论文部分内容阅读
该文采用弹性力学逆解法,求得了功能梯度曲梁在端部受弯矩作用的解析解。假设弹性模量E=E0rn沿径向呈幂函数的梯度分布。根据弹性力学平面问题的基本方程,在极坐标系下,引入应力函数,得到了弯曲问题的解析解。进而将功能梯度曲梁问题进行扩展,求得了整环或厚壁圆筒以及向错问题的解析解。将所得到的解退化到均匀弹性情况,与经典的理论解一致。最后对梯度函数按幂函数变化的算例进行了分析,结果显示梯度因子n对应力及位移的分布产生了巨大的影响。该文所得到的结论可以作为功能梯度曲梁构件优化设计的理论基础。
In this paper, the analytical solution of the functionally curved curved beam subjected to bending moments at the ends is obtained by the method of elastic mechanics. It is assumed that the elastic modulus E = E0rn is a power function gradient along the radial direction. According to the basic equations of elasticity plane problem, under the polar coordinate system, the stress function is introduced and the analytical solution of the bending problem is obtained. Furthermore, the problem of functional gradient curved beam is extended to obtain the analytical solution of the whole ring or thick-walled cylinder and the problem of the wrong-direction. Degenerate the solution to uniform elasticity, which is consistent with the classical theoretical solution. Finally, an example of the gradient function changing according to the power function is analyzed. The results show that the gradient factor n has a great influence on the distribution of stress and displacement. The conclusion obtained in this paper can be used as the theoretical basis for the optimization design of functionally graded curved beam members.