Моделирование предохранительных конструкций. Учебное пособие
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Uɫɦ J 1 |
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ɝɞɟ Uɞ ɩɥɨɬɧɨɫɬɶ ɩɪɨɞɭɤɬɨɜ ɞɟɬɨɧɚɰɢɢ
Uɫɦ ɩɥɨɬɧɨɫɬɶ ɢɫɯɨɞɧɨɣ ɫɦɟɫɢ
ɉɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶɢɫɬɟɱɟɧɢɹɨɩɪɟɞɟɥɹɟɬɫɹɤɚɤɨɬɧɨɲɟɧɢɟɨɛɴɟɦɚɩɪɨ ɞɭɤɬɨɜ ɞɟɬɨɧɚɰɢɢ ɤ ɪɚɫɯɨɞɭ ɢɫɬɟɱɟɧɢɹ ɱɟɪɟɡ ɩɪɨɟɦɵ
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ɝɞɟ 9 9Ƚȼɋ H – 9 ɨɛɴɟɦ ɩɪɨɞɭɤɬɨɜ ɫɝɨɪɚɧɢɹ; * 8ɤɪFɨɛɳ – ɪɚɫɯɨɞ ɢɫɬɟɱɟɧɢɹ ɱɟɪɟɡ ɩɪɨɟɦɵ;
Fɨɛɳ ɩɥɨɳɚɞɶ ɨɤɨɧɧɵɯ ɢ ɞɪɭɝɢɯ ɩɪɨɟɦɨɜ ɜ ɩɨɦɟɳɟɧɢɢ
Ɇɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɵɣ ɢɦɩɭɥɶɫ ɞɟɬɨɧɚɰɢɢ ɧɚ ɢɧɬɟɪɜɚɥɟ ɮɚɡɵ ɫɠɚɬɢɹ ɛɭɞɟɬ ɪɚɜɟɧ
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iɞ W 'Pɞ. |
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ɉɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɮɚɡɵ ɫɠɚɬɢɹ ɩɪɢ ɞɟɮɥɚɝɪɚɰɢɢ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɫ ɭɱɟɬɨɦɜɨɡɦɨɠɧɨɝɨɪɚɡɪɭɲɟɧɢɹɩɨɦɟɳɟɧɢɹɢɩɪɢɧɢɦɚɟɬɫɹɪɚɜɧɨɣɩɹɬɢɢɧɬɟɪ ɜɚɥɚɦ ɝɨɪɟɧɢɹ ɚ ɢɦɩɭɥɶɫ ɧɚ ɢɧɬɟɪɜɚɥɟ ɫɠɚɬɢɹ ɛɭɞɟɬ ɪɚɜɟɧ
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2.3.3. ǶȕȗȇȍȇȥȠȏȌ ȖȇȗȇȓȌșȗȢ ȉȕȎȋȚȟȔȕȐ ȚȋȇȗȔȕȐ ȉȕȒȔȢ Ȏȇ ȖȗȌȋȌȒȇȓȏ ȖȕȓȌȠȌȔȏȦ
ɉɨɥɭɱɟɧɧɵɟ ɪɚɫɱɟɬɧɵɟ ɮɨɪɦɭɥɵ ɩɨɡɜɨɥɹɸɬ ɩɨɥɭɱɢɬɶ ɡɧɚɱɟɧɢɹ ɞɚɜɥɟ ɧɢɣ ɢ ɢɦɩɭɥɶɫɨɜ ɜ ɡɨɧɚɯ ɜɡɪɵɜɧɨɝɨ ɝɨɪɟɧɢɹ ɜ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɨɦ ɩɨɦɟɳɟɧɢɢ ɉɪɢ ɜɵɫɨɤɢɯ ɷɧɟɪɝɢɹɯ ɜɡɪɵɜɚ ɩɨɦɟɳɟɧɢɟ ɛɭɞɟɬ ɪɚɡɪɭɲɟɧɨ ɢ ɨɛɪɚɡɨɜɚɜɲɟɟɫɹ ɜ ɡɨɧɟ ɝɨɪɟɧɢɹ ɜɵɫɨɤɨɟ ɞɚɜɥɟɧɢɟ ɛɭɞɟɬ ɜɨɡɞɟɣɫɬɜɨɜɚɬɶ ɧɚ ɨɤɪɭɠɚɸɳɭɸ ɜɨɡ ɞɭɲɧɭɸ ɫɪɟɞɭ ȼ ɪɟɡɭɥɶɬɚɬɟ ɜ ɨɤɪɭɠɚɸɳɟɦ ɜɨɡɞɭɯɟ ɭɠɟ ɡɚ ɩɪɟɞɟɥɚɦɢ ɡɨɧɵ ɜɡɪɵɜɧɨɝɨ ɝɨɪɟɧɢɹ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɜɨɡɞɭɲɧɚɹ ɭɞɚɪɧɚɹ ɜɨɥɧɚ ȼɍȼ
ɉɪɢɪɚɫɱɟɬɚɯɩɚɪɚɦɟɬɪɨɜȼɍȼɡɚɩɪɟɞɟɥɚɦɢɡɨɧɵɜɡɪɵɜɧɨɝɨɝɨɪɟɧɢɹɛɭ ɞɟɦ ɩɪɟɧɟɛɪɟɝɚɬɶ ɷɧɟɪɝɢɟɣ ɧɚ ɪɚɡɪɭɲɟɧɢɟ ɡɞɚɧɢɹ ɢ ɫɱɢɬɚɬɶ ɱɬɨ ɩɪɨɢɫɯɨɞɢɬ ɜɡɪɵɜ ɨɛɥɚɤɚ ɫɦɟɫɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɝɨ ɫɨɫɬɚɜɚ ɧɚ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɨɣ ɩɨɞ ɫɬɢɥɚɸɳɟɣ ɩɨɜɟɪɯɧɨɫɬɢ
ɉɚɪɚɦɟɬɪɵ ȼɍȼ ɧɚ ɪɚɫɫɬɨɹɧɢɹɯ ɩɪɟɜɵɲɚɸɳɢɯ ɪɚɞɢɭɫ ɨɛɥɚɤɚ ɫɦɟɫɢ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɭɪɚɜɧɟɧɢɹɦ ɩɨɥɭɱɟɧɧɵɦ ɩɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱɢ ɨ ɞɟɬɨɧɚɰɢɢ ɨɛɥɚɤɚɜɨɡɞɭɲɧɨ ɩɪɨɩɚɧɨɜɨɣɫɦɟɫɢ ɉɨɥɭɱɟɧɧɵɟɭɧɢɜɟɪɫɚɥɶɧɵɟɡɚɜɢɫɢɦɨɫɬɢ ɞɚɜɥɟɧɢɹ ɜɨ ɮɪɨɧɬɟ ɭɞɚɪɧɨɣ ɜɨɥɧɵ 'Ɋɮ ɢ ɭɞɟɥɶɧɨɝɨ ɢɦɩɭɥɶɫɚ i ɩɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱ ɨ ɪɚɡɪɭɲɢɬɟɥɶɧɵɯ ɩɨɫɥɟɞɫɬɜɢɹɯ ɜɡɪɵɜɚ ɞɚɸɬ ɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɨɟ ɫɨ
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ɝɥɚɫɨɜɚɧɢɟ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ ɞɥɹ ɫɝɨɪɚɧɢɹ ɢ ɞɪɭɝɢɯ ɭɝɥɟɜɨɞɨ ɪɨɞɧɵɯ ɫɦɟɫɟɣ ɫ ɜɨɡɞɭɯɨɦ ɢɥɢ ɤɢɫɥɨɪɨɞɨɦ
Ɋɚɫɫɦɨɬɪɢɦ ɷɬɢ ɡɚɜɢɫɢɦɨɫɬɢ Ⱦɚɜɥɟɧɢɟ ɜɨ ɮɪɨɧɬɟ ɜɨɡɞɭɲɧɨɣ ɭɞɚɪɧɨɣ ɜɨɥɧɵ ɢ ɭɞɟɥɶɧɵɣ ɢɦɩɭɥɶɫ
ɨɩɪɟɞɟɥɹɸɬɫɹ ɫ ɩɨɦɨɳɶɸ ɫɥɟɞɭɸɳɟɣ ɝɪɭɩɩɵ ɮɨɪɦɭɥ ɂɫɯɨɞɧɵɦɢ ɜɟɥɢɱɢɧɚɦɢ ɞɥɹ ɪɚɫɱɟɬɚ ɹɜɥɹɸɬɫɹ ɬɪɨɬɢɥɨɜɵɣ ɷɤɜɢɜɚɥɟɧɬ
ɜɡɪɵɜɚ ɢ ɩɪɢɜɟɞɟɧɧɵɣ ɪɚɞɢɭɫ ɜɡɪɵɜɚ Ɍɪɨɬɢɥɨɜɵɣ ɷɤɜɢɜɚɥɟɧɬ ɧɚɡɟɦɧɨɝɨ ɜɡɪɵɜɚ ɩɨɥɭɫɮɟɪɢɱɟɫɤɨɝɨ ɨɛɥɚɤɚ
ɪɚɜɟɧ
mT m |
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ɝɞɟ m ɪɚɫɱɟɬɧɚɹ ɦɚɫɫɚ ɚɜɚɪɢɣɧɨɝɨ ɜɟɳɟɫɬɜɚ ɜ ɩɨɦɟɳɟɧɢɢ ɤɝ;
P min{mɫɬɯ; m*; mS};
Q ɭɞɟɥɶɧɚɹ ɬɟɩɥɨɬɚ ɜɡɪɵɜɧɨɝɨ ɩɪɟɜɪɚɳɟɧɢɹ ɨɛɥɚɤɚ ɤȾɠ ɤɝ;
QɌ ɤȾɠ ɤɝ ɭɞɟɥɶɧɚɹ ɬɟɩɥɨɬɚ ɜɡɪɵɜɚ ɬɪɢɧɢɬɪɨɬɨɥɭɨɥɚ ɌɇɌ .
ɉɪɢɜɟɞɟɧɧɵɣ ɪɚɞɢɭɫ ɜɡɪɵɜɚ R ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɫɫɬɨɹɧɢɟɦ ɞɨ ɰɟɧɬɪɚ ɜɡɪɵɜɚ R ɦ ɢ ɬɪɨɬɢɥɨɜɵɦ ɷɤɜɢɜɚɥɟɧɬɨɦ ɜɡɪɵɜɚ mɌ ɤɝ:
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1 Ⱦɚɜɥɟɧɢɟ ɜɨ ɮɪɨɧɬɟ ɭɞɚɪɧɨɣ ɜɨɥɧɵ ɉɚ
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'Pɮ |
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P P |
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CɊ ɩɪɢɜɟɞɟɧɧɨɟ ɞɚɜɥɟɧɢɟ ɨɩɪɟɞɟɥɹɟɦɨɟ ɢɡ ɜɵɪɚɠɟɧɢɹ |
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2 ɍɞɟɥɶɧɵɣ ɢɦ ɩɭɥɶɫ L ɉɚǜɫ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ |
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ɝɞɟCi ɩɪɢɜɟɞɟɧɧɵɣɢɦɩɭɥɶɫ ɜɟɥɢɱɢɧɚɤɨɬɨɪɨɝɨɨɩɪɟɞɟɥɹɟɬɫɹɢɡɜɵɪɚɠɟɧɢɹ
OJi |
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R |
44OJ |
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3 Ⱦɥɢɬɟɥɶɧɨɫɬɶ ɮɚɡɵ ɫɠɚɬɢɹ W ɜɨɡɞɭɲɧɨɣ ɭɞɚɪɧɨɣ ɜɨɥɧɵ ɡɚ ɩɪɟ |
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ɞɟɥɚɦɢ ɩɨɦɟɳɟɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ |
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W 6 mT R. |
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4 Ⱦɚɜɥɟɧɢɟ ɨɬɪɚɠɟɧɢɹ ɉɪɢ ɞɨɫɬɢɠɟɧɢɢ ȼɍȼ ɜɧɟɲɧɟɝɨ ɩɪɟɩɹɬɫɬɜɢɹ ɤɪɨɦɟ 'Pɮ ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɝɨ ɧɚɛɟɝɚɸɳɭɸ ɧɚ ɩɪɟɩɹɬɫɬɜɢɟ ɜɨɥɧɭ ɧɟɨɛɯɨ ɞɢɦɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɞɚɜɥɟɧɢɟ ɨɬɪɚɠɟɧɢɹ ɜɨɡɧɢɤɚɸɳɟɟ ɧɚ ɩɪɟɩɹɬɫɬɜɢɢ ɢ ɹɜ ɥɹɸɳɟɟɫɹ ɨɫɧɨɜɧɵɦ ɩɨɪɚɠɚɸɳɢɦ ɮɚɤɬɨɪɨɦ ɞɥɹ ɧɟɝɨ ɬɚɤ ɤɚɤ ɫɭɳɟɫɬɜɟɧɧɨ ɩɪɟɜɵɲɚɟɬ ɢɡɛɵɬɨɱɧɨɟ ɞɚɜɥɟɧɢɟ ɜɨ ɮɪɨɧɬɟ ɧɚɛɟɝɚɸɳɟɣ ɜɨɥɧɵ
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ɂɡɛɵɬɨɱɧɨɟ ɞɚɜɥɟɧɢɟ ɨɬɪɚɠɟɧɢɹ ɨɩɪɟɞɟɥɢɦ ɩɨ ɮɨɪɦɭɥɟ
'Pɨɬɪ |
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'Pf 7P |
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Ɍɚɤɢɦɨɛɪɚɡɨɦ ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ ɫɬɟɩɟɧɢɡɚɝɚɡɨɜɚɧɧɨɫɬɢ ɡɚɩɵɥɟɧɧɨɫɬɢ ɩɨɦɟɳɟɧɢɹ ɩɨɥɭɱɟɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɮɨɪɦɭɥɵ ɞɥɹ ɪɚɫɱɟɬɚ ɨɫɧɨɜɧɵɯ ɩɚɪɚ ɦɟɬɪɨɜ ɜɡɪɵɜɚ ɜɨɡɞɭɲɧɵɯ ɫɦɟɫɟɣ ɜ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɨɦ ɩɨɦɟɳɟɧɢɢ ɢ ɡɚ ɟɝɨ ɩɪɟɞɟɥɚɦɢ ɂɫɯɨɞɹ ɢɡ ɡɧɚɱɟɧɢɣ ɷɬɢɯ ɩɚɪɚɦɟɬɪɨɜ ɢ ɤɨɧɤɪɟɬɧɵɯ ɭɫɥɨɜɢɣ ɩɪɨ ɢɡɜɨɞɫɬɜɚ ɜɵɛɢɪɚɸɬɫɹɫɩɨɫɨɛɵɡɚɳɢɬɵɢɨɩɪɟɞɟɥɹɸɬɫɹɩɚɪɚɦɟɬɪɵɩɪɟɞɨɯɪɚ ɧɢɬɟɥɶɧɵɯ ɤɨɧɫɬɪɭɤɰɢɣ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɫɛɪɨɫɨɜɵɯ ɨɬɜɟɪɫɬɢɣ ɞɥɹ ɨɬɜɨɞɚ ɩɪɨɞɭɤɬɨɜ ɫɝɨɪɚɧɢɹ ɡɚ ɩɪɟɞɟɥɵ ɩɨɦɟɳɟɧɢɹ
ɉɪɢ ɞɟɬɨɧɚɰɢɨɧɧɨɦ ɝɨɪɟɧɢɢ ɩɪɟɞɨɯɪɚɧɢɬɟɥɶɧɵɟ ɤɨɧɫɬɪɭɤɰɢɢ ɉɄ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɫɧɢɠɚɸɬ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɞɚɜɥɟɧɢɹ ɞɟɣɫɬɜɭɸɳɟɝɨ ɧɚɨɝɪɚɠɞɟ ɧɢɟ ɩɨɦɟɳɟɧɢɹ ɨɞɧɚɤɨ ɩɪɢ ɩɪɢɦɟɧɟɧɢɢ ɷɬɢɯ ɤɨɧɫɬɪɭɤɰɢɣ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɡɧɚɱɢɬɟɥɶɧɨɟ ɫɨɤɪɚɳɟɧɢɟ ɜɪɟɦɟɧɢ ɞɟɣɫɬɜɢɹ ɢɡɛɵɬɨɱɧɨɝɨ ɞɚɜɥɟɧɢɹ ɢ ɫɥɟɞɨ ɜɚɬɟɥɶɧɨ ɢɦɩɭɥɶɫɚ
ɇɚɢɛɨɥɟɟɷɮɮɟɤɬɢɜɧɨɩɪɢɦɟɧɟɧɢɟɉɄ ɞɥɹɫɧɢɠɟɧɢɹɜɡɪɵɜɧɵɯɧɚɝɪɭɡɨɤ ɩɪɢɞɟɮɥɚɝɪɚɰɢɨɧɧɨɦɝɨɪɟɧɢɢ ɩɨɷɬɨɦɭɩɟɪɟɣɞɟɦɤɨɰɟɧɤɟɫɬɟɩɟɧɢɡɚɝɚɡɨɜɚɧ ɧɨɫɬɢ ɩɨɦɟɳɟɧɢɹ ɩɪɢ ɚɜɚɪɢɢ ɧɟɨɛɯɨɞɢɦɨɣ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɩɚɪɚɦɟɬɪɨɜ ɞɟ ɮɥɚɝɪɚɰɢɨɧɧɨɝɨ ɜɡɪɵɜɚ
4 ǵȝȌȔȑȇ ȘșȌȖȌȔȏ ȎȇȊȇȎȕȉȇȔȔȕȘșȏ ȖȕȓȌȠȌȔȏȦ Ȗȗȏ ȋȌțȒȇȊȗȇȝȏȕȔȔȕȓ ȉȎȗȢȉȌ
2.4.1. ǹȌȜȔȕȒȕȊȏȞȌȘȑȇȦ ȌȓȑȕȘșȣ ȎȇȖȕȒȔȌȔȔȇȦ ȊȇȎȕȓ Ȗȕȋ ȋȇȉȒȌȔȏȌȓ
Ɋɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɨɟ ɩɨɦɟɳɟɧɢɟ ɨɛɴɟɦɨɦ V ɨɛɨɪɭɞɨ ɜɚɧɧɨɟ ɚɜɚɪɢɣɧɨɣ ɜɟɧɬɢɥɹɰɢɟɣ ɤɪɚɬɧɨɫɬɶɸ Ⱥɜ ɢɦɟɸɳɟɟ ɨɤɨɧɧɵɟ ɢ ɞɪɭɝɢɟ ɩɪɨɟɦɵ ɩɥɨɳɚɞɶɸ Fɨɛɳ ɢ ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɟɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɢɧɬɟɧɫɢɮɢɤɚ ɰɢɢ ɝɨɪɟɧɢɹ ɚ ɪɢɫ Ɍɟɦɩɟɪɚɬɭɪɚ ɜ ɩɨɦɟɳɟɧɢɢ tɩ.
ȼ ɩɨɦɟɳɟɧɢɢ ɪɚɫɩɨɥɨɠɟɧɨ ɢɥɢ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɤ ɭɫɬɚɧɨɜɤɟ ɬɟɯɧɨɥɨ ɝɢɱɟɫɤɨɟ ɭɫɬɪɨɣɫɬɜɨ ɫɧɚɛɠɟɧɧɨɟ ɩɨɞɜɨɞɹɳɢɦɢ ɢ ɨɬɜɨɞɹɳɢɦɢ ɬɪɭɛɨɩɪɨɜɨ ɞɚɦɢ ɜ ɰɟɩɢ ɤɨɬɨɪɵɯ ɢɦɟɟɬɫɹ ɤɨɦɩɪɟɫɫɨɪ ɩɨɞɚɸɳɢɣ ɝɚɡɢ ɫɨɡɞɚɸɳɢɣ ɢɡɛɵ ɬɨɱɧɨɟ ɪɚɛɨɱɟɟ ɞɚɜɥɟɧɢɟ 'Pɪɚɛ ɜɨ ɜɫɟɣ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɣ ɟɦɤɨɫɬɢ ɨɝɪɚɧɢɱɟɧ ɧɨɣ ɨɬɫɟɤɚɸɳɢɦɢ ɚɜɚɪɢɣɧɵɦɢ ɡɚɝɥɭɲɤɚɦɢ Ɉɛɴɟɦ ɚɩɩɚɪɚɬɚ ɪɚɛɨɱɚɹ ɬɟɦɩɟ ɪɚɬɭɪɚ ɜ ɧɟɦ ɢ ɪɚɡɦɟɪɵ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɢɡɜɟɫɬɧɵ ɂɡɜɟɫɬɧɨ ɬɚɤɠɟ ɜɪɟɦɹ ɫɪɚ ɛɚɬɵɜɚɧɢɹ ɨɬɫɟɤɚɸɳɢɯ ɡɚɝɥɭɲɟɤ ɩɪɢ ɪɚɡɝɟɪɦɟɬɢɡɚɰɢɢ ɭɫɬɪɨɣɫɬɜɚ ɤɚɤ ɩɪɚ ɜɢɥɨ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɵɦ ɦɢɧɭɬɚɦ ɩɪɢ ɪɭɱɧɨɦ ɡɚɤɪɵɬɢɢ ɡɚɝɥɭɲɟɤ ɢ ɦɢ ɧɭɬɚɦ ɩɪɢ ɚɜɬɨɦɚɬɢɱɟɫɤɨɦ
Ɉɬɧɨɫɢɬɟɥɶɧɨ ɩɪɨɰɟɫɫɚ ɚɜɚɪɢɢ ɨɬ ɦɨɦɟɧɬɚ ɪɚɡɝɟɪɦɟɬɢɡɚɰɢɢ ɞɨ ɦɨɦɟɧɬɚ ɜɡɪɵɜɚ ɩɪɢɧɢɦɚɟɦ ɫɥɟɞɭɸɳɢɟ ɞɨɩɭɳɟɧɢɹ
43
xɜɵɲɟɞɲɢɣ ɝɚɡ ɨɛɪɚɡɭɟɬ ɜ ɩɨɦɟɳɟɧɢɢ ɨɛɥɚɤɨ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɬɨ ɟɫɬɶ ɜɡɪɵɜ ɩɪɨɢɫɯɨɞɢɬ ɩɪɢ ɫɚɦɵɯ ɧɟɛɥɚɝɨɩɪɢɹɬ ɧɵɯ ɭɫɥɨɜɢɹɯ ɞɥɹ ɩɟɪɫɨɧɚɥɚ ɨɛɨɪɭɞɨɜɚɧɢɹ ɢ ɩɨɦɟɳɟɧɢɹ
xɚɜɚɪɢɣɧɚɹ ɜɟɧɬɢɥɹɰɢɹ ɜɤɥɸɱɚɟɬɫɹ ɜ ɦɨɦɟɧɬ ɪɚɡɝɟɪɦɟɬɢɡɚɰɢɢ ɩɪɢ ɱɟɦ ɟɟɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶɧɟ ɤɨɦɩɟɧɫɢɪɭɟɬɪɚɛɨɬɭɤɨɦɩɪɟɫɫɨɪɚ ɬɨ ɟɫɬɶ ɦɚɫɫɚ ɜɵɯɨɞɹɳɟɝɨ ɝɚɡɚ ɞɨ ɡɚɤɪɵɬɢɹ ɡɚɝɥɭɲɟɤ ɪɚɫɬɟɬ ɢ ɦɚɤɫɢ ɦɚɥɶɧɵɟ ɩɚɪɚɦɟɬɪɵ ɜɡɪɵɜɚ ɛɭɞɭɬ ɞɨɫɬɢɝɚɬɶɫɹ ɜ ɬɨɦ ɫɥɭɱɚɟ ɟɫɥɢ ɜɡɪɵɜ ɩɪɨɢɫɯɨɞɢɬ ɫɪɚɡɭ ɩɨɫɥɟ ɡɚɤɪɵɬɢɹ ɡɚɝɥɭɲɟɤ
ǷȏȘȚȔȕȑ ǹȌȜȔȕȒȕȊȏȞȌȘȑȇȦ ȌȓȑȕȘșȣ ȎȇȖȕȒȔȌȔȔȇȦ ȊȇȎȕȓ Ȗȕȋ ȋȇȉȒȌȔȏȌȓ
ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɪɚɫɱɟɬɨɜ ɩɪɢ ɫɞɟɥɚɧɧɵɯ ɞɨɩɭɳɟɧɢɹɯ ɛɭɞɟɬ ɢɦɟɬɶ
ɜɢɞ.
1. Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɝɚɡɚ ɜ ɚɩɩɚɪɚɬɟɈɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɝɚɡɚ ɩɨɫɬɭɩɚɸɳɟɝɨ ɢɡ ɤɨɦɩɪɟɫɫɨɪɚ
Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɝɚɡɚ ɨɫɬɚɸɳɟɣɫɹ ɜ ɩɨɦɟɳɟɧɢɢ ɫ ɭɱɟɬɨɦ ɪɚɛɨɬɵ ɚɜɚɪɢɣɧɨɣ ɜɟɧɬɢɥɹɰɢɢ
4.Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɝɚɡɚ ɫɨɡɞɚɸɳɟɣ ɜ ɩɨɦɟɳɟɧɢɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟ ɫɤɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ
5.Ɉɩɪɟɞɟɥɟɧɢɟ ɨɛɴɟɦɚ ɨɛɥɚɤɚ ɜɡɪɵɜɨɨɩɚɫɧɨɣ ɫɦɟɫɢ
6.Ɉɩɪɟɞɟɥɟɧɢɟ ɫɬɟɩɟɧɢ ɡɚɝɚɡɨɜɚɧɧɨɫɬɢ ɩɨɦɟɳɟɧɢɹ ɩɪɢ ɚɜɚɪɢɢ ɨɛɭ
ɫɥɚɜɥɢɜɚɸɳɟɣ ɧɚɢɯɭɞɲɢɟ ɩɨɫɥɟɞɫɬɜɢɹ ɜɡɪɵɜɚ Ɋɚɫɫɦɨɬɪɢɦ ɩɨɪɹɞɨɤ ɪɚɫɱɟɬɨɜ ɢ ɢɫɩɨɥɶɡɭɟɦɵɟ ɮɨɪɦɭɥɵ
Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɝɚɡɚ ɜ ɚɩɩɚɪɚɬɟ
ɉɪɢ ɚɜɚɪɢɢ ɧɚ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɦ ɨɛɨɪɭɞɨɜɚɧɢɢ ɜ ɤɨɬɨɪɨɦ ɝɚɡ ɧɚɯɨɞɢɬɫɹ ɩɪɢ ɩɨɜɵɲɟɧɧɵɯ ɬɟɦɩɟɪɚɬɭɪɟ ɢ ɞɚɜɥɟɧɢɢ ɦɚɫɫɚ ɝɚɡɚ ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɩɨɫɬɭ ɩɢɬɶ ɜ ɩɨɦɟɳɟɧɢɟ ɢɡ ɚɩɩɚɪɚɬɚ ɢ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
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ɝɞɟ Vɚ ɨɛɴɟɦ ɚɩɩɚɪɚɬɚ ɦ ;
l lɩ ɞɥɢɧɚ ɨɬɜɨɞɹɳɟɝɨ ɢ ɩɨɞɜɨɞɹɳɟɝɨ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɦ; d dɩ ɞɢɚɦɟɬɪ ɨɬɜɨɞɹɳɟɝɨ ɢ ɩɨɞɜɨɞɹɳɟɝɨ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɦ; Uɝɬ ɩɥɨɬɧɨɫɬɶ ɝɚɡɚ ɜ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɦ ɨɛɨɪɭɞɨɜɚɧɢɢ
Uɝɬ |
P P 'Pɪɚɛ |
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Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɝɚɡɚ ɩɨɫɬɭɩɚɸɳɟɝɨ ɢɡ ɤɨɦɩɪɟɫɫɨɪɚ
Ɇɚɫɫɚ ɝɚɡɚ ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɩɨɫɬɭɩɢɬɶ ɜ ɩɨɦɟɳɟɧɢɟ ɩɪɢ ɚɜɚɪɢɢ ɡɚ ɫɱɟɬ ɩɨɞɚɱɢ ɤɨɦɩɪɟɫɫɨɪɚ ɢɥɢ ɧɚɫɨɫɚ ɡɚ ɜɪɟɦɹ ɞɨ ɩɨɥɧɨɝɨ ɨɬɤɥɸɱɟɧɢɹ ɡɚɞɜɢɠɟɤ ɪɚɜɧɚ
mɧ qUɝQWɡ |
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ɝɞɟ q ɩɨɞɚɱɚ ɧɚɫɨɫɚ ɢɥɢ ɤɨɦɩɪɟɫɫɨɪɚ ɦ ɫ;
Wɡ ɜɪɟɦɹ ɡɚɤɪɵɬɢɹ ɡɚɝɥɭɲɟɤ;
Uɝɩ ɩɥɨɬɧɨɫɬɶ ɝɚɡɚ ɜ ɩɨɦɟɳɟɧɢɢ ɤɝ ɦ :
U |
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Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɝɚɡɚ ɨɫɬɚɸɳɟɣɫɹ ɜ ɩɨɦɟɳɟɧɢɢ ɫ ɭɱɟɬɨɦ ɪɚɛɨɬɵ ɚɜɚɪɢɣɧɨɣ ɜɟɧɬɢɥɹɰɢɢ
Ɉɫɧɨɜɧɵɦ ɩɚɪɚɦɟɬɪɨɦ ɜɟɧɬɢɥɹɰɢɢ ɹɜɥɹɟɬɫɹ ɤɪɚɬɧɨɫɬɶ ɜɨɡɞɭɯɨɨɛɦɟɧɚ ɜ ɩɨɦɟɳɟɧɢɢ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ
ȿɫɥɢ Ⱥɜ ɱí1 ɤɪɚɬɧɨɫɬɶ ɜɨɡɞɭɯɨɨɛɦɟɧɚ ɜ ɩɨɦɟɳɟɧɢɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɚ ɛɨɬɵ ɜɟɧɬɢɥɹɰɢɢ ɬɨ ɦɚɫɫɭ ɝɚɡɚ ɨɫɬɚɜɲɭɸɫɹ ɜ ɩɨɦɟɳɟɧɢɢ ɜɵɱɢɫɥɢɦ ɩɨ ɮɨɪ ɦɭɥɟ
m* |
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ɝɞɟ mɚ Pɧ ɩɨɫɬɭɩɢɜɲɚɹ ɜ ɩɨɦɟɳɟɧɢɟ ɦɚɫɫɚ ɝɨɪɸɱɟɝɨ ɜɟɳɟɫɬɜɚ
Wɡ ɜɪɟɦɹ ɡɚɤɪɵɬɢɹ ɡɚɝɥɭɲɟɤ ɫɟɤɭɧɞ ɩɪɢ ɚɜɬɨɦɚɬɢɱɟɫɤɨɦ ɡɚɤɪɵ ɬɢɢ ɫɟɤɭɧɞ ɩɪɢ ɪɭɱɧɨɦ ɡɚɤɪɵɬɢɢ
Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɝɚɡɚ ɫɨɡɞɚɸɳɟɣ ɜ ɩɨɦɟɳɟɧɢɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟ ɫɤɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ
ɉɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɦɚɫɫɚ ɝɚɡɚ ɫɨɡɞɚɸɳɚɹ ɜ ɩɨɦɟɳɟɧɢɢ ɫɬɟɯɢɨ ɦɟɬɪɢɱɟɫɤɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ ɡɚɜɢɫɢɬ ɨɬ ɩɚɪɚɦɟɬɪɨɜ ɜɟɳɟɫɬɜɚ 0 ɫɫɬɯ ɢ ɨɛɴ ɟɦɚ ɩɨɦɟɳɟɧɢɹ V :
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Ɉɩɪɟɞɟɥɟɧɢɟ ɨɛɴɟɦɚ ɨɛɥɚɤɚ ɜɡɪɵɜɨɨɩɚɫɧɨɣ ɫɦɟɫɢ
Ɉɛɴɟɦ ɨɛɥɚɤɚ ɫɦɟɫɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɝɨ ɫɨɫɬɚɜɚ ɪɚɜɟɧ
VȽȼɋ |
min{mɫɬɯ;m*} |
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2.4.2. ǹȌȜȔȕȒȕȊȏȞȌȘȑȇȦ ȌȓȑȕȘșȣ ȎȇȖȕȒȔȌȔȔȇȦ ȘȍȏȍȌȔȔȢȓ ȊȇȎȕȓ
ɉɪɨɢɡɜɨɞɫɬɜɟɧɧɨɟ ɩɨɦɟɳɟɧɢɟ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɟ ɨɛɨɪɭɞɨɜɚɧɢɟ ɜ ɧɟɦ ɢ ɞɨɩɭɳɟɧɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɪɨɰɟɫɫɚ ɚɜɚɪɢɢ ɨɬ ɦɨɦɟɧɬɚ ɪɚɡɝɟɪɦɟɬɢɡɚɰɢɢ ɞɨ ɦɨ ɦɟɧɬɚ ɜɡɪɵɜɚ ɚɧɚɥɨɝɢɱɧɵ ɩɪɟɞɵɞɭɳɟɦɭ ɫɥɭɱɚɸ ɪɢɫ .
Ɉɬɥɢɱɢɟ ɫɨɫɬɨɢɬ ɜ ɬɨɦ ɱɬɨ ɜ ɭɫɬɪɨɣɫɬɜɨ ɧɚɫɨɫɨɦ ɩɨɞɚɟɬɫɹ ɫɠɢɠɟɧɧɵɣ ɝɚɡ ɩɪɟɞɫɬɚɜɥɹɸɳɢɣ ɫɨɛɨɣ ɩɟɪɟɝɪɟɬɭɸ ɠɢɞɤɨɫɬɶ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ ɤɢɩɟɧɢɹ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɸɳɟɣ ɬɟɦɩɟɪɚɬɭɪɭ ɤɢɩɟɧɢɹ ɞɚɧɧɨɝɨ ɜɟɳɟɫɬɜɚ ɩɪɢ ɧɨɪ ɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɍɫɬɪɨɣɫɬɜɨ ɩɪɢ ɷɬɨɦ ɧɚ ɤɚɤɭɸ ɬɨ ɱɚɫɬɶ [ ɡɚɩɨɥɧɟɧɨ ɠɢɞ ɤɨɫɬɶɸ ɚ ɨɫɬɚɥɶɧɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ ɡɚɩɨɥɧɟɧɨ ɩɚɪɚɦɢ ɝɨɪɸɱɟɝɨ ɜɟɳɟɫɬɜɚ.
ɉɪɢ ɪɚɡɝɟɪɦɟɬɢɡɚɰɢɢ ɭɫɬɪɨɣɫɬɜɚ ɬɟɦɩɟɪɚɬɭɪɚ ɤɢɩɟɧɢɹ ɜɟɳɟɫɬɜɚ ɩɚɞɚɟɬ ɢ ɩɪɨɢɫɯɨɞɢɬ ɜɵɞɟɥɟɧɢɟ ɧɚɤɨɩɥɟɧɧɨɣ ɜɟɳɟɫɬɜɨɦ ɷɧɟɪɝɢɢ ɤɨɬɨɪɚɹ ɢɞɟɬ ɧɚ ɢɫ ɩɚɪɟɧɢɟ ɫɠɢɠɟɧɧɨɝɨ ɝɚɡɚ
ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɪɚɫɱɟɬɨɜ ɩɪɢ ɷɬɨɦ ɛɭɞɟɬ ɢɦɟɬɶ ɜɢɞ. 1. Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɠɢɞɤɨɫɬɢ ɜ ɚɩɩɚɪɚɬɟɈɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɠɢɞɤɨɫɬɢ ɩɨɫɬɭɩɚɸɳɟɣ ɢɡ ɧɚɫɨɫɚ.
Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɩɚɪɚ ɨɛɪɚɡɨɜɚɜɲɟɝɨɫɹ ɡɚ ɫɱɟɬ ɢɡɛɵɬɨɱɧɨɣ ɬɟɩ ɥɨɬɵ ɩɟɪɟɝɪɟɬɨɣ ɠɢɞɤɨɫɬɢ.
4.Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɩɚɪɚ ɜ ɚɩɩɚɪɚɬɟ.
5.Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɩɚɪɚ ɨɫɬɚɸɳɟɝɨɫɹ ɜ ɩɨɦɟɳɟɧɢɢ ɫ ɭɱɟɬɨɦ ɪɚ ɛɨɬɵ ɚɜɚɪɢɣɧɨɣ ɜɟɧɬɢɥɹɰɢɢ
6.Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɩɚɪɚ ɫɨɡɞɚɸɳɟɣ ɜ ɩɨɦɟɳɟɧɢɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟ ɫɤɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ
7.Ɉɩɪɟɞɟɥɟɧɢɟ ɨɛɴɟɦɚ ɨɛɥɚɤɚ ɜɡɪɵɜɨɨɩɚɫɧɨɣ ɫɦɟɫɢ
8.Ɉɩɪɟɞɟɥɟɧɢɟ ɫɬɟɩɟɧɢ ɡɚɝɚɡɨɜɚɧɧɨɫɬɢ ɩɨɦɟɳɟɧɢɹ ɩɪɢ ɚɜɚɪɢɢ ɨɛɭ
ɫɥɚɜɥɢɜɚɸɳɟɣ ɧɚɢɯɭɞɲɢɟ ɩɨɫɥɟɞɫɬɜɢɹ ɜɡɪɵɜɚ Ɋɚɫɫɦɨɬɪɢɦ ɩɨɪɹɞɨɤ ɪɚɫɱɟɬɨɜ ɢ ɢɫɩɨɥɶɡɭɟɦɵɟ ɮɨɪɦɭɥɵ
46
ǷȏȘȚȔȕȑǹȌȜȔȕȒȕȊȏȞȌȘȑȇȦ ȌȓȑȕȘșȣ ȎȇȖȕȒȔȌȔȔȇȦ ȘȍȏȍȌȔȔȢȓ ȊȇȎȕȓ
Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɠɢɞɤɨɫɬɢ ɜ ɚɩɩɚɪɚɬɟ
Ɇɚɫɫɚ ɠɢɞɤɨɫɬɢ ɜ ɚɩɩɚɪɚɬɟ ɪɚɜɧɚ
m |
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[ V |
S l d l d · |
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ɝɞɟ [ ɫɬɟɩɟɧɶ ɡɚɩɨɥɧɟɧɢɹ ɚɩɩɚɪɚɬɚ ɠɢɞɤɨɫɬɶɸ;
Uɠ ɩɥɨɬɧɨɫɬɶ ɠɢɞɤɨɫɬɢ
Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɠɢɞɤɨɫɬɢ ɩɨɫɬɭɩɚɸɳɟɣ ɢɡ ɧɚɫɨɫɚ
Ɇɚɫɫɚ ɠɢɞɤɨɫɬɢ ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɞɨɩɨɥɧɢɬɟɥɶɧɨ ɩɨɫɬɭɩɢɬɶ ɜ ɩɨɦɟɳɟɧɢɟ
ɢɡ ɧɚɫɨɫɚ ɞɨ ɨɬɤɥɸɱɟɧɢɹ ɡɚɞɜɢɠɟɤ ɪɚɜɧɚ: |
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mɧ q Wɡ Uɠ |
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Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɩɚɪɚ ɨɛɪɚɡɨɜɚɜɲɟɝɨɫɹ ɡɚ ɫɱɟɬ ɢɡɛɵɬɨɱɧɨɣ ɬɟɩ ɥɨɬɵ ɩɟɪɟɝɪɟɬɨɣ ɠɢɞɤɨɫɬɢ
Ɍɟɩɥɨɬɚ ɩɟɪɟɝɪɟɜɚ ɠɢɞɤɨɫɬɢ:
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Qɢɡɛ mɚ + mɧ Cɪ tɪ í tɤ |
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ɝɞɟ ɋɪ ɭɞɟɥɶɧɚɹ ɬɟɩɥɨɟɦɤɨɫɬɶ ɠɢɞɤɨɫɬɢ |
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tɪ ɪɚɛɨɱɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɜɟɳɟɫɬɜɚ ɜ ɚɩɩɚɪɚɬɟ |
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tɤ ɬɟɦɩɟɪɚɬɭɪɚ ɤɢɩɟɧɢɹ ɠɢɞɤɨɫɬɢ ɩɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ |
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Ɇɚɫɫɚ ɩɚɪɨɜ ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɨɛɪɚɡɨɜɚɬɶɫɹ ɡɚ ɫɱɟɬ ɬɟɩɥɨɬɵ ɩɟɪɟɝɪɟɜɚ |
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ɠɢɞɤɨɫɬɢ |
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m1 Qɢɡɛ r |
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ɝɞɟ r ɬɟɩɥɨɬɚ ɩɚɪɨɨɛɪɚɡɨɜɚɧɢɹ. |
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Ɋɚɫɱɟɬɧɭɸ ɦɚɫɫɭ ɩɚɪɨɜ ɨɬ ɢɫɩɚɪɟɧɢɹ ɩɟɪɟɝɪɟɬɨɣ ɠɢɞɤɨɫɬɢ ɨɩɪɟɞɟɥɢɦ |
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ɢɡ ɭɫɥɨɜɢɹ |
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mɩɠ=min{m1; mɚ mɧ}. |
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Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɩɚɪɚ ɜ ɚɩɩɚɪɚɬɟ
Ɇɚɫɫɚ ɩɚɪɨɜ ɜ ɨɛɴɟɦɟ ɚɩɩɚɪɚɬɚ ɫɜɨɛɨɞɧɨɦ ɨɬ ɠɢɞɤɨɫɬɢ ɢ ɧɚɯɨɞɹɳɢɯɫɹ ɩɪɢ ɩɨɜɵɲɟɧɧɨɦ ɞɚɜɥɟɧɢɢ ɢ ɬɟɦɩɟɪɚɬɭɪɟ ɨɩɪɟɞɟɥɢɦ ɢɡ ɜɵɪɚɠɟɧɢɹ
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mɩ |
Vɚ [ Uɝɬ |
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M P 'Pɪɚɛ |
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R tɪɚɛ |
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Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɩɚɪɚ ɨɫɬɚɸɳɟɝɨɫɹ ɜ ɩɨɦɟɳɟɧɢɢ ɫ ɭɱɟɬɨɦ ɪɚ ɛɨɬɵ ɚɜɚɪɢɣɧɨɣ ɜɟɧɬɢɥɹɰɢɢ
Ɉɛɳɚɹ ɦɚɫɫɚ ɩɚɪɨɜ ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɩɨɫɬɭɩɢɬɶ ɜ ɩɨɦɟɳɟɧɢɟ ɢ ɨɫɬɚɧɟɬɫɹ ɜ ɧɟɦ ɫ ɭɱɟɬɨɦ ɪɚɛɨɬɵ ɜɟɧɬɢɥɹɰɢɢ
m* |
mɩɠ mn |
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A W |
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Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɩɚɪɚ ɫɨɡɞɚɸɳɟɣ ɜ ɩɨɦɟɳɟɧɢɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟ ɫɤɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ
Ɇɚɫɫɚ ɧɟɨɛɯɨɞɢɦɚɹɞɥɹ ɫɨɡɞɚɧɢɹ ɜɩɨɦɟɳɟɧɢɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɣ ɤɨɧ ɰɟɧɬɪɚɰɢɢ ɪɚɜɧɚ
m |
M V ɫ |
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ɫɬɯ |
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ɫɬɯ RT |
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Ɉɩɪɟɞɟɥɟɧɢɟ ɨɛɴɟɦɚ ɨɛɥɚɤɚ ɜɡɪɵɜɨɨɩɚɫɧɨɣ ɫɦɟɫɢ
Ɉɛɴɟɦ ɨɛɥɚɤɚ ɫɦɟɫɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɝɨ ɫɨɫɬɚɜɚ ɪɚɜɟɧ
VȽȼɋ |
min{mɫɬɯ;m*} |
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Ɉɩɪɟɞɟɥɟɧɢɟ ɫɬɟɩɟɧɢ ɡɚɝɚɡɨɜɚɧɧɨɫɬɢ ɩɨɦɟɳɟɧɢɹ ɨɛɭɫɥɚɜɥɢɜɚɸɳɟɣ ɧɚɢɯɭɞɲɢɟ ɩɨɫɥɟɞɫɬɜɢɹ ɜɡɪɵɜɚ
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min{VȽȼɋ |
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2.4.3. ǧȉȇȗȏȐȔȢȐ ȗȇȎȒȏȉ ȍȏȋȑȕȘșȏ
ȼ ɨɬɥɢɱɢɟ ɨɬ ɩɪɟɞɵɞɭɳɢɯ ɫɥɭɱɚɟɜ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɨɟ ɩɨɦɟɳɟɧɢɟ ɞɨɩɨɥ ɧɢɬɟɥɶɧɨ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɥɢɧɟɣɧɵɦɢ ɪɚɡɦɟɪɚɦɢ ɚ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɟ ɨɛɨɪɭɞɨ ɜɚɧɢɟ ɡɚɦɟɧɟɧɨ ɪɟɡɟɪɜɭɚɪɨɦ ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɦɫɹ ɦɚɫɫɨɣ ɜɵɬɟɤɚɸɳɟɝɨ ɢɡ ɧɟɝɨ ɩɪɢ ɪɚɡɝɟɪɦɟɬɢɡɚɰɢɢ ɜɟɳɟɫɬɜɚ ɫ ɢɡɜɟɫɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ ɪɢɫ
ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɪɚɫɱɟɬɨɜ ɛɭɞɟɬ ɢɦɟɬɶ ɜɢɞ 1. Ɉɩɪɟɞɟɥɟɧɢɟ ɩɥɨɳɚɞɢ ɪɚɡɥɢɜɚ ɢ ɩɥɨɳɚɞɢ ɢɫɩɚɪɟɧɢɹɈɩɪɟɞɟɥɟɧɢɟ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɢɫɩɚɪɟɧɢɹ
48
Ɉɩɪɟɞɟɥɟɧɢɟ ɜɪɟɦɟɧɢ ɢɫɩɚɪɟɧɢɹ
4.Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɩɚɪɚ ɨɫɬɚɸɳɟɝɨɫɹ ɜ ɩɨɦɟɳɟɧɢɢ ɫ ɭɱɟɬɨɦ ɪɚ ɛɨɬɵ ɚɜɚɪɢɣɧɨɣ ɜɟɧɬɢɥɹɰɢɢ
5.Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɩɚɪɚ ɫɨɡɞɚɸɳɟɣ ɜ ɩɨɦɟɳɟɧɢɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟ ɫɤɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ
6.Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɧɚɫɵɳɟɧɧɨɝɨ ɩɚɪɚ ɜ ɩɨɦɟɳɟɧɢɢ
7.Ɉɩɪɟɞɟɥɟɧɢɟ ɨɛɴɟɦɚ ɨɛɥɚɤɚ ɜɡɪɵɜɨɨɩɚɫɧɨɣ ɫɦɟɫɢ
8.Ɉɩɪɟɞɟɥɟɧɢɟɫɬɟɩɟɧɢɡɚɝɚɡɨɜɚɧɧɨɫɬɢɩɨɦɟɳɟɧɢɹ ɨɛɭɫɥɚɜɥɢɜɚɸɳɟɣ ɧɚɢɯɭɞɲɢɟ ɩɨɫɥɟɞɫɬɜɢɹ ɜɡɪɵɜɚ
Ɋɚɫɫɦɨɬɪɢɦ ɩɨɪɹɞɨɤ ɪɚɫɱɟɬɨɜ ɢ ɢɫɩɨɥɶɡɭɟɦɵɟ ɮɨɪɦɭɥɵ
ǷȏȘȚȔȕȑǧȉȇȗȏȐȔȢȐ ȗȇȎȒȏȉ ȍȏȋȑȕȘșȏ
Ɉɩɪɟɞɟɥɟɧɢɟ ɩɥɨɳɚɞɢ ɪɚɡɥɢɜɚ ɢ ɩɥɨɳɚɞɢ ɢɫɩɚɪɟɧɢɹ
Ɇɚɤɫɢɦɚɥɶɧɚɹ ɩɥɨɳɚɞɶ ɪɚɡɥɢɜɚ ɠɢɞɤɨɫɬɢ ɡɚɜɢɫɢɬ ɨɬ ɦɚɫɫɵ ɩɥɨɬɧɨɫɬɢ ɢ ɤɨɷɮɮɢɰɢɟɧɬɚ ɪɚɫɬɟɤɚɟɦɨɫɬɢ ɩɨɫɬɭɩɢɜɲɟɣ ɜ ɩɨɦɟɳɟɧɢɟ ɠɢɞɤɨɫɬɢ mɠ Uɠ f:
S fmɠ Uɠ |
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Ɂɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɪɚɫɬɟɤɚɟɦɨɫɬɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɫɨɞɟɪɠɚɧɢɸ ɪɚɫɬɜɨɪɢɬɟɥɹ ɜ ɠɢɞɤɨɫɬɢ
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° |
oTd |
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f |
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5 |
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® |
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° |
oT! |
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¯ |
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ɝɞɟ ș – ɫɨɞɟɪɠɚɧɢɟ ɪɚɫɬɜɨɪɢɬɟɥɹ
ɉɥɨɳɚɞɶ ɢɫɩɚɪɟɧɢɹ ɨɱɟɜɢɞɧɨ ɧɟ ɦɨɠɟɬ ɩɪɟɜɵɲɚɬɶ ɩɥɨɳɚɞɢ ɩɨɦɟɳɟ
ɧɢɹ
Fɢ min^S L B` |
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ɝɞɟ L ɢ B ɞɥɢɧɚ ɢ ɲɢɪɢɧɚ ɩɨɦɟɳɟɧɢɹ |
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Ɉɩɪɟɞɟɥɟɧɢɟ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɢɫɩɚɪɟɧɢɹ
ɂɧɬɟɧɫɢɜɧɨɫɬɶ ɢɫɩɚɪɟɧɢɹ Wɢ ɤɝ ɫ·ɦ ɨɩɪɟɞɟɥɹɸɬ ɩɨ ɫɩɪɚɜɨɱɧɵɦ ɢɥɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ
ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɞɚɧɧɵɯ ɡɧɚɱɟɧɢɟ Wɢ ɦɨɠɧɨ ɪɚɫɫɱɢɬɵɜɚɬɶ ɩɨ ɮɨɪɦɭɥɟ
W |
6 P K M |
7 |
u |
s |
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ɝɞɟ Ɇ ɦɨɥɹɪɧɚɹ ɦɚɫɫɚ;
Ps ɞɚɜɥɟɧɢɟ ɧɚɫɵɳɟɧɧɵɯ ɩɚɪɨɜ;
Ș ɤɨɷɮɮɢɰɢɟɧɬ ɭɱɢɬɵɜɚɸɳɢɣ ɜɥɢɹɧɢɟ ɫɤɨɪɨɫɬɢ ɢ ɬɟɦɩɟɪɚɬɭɪɵ ɜɨɡ ɞɭɲɧɨɝɨ ɩɨɬɨɤɚ ɧɚ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɢɫɩɚɪɟɧɢɹ.
Ʉɨɷɮɮɢɰɢɟɧɬ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɢɫɩɚɪɟɧɢɹ Kɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɫɩɪɚɜɨɱɧɨɣ ɬɚɛɥɢɰɟ ɉɪɢɥɨɠɟɧɢɹ ɜɯɨɞɚɦɢ ɜ ɤɨɬɨɪɭɸ ɫɥɭɠɚɬ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɜɨɡ ɞɭɯɚ ɜ ɩɨɦɟɳɟɧɢɢ ɢ ɬɟɦɩɟɪɚɬɭɪɚ ɜ ɩɨɦɟɳɟɧɢɢ
ɋɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɜɨɡɞɭɯɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɜɵɪɚɠɟɧɢɹ
U AɜL |
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ɝɞɟ L ɞɥɢɧɚ ɩɨɦɟɳɟɧɢɹ ɦ.
Ⱦɚɜɥɟɧɢɟ ɧɚɫɵɳɟɧɧɵɯ ɩɚɪɨɜ Ɋs ɞɥɹ ɢɧɞɢɜɢɞɭɚɥɶɧɵɯ ɜɟɳɟɫɬɜ ɚ ɬɚɤɠɟ ɫɦɟɫɟɣ ɢ ɞɪɭɝɢɯ ɬɟɯɧɢɱɟɫɤɢɯ ɩɪɨɞɭɤɬɨɜ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
A |
B |
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P |
C tɠ |
9 |
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s |
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ɝɞɟ tɠ ɬɟɦɩɟɪɚɬɭɪɚɠɢɞɤɨɫɬɢ ɪɚɜɧɚɹɫɪɟɞɧɟɚɪɢɮɦɟɬɢɱɟɫɤɨɦɭɡɧɚɱɟɧɢɸɪɚ ɛɨɱɟɣ ɬɟɦɩɟɪɚɬɭɪɵ ɠɢɞɤɨɫɬɢ tɪɚɛ ɢ ɬɟɦɩɟɪɚɬɭɪɵ ɜɨɡɞɭɯɚ tɩ ɜ ɩɨɦɟɳɟɧɢɢ
tɠ tɪɚɛ + tɩ |
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Ⱥ ȼ ɋ ɤɨɧɫɬɚɧɬɵ ɨɩɪɟɞɟɥɹɟɦɵɟ ɩɨ ɫɩɪɚɜɨɱɧɨɣ ɬɚɛɥɢɰɟ 1 ɉɪɢɥɨɠɟɧɢɹ .
Ɉɩɪɟɞɟɥɟɧɢɟ ɜɪɟɦɟɧɢ ɢɫɩɚɪɟɧɢɹ
ȼɪɟɦɹ ɩɨɥɧɨɝɨ ɢɫɩɚɪɟɧɢɹ ɪɚɡɥɢɜɲɟɣɫɹ ɠɢɞɤɨɫɬɢ Wɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɜɵ ɪɚɠɟɧɢɹ
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Wɢ mɠ WɢǜFɢ . |
71 |
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Ɋɚɫɱɟɬɧɨɟ ɜɪɟɦɹ ɢɫɩɚɪɟɧɢɹ Wɪ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɦɚɫɫɵ ɢɫɩɚɪɢɜɲɟɣɫɹ |
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ɠɢɞɤɨɫɬɢ ɩɪɢɧɢɦɚɸɬ ɪɚɜɧɵɦ Wɢ ɧɨ ɧɟ ɛɨɥɟɟ ɫ ɬɨ ɟɫɬɶ |
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Wɪ = min{tɢ; `. |
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Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɩɚɪɚ ɨɫɬɚɸɳɟɝɨɫɹ ɜ ɩɨɦɟɳɟɧɢɢ ɫ ɭɱɟɬɨɦ ɪɚ |
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ɛɨɬɵ ɚɜɚɪɢɣɧɨɣ ɜɟɧɬɢɥɹɰɢɢ |
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ɂɦɟɹ ɩɨɥɭɱɟɧɧɵɟ ɞɚɧɧɵɟ ɦɨɠɧɨ ɜɵɱɢɫɥɢɬɶ ɦɚɫɫɭ ɠɢɞɤɨɫɬɢ ɢɫɩɚɪɢɜ |
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ɲɟɣɫɹ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɡɥɢɜɚ Fɢ: |
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mɢ WɢFɢWɪ |
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ɚ ɫ ɭɱɟɬɨɦ ɪɚɛɨɬɵ ɚɜɚɪɢɣɧɨɣ ɜɟɧɬɢɥɹɰɢɢ |
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