弹性力学双语课件第三章1.ppt

1 Chapter of Plane Problems in Rectangular Coordinates Chapter 3. Solution of Plane Problems in Rectangular Coordinates § Solution by Polynomials [p? li \n? umi ? lz] In this section, we shall use the inverse method to obtain the solutions of some simple plane problems by stress functions in the form of polynomials, assuming that there are no body forces acting, ., X=Y=0 2 Chapter of Plane Problems in Rectangular Coordinates § Solution by Polynomials [p? li \n? umi ? lz] § Take a polynomial of the first degree as stress function . cy bx a????.0 ,0,0 2 2 2 2 2???????????????yxxy yx xy y x??????? patibility equation () is satisfied for all values of the constants a,b,and c. The stress components given by E qs () are 3 Chapter of Plane Problems in Rectangular Coordinates § Take a polynomial of the first degree as stress function The stress boundary conditions () always give , regardless of the shape and the coordinate axes chosen. 0??YX Thus, we conclude that 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. 4 Chapter of Plane Problems in Rectangular Coordinates T patibility equation () is satisfied for all values of the constants a. The ponents given by E qs () are. § Take as stress function 2ax??.0 ,2,0 2 2 2 2 2???????????????yx axy yx xy y x??????? 5 Chapter of Plane Problems in Rectangular Coordinates O xy a2a2 For a rectangular plate with its edges parallel to the coordinate axes, the stress function can solve the problem of uniform tension (a>0) or uniform compression (a<0) of a rectangular plate in y direction. 2ax??§ Take as stress function 2ax??6 Chapter of Plane Problems in Rectangular Coordinates T pati