theoryofelasticity彈性力學(xué)(編輯修改稿)
2024-11-04 19:53 本頁面
【文章內(nèi)容簡介】 of the other two leaving two constants to be determined by the boundary conditions.(由上式 就可求出所有系數(shù) ) 4 2 2 44 0 2 2 4 0f A x A x y A y? ? ? ?4 2 2 440 22 40 0A x A x y A y? ? ?02 4422444 ?????? ???? yyxx ???滿足雙調(diào)各方程 : Cartesian Coordinate Solutions Using Polynomials （直角坐標(biāo)下的多項式解答） 00mnf m nmnx y A x y?????? ??( , )Chapter Page 8 10 the general relation that must be satisfied to ensure that the polynomial grouping is biharmonic(對于任意階多項式要滿足雙調(diào)和方程 ) 02 4422444 ?????? ???? yyxx ???滿足雙調(diào)各方程 : 22222 1 1 2 1 12 1 1 0m n m mmnm m m m A m m n n An n n n A????? ? ? ? ? ?? ? ? ? ?,( ) ( ) ( ) ( ) ( )( ) ( ) ( ) Uniaxial Tension of a Beam (單軸拉伸梁 ) Chapter Page plane stress case Saint Venant approximation to the more general case with nonuniformly distributed tensile forces at the ends x =177。 l. (由圣維南原理可知對于在 x =177。 l處拉力分布不均但靜力等效的情況也適用 ) Solution( inverse method) (逆解法 ): The boundary conditions (邊界條件 ): 0)(,)(0)(,0)(????????????lxxylxxcyxycyyT ????8 11 Problem: Chapter Page constant stresses on each of the beam’s boundaries: 求應(yīng)力函數(shù) Φ 0)(,)( ?? ???? lxxylxx T ??Therefore, this problem is given by: 8 12 202Ay? ?2 2 222x y x yy x x y? ? ?? ? ?? ? ?? ? ? ?? ? ? ?,022 , 0x y x yA? ? ?? ? ?02 2AT?0x y x yT? ? ?? ? ?,Boundary condition polynomial is biharmonic Uniaxial Tension of a Beam (單軸拉伸梁 ) Chapter Page 求 u ,ε //xyTETE??????yETvxETu????11x x yy y xuTvx E EvTvvy E E? ? ?? ? ??? ? ? ???? ? ? ? ??()()Tu x f yETv v y g xE??? ? ?()()2 0 ( ) ( ) 0xyxyuv f y g xyx ?? ??? ??? ? ? ? ? ? ??? ( ) ( ) c ons t a n tg x f y??? ? ?()()oooof y y ug x x v??? ? ???0fg??0x y x yT? ? ?? ? ?,Integral(積分 ) Uniaxial Tension of a Beam (單軸拉伸梁 ) 022 , 0x y x yA? ? ?? ? ?Chapter Page inverse method(逆解法 ) 0)(,)( ?? ???? lxxylxx T ??Physical Equations ?e u Geometrical Equations 02 4422444 ?????? ???? yyxx ???8 14 202Ay? ? Uniaxial Tension of a Beam (單軸拉伸梁 ) Chapter Page Bending of a Beam by Uniform Transverse Loading(受均勻橫向載荷的梁彎曲問題 ) Airy stress function(艾里應(yīng)力函數(shù) ) x y l l ql ql 1 y z h/2 h/2 q stress field(應(yīng)力場 ) Boundary Conditions(邊界條件 ) pare with elementary strength of materials(和材力結(jié)果相比 ) 8 15 Chapter Page 8 16 plane stress conditions (semiinverse method 半逆解法 ) x y l l ql ql 1 y z h/2 h/2 q 1, Airy stress function y?x?xy
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