双材料叠合悬臂梁端部受集中力作用的理论解

Analytical solution for bi-material superposed cantilever beam subjected to concentrated force

文章采用弹性力学的应力函数法,求得了双材料叠合悬臂梁在自由端受集中力作用时的理论解,所得到的应力理论解可退化为已有的单材料悬臂梁在自由端受集中力作用时的理论解;运用有限元分析软件An-sys,对用钢和铝合金叠合成的悬臂梁进行了数值计算,验证了所得到的理论解的正确性。

By use of the stress function method of the elasticity, the analytical solution is presented for a bi-material superposed cantilever beam subjected to a concentrated force at the free end. The solution of the stresses can be degenerated into one of the single material cantilever beam subjected to a concentrated force at the free end, which can be found in the literature. For verification of the correctness of the analytical solution obtained in this paper, a cantilever beam superposed by the steel and aluminium alloy layers is calculated numerically using the finite element code Ansys. The numerical results coincide with the analytical ones.