theoryofelasticity彈性力學-資料下載頁
2025-07-17 17:36本頁面
【正文】 is a solution to the fundamental equations with prescribed body forces and surface traction , then the state will be a solution to the problem with body forces and surface tractions . (對于給定的問題 ,如果一彈性體在體力 面力 作用下狀態(tài)為 ,而在體力 面力 作用下狀態(tài)為 ,則在體力 面力 作用下狀態(tài)為 ) (1) (1) (1){ , , }i j i j iu??(1)iF (1)iT ( 2 ) ( 2 ) ( 2 ){ , , }i j i j iu??(2)iF (2)iT( 1 ) ( 2 ) ( 1 ) ( 2 ) ( 1 ) ( 2 ){ , , }i j i j i j i j i iuu? ? ? ?? ? ?(1) (2)iiFF? (1) (2)iiTT?(1)iF(1)iT (1) (1) (1){ , , }i j i j iu??(2)iF (2)iT ( 2 ) ( 2 ) ( 2 ){ , , }i j i j iu?? (1) (2)iiFF? (1) (2)iiTT?( 1 ) ( 2 ) ( 1 ) ( 2 ) ( 1 ) ( 2 ){ , , }i j i j i j i j i iuu? ? ? ?? ? ?small deformations（小變形） linear elastic constitutive behavior（線彈性本構關系） the usual boundary conditions（通常邊界條件） Principle of Superposition (疊加原理 ) Chapter Page All governing equations are linear, and the superposition concept can be applied (疊加原理適用于線性控制方程 ) 6 23 Required conditions:(應用條件 ) Principle of Superposition (疊加原理 ) Chapter Page ？ ＝ 6 24 Example: SaintVenant’s Principle (圣維南原理 ) Chapter Page 1797－ 1886 6 25 SaintVenant’s Principle SaintVenant’s Principle (圣維南原理 ) Chapter Page SaintVenant’s Principle: The stress, strain, and displacement fields caused by two different statically equivalent force distributions on parts of the body far away from the loading points are approximately the same. (在彈性體表面某一不大的局部面積用一靜力等效的力系代替另一力系 ,則在近處載荷分布無顯著變化 .) 6 26 Chapter Page SaintVenant’s Principle (圣維南原理 ) Example: 薄板受集中力和與其靜力等效的均布力 6 27 SaintVenant’s Principle (圣維南原理 ) Chapter Page 6 28 放大 放大 Example: Vocabulary(詞匯 ) Chapter Page 6 29 boundary condition 邊界條件 geometrical Equation 幾何方程 equilibrium Equation 平衡方程 physical Equation 物理方程 principle of superposition 疊加原理 SaintVenant’s Principle 圣維南原理 Homework 54 Chapter Page Express all boundary conditions for each of the problems illustrated in the following figure. 6 30
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