弹性力学大作业.docVIP

The group task of mechanics of elasticity Group： Four Member： Tonghai Sun; Xueyin Li Our task: A wedge given in wedge in Fig. 4(a) subjected to symmetric distributed loads q on both lateral sides. Try to use the stress functionto calculate the stress components; and use PDE tool to develop the FEM solution and make a comparison with the analytical solution. Analytic solutions: According to the dimentional analysis, the dimention of 、、 is , the dimention of is ,so we know that . And we can get. According to the compatibility equations,we have:, so we can get:; From the characteristic equation:,we get these solutions: . So:; ; ; . According to the boundary condition,we get: ,,,; so:A=0,B=0,C=0,D=. So we can get the stress components in polar coordinates:;;. From the Coordinate transformation type: ; ; . So we can get the stress components in rectangular coordinate system:;;. Arithmetic solution: At first,input the Young抯 modulus = 1000,Poisson ratio = 0.3 And the coordinwates shown in the picture A（0，0），B（，），C（，） According to the topic,there are uniformly distributed load of instensity q shown in the picture.Besides,because it’s a infinite large plates,the displacement far away is 0. From these message,we can define the boundary conditon.And the edge AB and AC must satisfy the Neumann condition,BC must satisfy the Dirichlet condition,It’s shown as follows: （PS：in matlab,we can’t input （square root of three over three）,so we take place it by 0.57735) . AB:The uniformly distributed load q on the edge AB is decomposed into and .We can get the Neumann condition on the edge AB：,; AC:The uniformly distributed load q on the edge AC is decomposed into and .We can get the Neumann condition on the edge AC:,; The edge BC is supposed as the boundary of the plate，so the displacement is zero.Then we can get the Dirichlet condition:，。 After these,click the button we can get t