9.3.1.6. Host and Product selection for a particular analysis .......................................	35
1.3.9.3.2. Files Needed for Parallel Run .................................................................................	36
1.3.9.3.3. Controlling Server Processes .................................................................................	37
1.3.9.3.4. Initiate Parallel Run ...............................................................................................	38
1.3.10. Fit and Use Response Surfaces ..............................................................................................	38
1.3.10.1. About Response Surface Sets .......................................................................................	39
1.3.10.2. Fitting a Response Surface ...........................................................................................	39
1.3.10.3. Plotting a Response Surface .........................................................................................	40
1.3.10.4. Printing a Response Surface .........................................................................................	40
1.3.10.5. Generating Monte Carlo Simulation Samples on the Response Surfaces ........................	41
1.3.11. Review Results Data .............................................................................................................	41
1.3.11.1. Viewing Statistics .........................................................................................................	42
1.3.11.2. Viewing Trends ............................................................................................................	43
1.3.11.3. Creating Reports ..........................................................................................................	44
1.4. Guidelines for Selecting Probabilistic Design Variables .....................................................................	44
1.4.1. Choosing and Defining Random Input Variables .....................................................................	44
1.4.1.1. Random Input Variables for Monte Carlo Simulations .....................................................	45
1.4.1.2. Random Input Variables for Response Surface Analyses ..................................................	45
1.4.1.3. Choosing a Distribution for a Random Variable ...............................................................	45
1.4.1.3.1. Measured Data .....................................................................................................	45

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1.4.1.3.2. Mean Values, Standard Deviation, Exceedence Values .............................................	46
1.4.1.3.3. No Data ................................................................................................................	46
1.4.1.4. Distribution Functions ...................................................................................................	49
1.4.2. Choosing Random Output Parameters ....................................................................................	50
1.5. Probabilistic Design Techniques ......................................................................................................	51
1.5.1. Monte Carlo Simulations ........................................................................................................	51
1.5.1.1. Direct Sampling .............................................................................................................	51
1.5.1.2. Latin Hypercube Sampling .............................................................................................	52
1.5.1.3. User-Defined Sampling ..................................................................................................	53
1.5.2. Response Surface Analysis Methods .......................................................................................	55
1.5.2.1. Central Composite Design Sampling ..............................................................................	56
1.5.2.2. Box-Behnken Matrix Sampling .......................................................................................	58
1.5.2.3. User-Defined Sampling ..................................................................................................	58
1.6. Postprocessing Probabilistic Analysis Results ...................................................................................	59
1.6.1. Statistical Postprocessing .......................................................................................................	59
1.6.1.1. Sample History ..............................................................................................................	59
1.6.1.2. Histogram .....................................................................................................................	60
1.6.1.3. Cumulative Distribution Function ..................................................................................	60
1.6.1.4. Print Probabilities ..........................................................................................................	62
1.6.1.5. Print Inverse Probabilities ...............................................................................................	62
1.6.2. Trend Postprocessing .............................................................................................................	62
1.6.2.1. Sensitivities ...................................................................................................................	62
1.6.2.2. Scatter Plots ..................................................................................................................	65
1.6.2.3. Correlation Matrix ..........................................................................................................	67
1.6.3. Generating an HTML Report ...................................................................................................	67
1.7. Multiple Probabilistic Design Executions .........................................................................................	67
1.7.1. Saving the Probabilistic Design Database ................................................................................	68
1.7.2. Restarting a Probabilistic Design Analysis ...............................................................................	68
1.7.3. Clearing the Probabilistic Design Database .............................................................................	69
1.8. Example Probabilistic Design Analysis .............................................................................................	69
1.8.1. Problem Description ..............................................................................................................	69
1.8.2. Problem Specifications ...........................................................................................................	69
1.8.2.1. Problem Sketch .............................................................................................................	70
1.8.3. Using a Batch File for the Analysis ...........................................................................................	70
1.8.4. Using the GUI for the PDS Analysis ..........................................................................................	72
2. Variational Technology .........................................................................................................................	75
2.1. Harmonic Sweep Using VT Accelerator ............................................................................................	75
2.1.1. Structural Elements Supporting Frequency-Dependent Properties ..........................................	76
2.1.2. Harmonic Sweep for Structural Analysis with Frequency-Dependent Material Properties .........	76
2.1.2.1. Beam Example ...............................................................................................................	77
3. Adaptive Meshing .................................................................................................................................	79
3.1. Prerequisites for Adaptive Meshing .................................................................................................	79
3.2. Employing Adaptive Meshing .........................................................................................................	79
3.3. Modifying the Adaptive Meshing Process ........................................................................................	80
3.3.1. Selective Adaptivity ...............................................................................................................	80
3.3.2. Customizing the ADAPT Macro with User Subroutines ............................................................	81
3.3.2.1. Creating a Custom Meshing Subroutine (ADAPTMSH.MAC) ............................................	81
3.3.2.2. Creating a Custom Subroutine for Boundary Conditions (ADAPTBC.MAC) .......................	82
3.3.2.3. Creating a Custom Solution Subroutine (ADAPTSOL.MAC) ..............................................	82
3.3.2.4. Some Further Comments on Custom Subroutines ..........................................................	82
3.3.3. Customizing the ADAPT Macro (UADAPT.MAC) .......................................................................	83
3.4. Adaptive Meshing Hints and Comments ..........................................................................................	83

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3.5. Where to Find Examples ..................................................................................................................	84
4. Rezoning ...............................................................................................................................................	87
4.1. Benefits and Limitations of Rezoning ...............................................................................................	87
4.1.1. Rezoning Limitations ..............................................................................................................	89
4.2. Rezoning Requirements ..................................................................................................................	90
4.3. Understanding the Rezoning Process ..............................................................................................	92
4.3.1. Overview of the Rezoning Process Flow ..................................................................................	93
4.3.2. Key Commands Used in Rezoning ..........................................................................................	96
4.4. Step 1: Determine the Substep to Initiate Rezoning ..........................................................................	97
4.5. Step 2. Initiate Rezoning ..................................................................................................................	98
4.6. Step 3: Select a Region to Remesh ...................................................................................................	98
4.7. Step 4: Perform the Remeshing Operation .......................................................................................	99
4.7.1. Choosing a Remeshing Method ..............................................................................................	99
4.7.1.1. Remeshing Using a Program-Generated New Mesh (2-D) ..............................................	100
4.7.1.1.1. Creating an Area to Remesh ................................................................................	100
4.7.1.1.2. Using Nodes From the Old Mesh .........................................................................	100
4.7.1.1.3. Hints for Remeshing Multiple Regions ................................................................	101
4.7.1.1.4. Generating a New Mesh .....................................................................................	101
4.7.1.2. Remeshing Using a Generic New Mesh (2-D and 3-D) ...................................................	101
4.7.1.2.1. Using the REMESH Command with a Generic New Mesh ......................................	102
4.7.1.2.2. Requirements for the Generic New Mesh .............................................................	102
4.7.1.2.3. Using the REGE and KEEP Remeshing Options .....................................................	103
4.7.1.3. Remeshing Using Manual Mesh Splitting (2-D and 3-D) ................................................	105
4.7.1.3.1. Understanding Mesh Splitting .............................................................................	105
4.7.1.3.2. Geometry Details for Mesh Splitting ...................................................................	105
4.7.1.3.3. Using the REMESH Command for Mesh Splitting ..................................................	108
4.7.1.3.4. Mesh-Transition Options for 2-D Mesh Splitting ...................................................	108
4.7.1.3.5. Mesh-Transition Options for 3-D Mesh Splitting ...................................................	110
4.7.1.3.6. Improving the Local Topology of Tetrahedral Meshes via Edge and Face Swap-
ping .................................................................................................................................	112
4.7.1.3.7. Improving Tetrahedral Element Quality via Mesh Morphing .................................	113
4.7.2. Mesh Control .......................................................................................................................	114
4.7.3. Remeshing Multiple Regions at the Same Substep ................................................................	115
4.8. Step 5: Verify Applied Contact Boundaries, Surface-Effect Elements, Loads, and Boundary Condi-
tions ...................................................................................................................................................	116
4.8.1. Contact Boundaries ..............................................................................................................	116
4.8.2. Surface-Effect Elements .......................................................................................................	116
4.8.3. Pressure and Contiguous Displacements ...............................................................................	116
4.8.4. Forces and Isolated Applied Displacements ...........................................................................	117
4.8.5. Nodal Temperatures .............................................................................................................	117
4.8.6. Other Boundary Conditions and Loads .................................................................................	117
4.9. Step 6: Automatically Map Variables and Balance Residuals ............................................................	118
4.9.1. Mapping Solution Variables ..................................................................................................	118
4.9.2. Balancing Residual Forces .....................................................................................................	118
4.9.3. Interpreting Mapped Results ................................................................................................	119
4.9.4. Handling Convergence Difficulties ........................................................................................	120
4.10. Step 7: Perform a Multiframe Restart ............................................................................................	120
4.11. Repeating the Rezoning Process if Necessary ...............................................................................	120
4.11.1. File Structures for Repeated Rezonings ...............................................................................	121
4.12. Postprocessing Rezoning Results .................................................................................................	121
4.12.1. The Database Postprocessor ...............................................................................................	121
4.12.1.1. Listing the Rezoning Results File Summary .................................................................	122

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4.12.1.2. Animating the Rezoning Results .................................................................................	122
4.12.1.3. Using the Results Viewer for Rezoning ........................................................................	122
4.12.2. The Time-History Postprocessor ..........................................................................................	123
4.13. Rezoning Restrictions ..................................................................................................................	123
4.14. Rezoning Examples .....................................................................................................................	124
4.14.1. Example: Rezoning Using a Program-Generated New Mesh .................................................	124
4.14.1.1. Initial Input for the Analysis ........................................................................................	125
4.14.1.2. Rezoning Input for the Analysis ..................................................................................	127
4.14.2. Example: Rezoning Using a Generic New Mesh ....................................................................	127
4.14.2.1. Initial Input for the Analysis ........................................................................................	128
4.14.2.2. Exporting the Distorted Mesh as a CDB File ................................................................	130
4.14.2.3. Importing the File into ANSYS ICEM CFD and Generating a New Mesh .........................	131
4.14.2.4. Rezoning Using the New CDB Mesh ...........................................................................	132
5. Mesh Nonlinear Adaptivity .................................................................................................................	135
5.1. Mesh Nonlinear Adaptivity Benefits, Limitations and Requirements ................................................	135
5.1.1. Rubber Seal Simulation ........................................................................................................	136
5.1.2. Crack Simulation ..................................................................................................................	139
5.2. Understanding the Mesh Nonlinear Adaptivity Process ..................................................................	142
5.2.1. Checking Nonlinear Adaptivity Criteria .................................................................................	143
5.2.1.1. Defining Element Components ....................................................................................	143
5.2.1.2. Defining Nonlinear Adaptivity Criteria ..........................................................................	144
5.2.1.3. Defining Criteria-Checking Frequency ..........................................................................	144
5.3. Mesh Nonlinear Adaptivity Criteria ................................................................................................	144
5.3.1. Energy-Based .......................................................................................................................	144
5.3.2. Position-Based .....................................................................................................................	144
5.3.3. Contact-Based ......................................................................................................................	145
5.3.4. Frequency of Criteria Checking .............................................................................................	145
5.4. How a New Mesh Is Generated ......................................................................................................	146
5.5. Convergence at Substeps with the New Mesh ................................................................................	149
5.6. Controlling Mesh Nonlinear Adaptivity ..........................................................................................	150
5.7. Postprocessing Mesh Nonlinear Adaptivity Results ........................................................................	150
5.8. Mesh Nonlinear Adaptivity Examples .............................................................................................	150
5.8.1. Example: Rubber Seal Simulation ..........................................................................................	151
5.8.2. Example: Crack Simulation ....................................................................................................	153
6. 2-D to 3-D Analysis ..............................................................................................................................	155
6.1. Benefits of 2-D to 3-D Analysis .......................................................................................................	155
6.2. Requirements for a 2-D to 3-D Analysis .........................................................................................	155
6.3. Overview of the 2-D to 3-D Analysis Process ..................................................................................	157
6.3.1. Overview of the 2-D to 3-D Analysis Process Flow ..................................................................	157
6.3.2. Key Commands Used in 2-D to 3-D Analysis ..........................................................................	158
6.4. Performing a 2-D to 3-D Analysis ...................................................................................................	159
6.4.1. Step 1: Determine the Substep to Initiate ..............................................................................	159
6.4.2. Step 2: Initiate the 2-D to 3-D Analysis ...................................................................................	160
6.4.3. Step 3: Extrude the 2-D Mesh to the New 3-D Mesh ..............................................................	160
6.4.4. Step 4: Map Solution Variables from 2-D to 3-D Mesh .............................................................	161
6.4.5. Step 5: Perform an Initial-State-Based 3-D Analysis ................................................................	161
6.5. 2-D to 3-D Analysis Restrictions .....................................................................................................	161
7. Cyclic Symmetry Analysis ....................................................................................................................	163
7.1. Understanding Cyclic Symmetry Analysis ......................................................................................	163
7.1.1. How the Program Automates a Cyclic Symmetry Analysis ......................................................	163
7.1.2. Commands Used in a Cyclic Symmetry Analysis .....................................................................	164
7.2. Cyclic Modeling ............................................................................................................................	164

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7.2.1. The Basic Sector ...................................................................................................................	165
7.2.2. Edge Component Pairs .........................................................................................................	166
7.2.2.1. CYCOPT Auto Detection Tolerance Adjustments for Difficult Cases ...............................	166
7.2.2.2. Identical vs. Dissimilar Edge Node Patterns ...................................................................	169
7.2.2.3. Unmatched Nodes on Edge-Component Pairs ..............................................................	170
7.2.2.4. Identifying Matching Node Pairs ..................................................................................	170
7.2.3. Modeling Limitations ...........................................................................................................	170
7.2.4. Model Verification (Preprocessing) ........................................................................................	171
7.3. Solving a Cyclic Symmetry Analysis ...............................................................................................	171
7.3.1. Understanding the Solution Architecture ..............................................................................	171
7.3.1.1. The Duplicate Sector ....................................................................................................	171
7.3.1.2. Coupling and Constraint Equations (CEs) ......................................................................	172
7.3.1.3. Non-Cyclically Symmetric Loading ...............................................................................	173
7.3.1.3.1. Specifying Non-Cyclic Loading ............................................................................	174
7.3.1.3.2. Commands Affected by Non-Cyclic Loading ........................................................	176
7.3.1.3.3. Plotting and Listing Non-Cyclic Boundary Conditions ...........................................	176
7.3.1.3.4. Graphically Picking Non-Cyclic Boundary Conditions ...........................................	176
7.3.2. Solving a Static Cyclic Symmetry Analysis ..............................................................................	176
7.3.3. Solving a Modal Cyclic Symmetry Analysis ............................................................................	178
7.3.3.1. Understanding Harmonic Index and Nodal Diameter ....................................................	178
7.3.3.2. Solving a Stress-Free Modal Analysis ............................................................................	179
7.3.3.3. Solving a Prestressed Modal Analysis ............................................................................	180
7.3.3.4. Solving a Large-Deflection Prestressed Modal Analysis .................................................	181
7.3.3.4.1. Solving a Large-Deflection Prestressed Modal Analysis with VT Accelerator ..........	183
7.3.4. Solving a Linear Buckling Cyclic Symmetry Analysis ...............................................................	183
7.3.5. Solving a Harmonic Cyclic Symmetry Analysis .......................................................................	184
7.3.5.1. Solving a Full Harmonic Cyclic Symmetry Analysis ........................................................	184
7.3.5.1.1. Solving a Prestressed Full Harmonic Cyclic Symmetry Analysis .............................	185
7.3.5.2. Solving a Mode-Superposition Harmonic Cyclic Symmetry Analysis ..............................	186
7.3.5.2.1. Perform a Static Cyclic Symmetry Analysis to Obtain the Prestressed State ............	187
7.3.5.2.2. Perform a Linear Perturbation Modal Cyclic Symmetry Analysis ............................	188
7.3.5.2.3. Restart the Modal Analysis to Create the Desired Load Vector from Element
Loads ...............................................................................................................................	188
7.3.5.2.4. Obtain the Mode-Superposition Harmonic Cyclic Symmetry Solution ...................	189
7.3.5.2.5. Review the Results ..............................................................................................	190
7.3.6. Solving a Magnetic Cyclic Symmetry Analysis ........................................................................	191
7.3.7. Database Considerations After Obtaining the Solution ..........................................................	192
7.3.8. Model Verification (Solution) .................................................................................................	192
7.4. Postprocessing a Cyclic Symmetry Analysis ....................................................................................	193
7.4.1. General Considerations ........................................................................................................	193
7.4.1.1. Using the /CYCEXPAND Command ...............................................................................	193
7.4.1.1.1. /CYCEXPAND Limitations .....................................................................................	194
7.4.1.2. Result Coordinate System ............................................................................................	194
7.4.2. Modal Solution .....................................................................................................................	195
7.4.2.1. Real and Imaginary Solution Components ....................................................................	195
7.4.2.2. Expanding the Cyclic Symmetry Solution .....................................................................	196
7.4.2.3. Applying a Traveling Wave Animation to the Cyclic Model .............................................	196
7.4.2.4. Phase Sweep of Repeated Eigenvector Shapes .............................................................	197
7.4.3. Static, Buckling, and Full Harmonic Solutions .........................................................................	198
7.4.4. Mode-Superposition Harmonic Solution ...............................................................................	198
7.5. Example Modal Cyclic Symmetry Analysis ......................................................................................	198
7.5.1. Problem Description .............................................................................................................	199

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7.5.2. Problem Specifications .........................................................................................................	199
7.5.3. Input File for the Analysis ......................................................................................................	200
7.5.4. Analysis Steps ......................................................................................................................	202
7.6. Example Buckling Cyclic Symmetry Analysis ..................................................................................	203
7.6.1. Problem Description .............................................................................................................	203
7.6.2. Problem Specifications .........................................................................................................	203
7.6.3. Input File for the Analysis ......................................................................................................	204
7.6.4. Analysis Steps ......................................................................................................................	207
7.6.5. Solve For Critical Strut Temperature at Load Factor = 1.0 ........................................................	208
7.7. Example Harmonic Cyclic Symmetry Analysis .................................................................................	210
7.7.1. Problem Description .............................................................................................................	211
7.7.2. Problem Specifications .........................................................................................................	211
7.7.3. Input File for the Analysis ......................................................................................................	211
7.7.4. Analysis Steps ......................................................................................................................	213
7.8. Example Magnetic Cyclic Symmetry Analysis .................................................................................	216
7.8.1. Problem Description .............................................................................................................	216
7.8.2. Problem Specifications .........................................................................................................	217
7.8.3. Input file for the Analysis ......................................................................................................	218
8. Rotating Structure Analysis ................................................................................................................	223
8.1. Understanding Rotating Structure Dynamics .................................................................................	223
8.2. Using a Stationary Reference Frame ...............................................................................................	224
8.2.1. Campbell Diagram ...............................................................................................................	225
8.2.2. Harmonic Analysis for Unbalance or General Rotating Asynchronous Forces ..........................	227
8.2.3. Orbits ...................................................................................................................................	228
8.3. Using a Rotating Reference Frame .................................................................................................	228
8.4. Choosing the Appropriate Reference Frame Option .......................................................................	230
8.5. Example Campbell Diagram Analysis .............................................................................................	231
8.5.1. Problem Description .............................................................................................................	231
8.5.2. Problem Specifications .........................................................................................................	231
8.5.3. Input for the Analysis ............................................................................................................	231
8.5.4. Analysis Steps ......................................................................................................................	232
8.6. Example Coriolis Analysis ..............................................................................................................	234
8.6.1. Problem Description .............................................................................................................	234
8.6.2. Problem Specifications .........................................................................................................	234
8.6.3. Input for the Analysis ............................................................................................................	234
8.6.4. Analysis Steps ......................................................................................................................	235
8.7. Example Unbalance Harmonic Analysis .........................................................................................	236
8.7.1. Problem Description .............................................................................................................	236
8.7.2. Problem Specifications .........................................................................................................	237
8.7.3. Input for the Analysis ............................................................................................................	237
8.7.4. Analysis Steps ......................................................................................................................	239
9. Submodeling .......................................................................................................................................	245
9.1. Understanding Submodeling ........................................................................................................	245
9.1.1. Nonlinear Submodeling .......................................................................................................	246
9.2. Using Submodeling ......................................................................................................................	246
9.2.1. Create and Analyze the Coarse Model ...................................................................................	247
9.2.2. Create the Submodel ............................................................................................................	248
9.2.3. Perform Cut-Boundary Interpolation .....................................................................................	249
9.2.4. Analyze the Submodel .........................................................................................................	250
9.2.5. Verify the Distance Between the Cut Boundaries and the Stress Concentration ......................	252
9.3. Example Submodeling Analysis Input ............................................................................................	253
9.3.1. Submodeling Analysis Input: No Load-History Dependency ...................................................	253

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9.3.2. Submodeling Analysis Input: Load-History Dependency ........................................................	254
9.4. Shell-to-Solid Submodels ..............................................................................................................	259
9.5. Where to Find Examples ................................................................................................................	261
10. Substructuring ..................................................................................................................................	263
10.1. Benefits of Substructuring ...........................................................................................................	263
10.2. Using Substructuring ..................................................................................................................	263
10.2.1. Step 1: Generation Pass (Creating the Superelement) ...........................................................	264
10.2.1.1. Building the Model ....................................................................................................	265
10.2.1.2. Applying Loads and Creating the Superelement Matrices ...........................................	266
10.2.1.2.1. Applicable Loads in a Substructure Analysis .......................................................	268
10.2.2. Step 2: Use Pass (Using the Superelement) ..........................................................................	270
10.2.2.1. Clear the Database and Specify a New Jobname .........................................................	270
10.2.2.2. Build the Model .........................................................................................................	271
10.2.2.3. Apply Loads and Obtain the Solution .........................................................................	273
10.2.3. Step 3: Expansion Pass (Expanding Results Within the Superelement) ..................................	275
10.3. Sample Analysis Input .................................................................................................................	278
10.4. Top-Down Substructuring ...........................................................................................................	279
10.5. Automatically Generating Superelements ....................................................................................	281
10.6. Nested Superelements ................................................................................................................	282
10.7. Prestressed Substructures ...........................................................................................................	282
10.7.1. Static Analysis Prestress ......................................................................................................	283
10.7.2. Substructuring Analysis Prestress ........................................................................................	283
10.8. Where to Find Examples ..............................................................................................................	283
11. Component Mode Synthesis .............................................................................................................	285
11.1. Understanding Component Mode Synthesis ................................................................................	285
11.1.1. CMS Methods Supported ....................................................................................................	285
11.1.2. Solvers Used in Component Mode Synthesis .......................................................................	286
11.2. Using Component Mode Synthesis ..............................................................................................	287
11.2.1. The CMS Generation Pass: Creating the Superelement .........................................................	287
11.2.2. The CMS Use and Expansion Passes .....................................................................................	289
11.2.3. Superelement Expansion in Transformed Locations .............................................................	290
11.2.4. Plotting or Printing Mode Shapes .......................................................................................	290
11.3. Example Component Mode Synthesis Analysis ............................................................................	290
11.3.1. Problem Description ...........................................................................................................	290
11.3.2. Problem Specifications .......................................................................................................	290
11.3.3. Input for the Analysis: Fixed-Interface Method .....................................................................	293
11.3.4. Analysis Steps: Fixed-Interface Method ................................................................................	297
11.3.5. Input for the Analysis: Free-Interface Method ......................................................................	300
11.3.6. Analysis Steps: Free-Interface Method .................................................................................	301
11.3.7. Input for the Analysis: Residual-Flexible Free-Interface Method ............................................	302
11.3.8. Analysis Steps: Residual-Flexible Free-Interface Method .......................................................	304
11.3.9. Example: Superelement Expansion in a Transformed Location .............................................	305
11.3.9.1. Analysis Steps: Superelement Expansion in a Transformed Location ............................	307
11.3.10. Example: Reduce the Damping Matrix and Compare Full and CMS Results with RSTMAC ....	308
12. Rigid-Body Dynamics and the ANSYS-ADAMS Interface ..................................................................	315
12.1. Understanding the ANSYS-ADAMS Interface ................................................................................	315
12.2. Building the Model ......................................................................................................................	316
12.3. Modeling Interface Points ...........................................................................................................	317
12.4. Exporting to ADAMS ...................................................................................................................	318
12.4.1. Exporting to ADAMS via Batch Mode ..................................................................................	320
12.4.2. Verifying the Results ...........................................................................................................	320
12.5. Running the ADAMS Simulation ..................................................................................................	321

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12.6. Transferring Loads from ADAMS ..................................................................................................	321
12.6.1. Transferring Loads on a Rigid Body .....................................................................................	321
12.6.1.1. Exporting Loads in ADAMS ........................................................................................	322
12.6.1.2. Importing Loads ........................................................................................................	323
12.6.1.3. Importing Loads via Commands .................................................................................	324
12.6.1.4. Reviewing the Results ................................................................................................	324
12.6.2. Transferring the Loads of a Flexible Body .............................................................................	324
12.7. Methodology Behind the ANSYS-ADAMS Interface ......................................................................	325
12.7.1. The Modal Neutral File ........................................................................................................	325
12.7.2. Adding Weak Springs .........................................................................................................	326
12.8. Example Rigid-Body Dynamic Analysis ........................................................................................	326
12.8.1. Problem Description ...........................................................................................................	326
12.8.2. Problem Specifications .......................................................................................................	327
12.8.3. Command Input .................................................................................................................	328
13. Element Birth and Death ...................................................................................................................	331
13.1. Elements Supporting Birth and Death .........................................................................................	331
13.2. Understanding Element Birth and Death .....................................................................................	331
13.3. Element Birth and Death Usage Hints ..........................................................................................	332
13.3.1. Changing Material Properties .............................................................................................	333
13.4. Using Birth and Death .................................................................................................................	333
13.4.1. Build the Model ..................................................................................................................	333
13.4.2. Apply Loads and Obtain the Solution ..................................................................................	333
13.4.2.1. Define the First Load Step ..........................................................................................	333
13.4.2.1.1. Sample Input for First Load Step ........................................................................	334
13.4.2.2. Define Subsequent Load Steps ...................................................................................	334
13.4.2.2.1. Sample Input for Subsequent Load Steps ...........................................................	334
13.4.3. Review the Results ..............................................................................................................	334
13.4.4. Use Analysis Results to Control Birth and Death ...................................................................	335
13.4.4.1. Sample Input for Deactivating Elements .....................................................................	335
13.5. Where to Find Examples ..............................................................................................................	335
14. User-Programmable Features and Nonstandard Uses .....................................................................	337
14.1. User-Programmable Features (UPFs) ............................................................................................	337
14.1.1. Understanding UPFs ...........................................................................................................	337
14.1.2. Types of UPFs Available .......................................................................................................	338
14.2. Nonstandard Uses of the ANSYS Program ....................................................................................	339
14.2.1. What Are Nonstandard Uses? ..............................................................................................	339
14.2.2. Hints for Nonstandard Use of ANSYS ...................................................................................	340
15. State-Space Matrices Export .............................................................................................................	341
15.1. State-Space Matrices Based on Modal Analysis .............................................................................	341
15.1.1. Examples of SPMWRITE Command Usage ..........................................................................	341
15.1.2. Example of Reduced Model Generation in ANSYS and Usage in Simplorer ...........................	342
15.1.2.1. Problem Description ..................................................................................................	342
15.1.2.2. Problem Specifications ...............................................................................................	343
15.1.2.3. Input File for the Analysis ...........................................................................................	343
16. Soil-Pile-Structure Analysis ...............................................................................................................	347
16.1. Soil-Pile-Structure Interaction Analysis .........................................................................................	347
16.1.1. Automatic Pile Subdivision .................................................................................................	348
16.1.2. Convergence Criteria ..........................................................................................................	348
16.1.3. Soil Representation ............................................................................................................	349
16.1.4. Mudslides ..........................................................................................................................	354
16.1.5. Soil-Pile Interaction Results .................................................................................................	355
16.1.5.1. Displacements and Reactions .....................................................................................	355

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16.1.5.2. Forces and Stresses ....................................................................................................	355
16.1.5.3. UNITY Check Data ......................................................................................................	355
16.2. Soil Data Definition and Examples ...............................................................................................	357
16.2.1. Soil Profile Data Definition ..................................................................................................	357
16.2.1.1. Mudline Position Definition ........................................................................................	359
16.2.1.2. Common Factors for P-Y, T-Z Curves ............................................................................	359
16.2.1.3. Horizontal Soil Properties (P-Y) ...................................................................................	360
16.2.1.3.1. P-Y curves defined explicitly ..............................................................................	361
16.2.1.3.2. P-Y curves generated from given soil properties ................................................	361
16.2.1.4. Vertical Soil Properties (T-Z) .......................................................................................	363
16.2.1.4.1. T-Z curves defined explicitly ..............................................................................	363
16.2.1.4.2. T-Z curves generated from given soil properties .................................................	364
16.2.1.5. End Bearing Properties (ENDB) ...................................................................................	365
16.2.1.5.1. ENDB curve defined explicitly ............................................................................	365
16.2.1.5.2. ENDB curves generated from given soil properties .............................................	366
16.2.1.6. Mudslide Definition ...................................................................................................	367
16.2.2. Soil Data File Examples .......................................................................................................	367
16.2.2.1. Example 1: Constant Linear Soil ..................................................................................	368
16.2.2.2. Example 2: Non-Linear Soil .........................................................................................	368
16.2.2.3. Example 3: Soil Properties Defined in 5 Layers .............................................................	369
16.2.2.4. Example 4: Soil Properties Defined in 5 Layers with Mudslide ......................................	369
16.3. Performing a Soil-Pile Interaction Analysis ...................................................................................	370
16.3.1. Overview of Mechanical APDL Commands Used for Soil-Pile Interaction Analysis .................	370
16.3.2. Mechanical APDL Component System Example ..................................................................	370
16.3.3. Static Structural Component System Example .....................................................................	371
16.4. Soil-Pile-Structure Results ............................................................................................................	373
16.5. References ..................................................................................................................................	374
17. Coupling to External Aeroelastic Analysis of Wind Turbines ............................................................	375
17.1. Sequential Coupled Wind Turbine Solution in Mechanical APDL ...................................................	375
17.1.1. Procedure for a Sequentially Coupled Wind Turbine Analysis ...............................................	375
17.1.2. Output from the OUTAERO Command ................................................................................	376
17.1.3. Example Substructured Analysis to Write Out Aeroelastic Analysis Input Data ......................	377
18. Applying Ocean Loading from a Hydrodynamic Analysis ................................................................	381
18.1. How Hydrodynamic Analysis Data Is Used ....................................................................................	381
18.2. Hydrodynamic Load Transfer with Forward Speed ........................................................................	382
18.3. Hydrodynamic Data File Format ..................................................................................................	382
18.3.1. Comment (Optional) ..........................................................................................................	382
18.3.2. General Model Data ............................................................................................................	383
18.3.3. Hydrodynamic Surface Geometry .......................................................................................	383
18.3.4. Wave Periods ......................................................................................................................	384
18.3.5. Wave Directions ..................................................................................................................	384
18.3.6. Panel Pressures ...................................................................................................................	385
18.3.7. Morison Element Hydrodynamic Definition .........................................................................	385
18.3.8. Morison Element Wave Kinematics Definition ......................................................................	386
18.3.9. RAO Definition ...................................................................................................................	387
18.3.10. Mass Properties ................................................................................................................	388
18.4. Example Analysis Using Results from a Hydrodynamic Diffraction Analysis ...................................	388
Index ........................................................................................................................................................	393

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List of Figures
1.1. A Beam Under a Snow Load ....................................................................................................................	4
1.2. Probabilistic Design Data Flow ................................................................................................................	8
1.3. A Beam Under a Snow Load ..................................................................................................................	10
1.4. Histograms for the Snow Height H1 and H2 ...........................................................................................	19
1.5. A Scatter Plot of Snow Height H1 vs. H2 .................................................................................................	21
1.6. The PDS Method Determination Wizard .................................................................................................	25
1.7. Graph of X1 and X2 Showing Two Samples with Close Values .................................................................	52
1.8. Graph of X1 and X2 Showing Good Sample Distribution ........................................................................	53
1.9. Locations of Sampling Points for Problem with Three Input Variables for CCD .........................................	57
1.10. Location of Sampling Points for Problem with Three Input Variables for BBM ........................................	58
1.11. Cumulative Distribution Function of X .................................................................................................	61
1.12. Sensitivities ........................................................................................................................................	63
1.13. Range of Scatter ..................................................................................................................................	63
1.14. Effects of Reducing and Shifting Range of Scatter ................................................................................	66
1.15. The Simple Indeterminate Three-Bar Truss for the Example Problem .....................................................	70
2.1. Y-Displacement Difference at End of Beam ............................................................................................	78
3.1. Selective Adaptivity ..............................................................................................................................	81
4.1. Rezoning Using a Program-Generated New Mesh ..................................................................................	93
4.2. Rezoning Using a Generic New Mesh Generated by Another Application ...............................................	94
4.3. Rezoning Using Manual Splitting of an Existing Mesh ............................................................................	95
4.4. Boundary Geometry of a Generic (CDB) New Mesh ..............................................................................	103
4.5. Remeshing Options when Using a Generic (CDB) New Mesh ................................................................	103
4.6. Splitting Quadrilateral and Degenerate Linear Elements (PLANE182) ....................................................	106
4.7. Splitting Quadrilateral, Degenerate and Triangular Quadratic Elements (PLANE183) ..............................	107
4.8. Splitting Tetrahedral Linear Elements (SOLID285)) ................................................................................	108
4.9. Transition Element Generation Methods for 2-D ...................................................................................	109
4.10. Phase 1 Transition Creation: Tetrahedra with One and Two Nodes Selected for Splitting ......................	111
4.11. Phase 2(a) Transition Creation: Prism (Wedge) Element Is Split into Three Tetrahedra ..........................	112
4.12. Phase 2(b) Transition Creation: Pyramid Element Is Split into Two Tetrahedra ......................................	112
4.13. Edge/Face Swapping for Tetrahedral Elements ...................................................................................	113
4.14. Mesh Morphing Using Cotangent-Weighted Laplacian Equation ........................................................	114
4.15. /PREP7 Mesh-Control Commands Available in Rezoning .....................................................................	114
5.1. Rubber Seal with Coarse Mesh ............................................................................................................	136
5.2. Deformed Rubber Seal with Coarse Mesh ............................................................................................	136
5.3. Rubber Seal Model with Initial Mesh Refinement .................................................................................	137
5.4. Rubber Seal Model with Second Mesh Refinement ..............................................................................	138
5.5. Deformed Rubber Seal with Mesh Refinements ...................................................................................	139
5.6. Crack Simulation Model with Coarse Mesh ...........................................................................................	139
5.7. Crack Simulation Solution with Coarse Mesh .......................................................................................	140
5.8. Crack Simulation Solution with Three Mesh Refinements .....................................................................	141
5.9. Crack Simulation Solution with Fine Mesh and No Mesh Nonlinear Adaptivity ......................................	142
5.10. Mesh Nonlinear Adaptivity During Solution .......................................................................................	143
5.11. Rigid Target-Contact Interface ...........................................................................................................	147
5.12. Gap Reduction with Successive Mesh Refinement by Element Splitting ..............................................	148
5.13. Contact-Status-Based Determination for Splitting ..............................................................................	148
5.14. Effect of Transitional Element Generation on Size and Numbering Criteria ..........................................	149
6.1. 2-D to 3-D Process Flow .......................................................................................................................	158
6.2. 2-D Plane Strain to 3-D Solid Extrusion .................................................................................................	160
6.3. Axisymmetric to 3-D Solid Extrusion ....................................................................................................	160
7.1. Hydro Rotor -- Model of a Cyclically Symmetric Structure .....................................................................	163

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7.2. A Basic Sector in a Cyclically Symmetric Structure ................................................................................	165
7.3. Basic Sector Definition ........................................................................................................................	165
7.4. Full Cyclic Model .................................................................................................................................	167
7.5. Cyclic Sector .......................................................................................................................................	167
7.6. Successful Auto Detection with Default FACETOL = 15 Deg ................................................................	168
7.7. Auto Detection Failure Due to Large Face Tolerance .............................................................................	169
7.8. Connecting Low and High Edges of Basic and Duplicate Sectors ..........................................................	172
7.9. Process Flow for a Static Cyclic Symmetry Analysis (Cyclic Loading) ......................................................	177
7.10. Process Flow for a Static Cyclic Symmetry Analysis (Non-Cyclic Loading) .............................................	177
7.11. Examples of Nodal Diameters (i) ........................................................................................................	178
7.12. Process Flow for a Stress-Free Modal Cyclic Symmetry Analysis ...........................................................	180
7.13. Process Flow for a Prestressed Modal Cyclic Symmetry Analysis ..........................................................	181
7.14. Process Flow for a Large-Deflection Prestressed Modal Cyclic Symmetry Analysis ...............................	182
7.15. Process Flow for a Linear Buckling Cyclic Symmetry Analysis ..............................................................	183
7.16. Process Flow for a Full Harmonic Cyclic Symmetry Analysis (Non-Cyclic Loading) ................................	185
7.17. Process Flow for a Prestressed Full Harmonic Cyclic Symmetry Analysis ..............................................	186
7.18. Process Flow for a Pre-Stressed Mode-Superposition Harmonic Cyclic Symmetry Analysis ...................	187
7.19. Cyclic Results Coordinate Systems with RSYS,SOLU ............................................................................	195
7.20. Traveling Wave Animation Example ...................................................................................................	196
7.21. Example Modal Cyclic Symmetry Analysis Results ..............................................................................	203
7.22. Example Buckling Cyclic Symmetry Analysis Results ...........................................................................	208
7.23. Buckling Cyclic Symmetry Results: Load Factor Iterations ....................................................................	208
7.24. Buckling Cyclic Symmetry Results: Load Factor Results Graph ............................................................	210
7.25. Element Plot Showing Pressure Load on Sector 3 ...............................................................................	214
7.26. Contour Plot of Displacement Sum at Frequency of 866 HZ ................................................................	215
7.27. Displacement Plot as a Function of Excitation Frequency ...................................................................	216
7.28. Two-Phase Electric Machine – Full Model ...........................................................................................	217
7.29. Two-Phase Electric Machine – Half Model ..........................................................................................	217
7.30. Vector Plot of Cyclic Flux Density (B) - Half Model ...............................................................................	222
7.31. Contour Line Plot of Equipotentials ...................................................................................................	222
9.1. Submodeling of a Pulley .....................................................................................................................	245
9.2. Coarse Model ......................................................................................................................................	247
9.3. Submodel Superimposed Over Coarse Model ......................................................................................	248
9.4. Cut Boundaries on the Submodel ........................................................................................................	249
9.5. Loads on the Submodel ......................................................................................................................	252
9.6. Data Flow Diagram for Submodeling (Without Temperature Interpolation) ..........................................	252
9.7. Contour Plots to Compare Results .......................................................................................................	253
9.8. Path Plots to Compare Results .............................................................................................................	253
9.9. Coarse-Mesh Model, Submodel, and Fine-Mesh Model .........................................................................	256
9.10. Equivalent Plastic Strain Through Various Cut-Boundary Conditions and Load Steps ...........................	257
9.11. Equivalent Plastic Strain Distributions in a Submodeling Analysis with Load-History Dependency .......	258
9.12. 3-D Solid Submodel Superimposed on Coarse Shell Model .................................................................	260
9.13. Node Rotations .................................................................................................................................	261
10.1. Applicable Solvers in a Typical Substructuring Analysis ......................................................................	264
10.2. Example of a Substructuring Application ...........................................................................................	264
10.3. Node Locations .................................................................................................................................	271
11.1. Applicable CMS Solvers and Files .......................................................................................................	286
11.2. Process Flow for Creating a CMS Superelement Matrix .......................................................................	288
11.3. Example CMS Analysis Results: Fixed-Interface Method ......................................................................	300
12.1. Connecting a Structure to an Interface Point ......................................................................................	318
12.2. Export to ADAMS Dialog Box .............................................................................................................	319
12.3. ADAMS Export FEA Loads Dialog Box ................................................................................................	322

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12.4. Import from ADAMS Dialog Box ........................................................................................................	323
12.5. Linkage Assembly .............................................................................................................................	327
12.6. Link3 Component .............................................................................................................................	327
15.1. Simulation Schematic ........................................................................................................................	345
15.2. Evolution of Spring Force ..................................................................................................................	345
16.1. Pile/Spring Foundation Model ...........................................................................................................	349
16.2. Soil/load Deflection Characteristics ...................................................................................................	350
16.3. P-Y Curve for Sand ............................................................................................................................	352
16.4. P-Y Curve for Clay: Static Loading .......................................................................................................	353
16.5. P-Y Curve for Clay: Cyclic Loading ......................................................................................................	353
16.6. T-Z Curve for Clay and Sand ...............................................................................................................	354
16.7. ENDB Curve for Clay and Sand ...........................................................................................................	354
18.1. Hydrodynamic Diffraction Analysis Pressure Results ...........................................................................	389
18.2. Analysis Results Using Pressure Data from a Hydrodynamic Diffraction Analysis .................................	391

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List of Tables
7.1. Valid Non-Cyclically Symmetric Loads ..................................................................................................	173
7.2. Buckling Cyclic Symmetry: Load Factor Iteration Results .......................................................................	210
10.1. Substructure Analysis Loads ..............................................................................................................	269

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