[经济学]弹性力学双语讲义Chapter3.ppt

Chapter 3 solution of plane problems in rectangular coordinates 第三章 平面问题的直角坐标解答 3.1 solution by polynomials 3.1 多项式解答 Review: Inverse method 逆解法 Select ? satisfying the compatibility equation 设定 ?，并 满足相容方程 ?4 ? =0 (2.12.11) find the stress components by 由下式求出应力分量 ?x=?2?/?y2-Xx ?y= ?2?/?x2-Yy ?xy=-?2?/?x?y (2.12.10) find the surface force components by 由下式对给定坐标的物体求出面力分量 (l?x+m ?yx)s = X (m?y+l?xy)s =Y (2.7.2) Identify the problem which the ? selected can solve确定所设定的 ? 能解决的问题 A. ?=a+bx+cy , X=0, Y=0 It satisfies the compatibility equation ?4 ? =0 find the stress components by ?x=?2?/?y2=0 ?y= ?2?/?x2=0 ?xy=-?2?/?x?y=0 find the surface force components by (l?x+m ?yx)s=X=0 (m?y+l?xy)s =Y=0 a linear stress function corresponds to the case of no surface forces and no stress . The superposition of a linear function to the stress function for any problem does not affect the stresses. A. ?=a+bx+cy , X=0 Y=0 满足相容方程 ?4 ? =0 由下式求出应力分量 ?x=?2?/?y2=0 ?y= ?2?/?x2=0 ?xy=-?2?/?x?y=0 由下式对给定坐标的物体求出面力分量 (l?x+m ?yx)s=X=0 (m?y+l?xy)s =Y=0 确定所设定的 ? 能解决的问题为：任意物体无体力，无面力，无应力。 应力函数加或减一个线性项不影响应力。 B. ?=ax2 , X=0, Y=0 It satisfies the compatibility equation ?4 ? =0 find the stress components by ?x=?2?/?y2=0 ?y= ?2?/?x2=2a ?xy=-?2?/?x?y=0 for a rectangular plate with its edges parallel to the coordinate axes, find the surface force components by (l?x+m ?yx)s=X (m?y+l?xy)s =Y the stress function ?=ax2 can solve the problem of uniform tension (a0) or uniform compression (a0) of a rectangular plate in y direction. P37 Fig.3.1.1(a) B. ?=ax2 , X=0, Y=0 满足相容方程 ?4 ? =0 由下式求出应力分量 ?x=?2?/?y2=0 ?y= ?2?/?