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Solving a Cyclic Symmetry Analysis

Superelement (MATRIX50)

Generalized plane strain option (such as PLANE183 with KEYOPT(3) = 5)

Birth and death of elements (EKILL and EALIVE) is not supported in a cyclic symmetry solution.

7.2.4. Model Verification (Preprocessing)

If the CYCLIC command's default automatic detection capability accepts your model for cyclic analysis, the program will have already verified the following two essential conditions for a cyclic analysis:

When your model rotates by the cyclic angle about the local Z axis of the cyclic coordinate system, the edges identified as "low" occupy the same space as those identified by "high" prior to the rotation.

The cyclic angle divides evenly into 360°.

If you specify edge components and cyclic quantities manually, you must verify the two conditions yourself.

7.3. Solving a Cyclic Symmetry Analysis

The program solves for the full cyclically symmetric model using the basic sector model that you have set up during preprocessing with the appropriate boundary conditions, loading, and any coupling and constraint equations. (For more information, see Cyclic Modeling (p. 164).)

This section provides specific information for obtaining the solution to various types of cyclic symmetry analyses and covers the following topics:

7.3.1.Understanding the Solution Architecture

7.3.2.Solving a Static Cyclic Symmetry Analysis

7.3.3.Solving a Modal Cyclic Symmetry Analysis

7.3.4.Solving a Linear Buckling Cyclic Symmetry Analysis

7.3.5.Solving a Harmonic Cyclic Symmetry Analysis

7.3.6.Solving a Magnetic Cyclic Symmetry Analysis

7.3.7.Database Considerations After Obtaining the Solution

7.3.8.Model Verification (Solution)

7.3.1. Understanding the Solution Architecture

At the solution (SOLVE) stage of a cyclic symmetry analysis, the program applies the appropriate cyclic symmetry boundary conditions for each harmonic index solution requested (via the CYCOPT command) and solves. The program performs each harmonic index solution as a separate load step.

The following solution architecture topics are available for cyclic symmetry analysis:

7.3.1.1.The Duplicate Sector

7.3.1.2.Coupling and Constraint Equations (CEs)

7.3.1.3.Non-Cyclically Symmetric Loading

7.3.1.1. The Duplicate Sector

The architecture of the cyclic symmetry solution process depends upon how the compatibility and equilibrium conditions of the cyclic sector are enforced in the matrix-solution process. The two most common solution methods are Duplicate Sector and Complex Hermitian. For faster performance, the program uses the Duplicate Sector method.

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During the solution stage, the program generates a duplicate sector of elements at the same geometric location as the basic sector. (Duplicate sector creation occurs automatically and transparently.) The program applies all loading, boundary conditions, and coupling and constraint equations present on the basic sector to the duplicate sector.

7.3.1.2. Coupling and Constraint Equations (CEs)

The program enforces cyclic symmetry compatibility conditions for each nodal-diameter solution via coupling and/or constraint equations (CEs) connecting the nodes on the lowand high-edge components on the basic and duplicate sectors. The program deletes the coupling and/or constraint equations after each nodal-diameter solution, preserving any internal coupling and constraint equations that you may have defined on the basic sector for subsequent analyses. The constraint equations for edge-component nodes have the form shown in Equation 7.1 (p. 172).

Note

Internal CEs cannot be listed or viewed after a cyclic symmetry solution.

During the solution stage of a cyclic symmetry analysis, the program automatically rotates the nodal coordinate systems of all nodes on the low and high sector edges to be parallel with the cyclic coordinate system.

Figure 7.8: Connecting Low and High Edges of Basic and Duplicate Sectors

 

A

 

 

 

 

 

 

 

 

High

=

 

 

 

 

 

BHigh

 

 

where,

 

α

 

 

A

 

 

 

 

α

 

 

k

α

k

 

 

Low

(7.1)

 

 

α

 

 

 

 

 

 

 

 

 

k

 

k

 

BLow

 

k = Harmonic index -- (0,1,2,…,N / 2) when N is even, (0,1,2,…,(N-1) / 2) when N is odd. (N is an integer representing the number of sectors in 360°.)

α = Sector angle (2π / N)

U = Vector of displacement and rotational degrees of freedom UALow represents the basic sector low side edge

UAHigh represents the basic sector high side edge

 

Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information

172

of ANSYS, Inc. and its subsidiaries and affiliates.