双材料叠合悬臂梁受集中荷载作用的解析解和有限元分析

Analytical Solution and Finite Element Analysis of Bimaterial Composite Cantilever Beams Subjected to Concentrated Loads

以两根等长等宽等高的矩形截面异质双材料叠合悬臂梁为对象,研究双材料叠合悬臂梁受集中荷载作用时的解析解和有限元解。先利用弹性理论对双材料叠合悬臂梁进行内力分析,然后利用有限元分析软件对双材料叠合悬臂梁进行数值模拟分析,并将模拟结果和应力解析解进行比较。结果表明:叠合梁上、下两层梁中,弯矩-剪力是按照其刚度来分布的,当上层梁自由端上所承受的外力总和大于或等于某值时,上层梁与下层梁的弯矩才能维持相对稳定的接触;解析解和有限元解比较一致,验证了弹性理论应力解析解的正确性。

The analytical and finite element solutions of two heterogeneous bimaterial composite cantilever beams with rectangular cross-sections of equal length,width,and height under concentrated loads are studied.Firstly,the internal force analysis of the bimaterial composite cantilever beamis conducted by using elastic theory.Then,numerical simulation analy-sis of the bimaterial composite cantilever beamis carried out by using finite element analysis software,and the simulation re-sults are compared with the stress analytical solution.The results show that in the upper and lower beams of the composite beam,the bending moment shear force is distributed according toits stiffness.When the total external force borne by the free end of the upper beamis greater than or equal toa certain value,the bending moment of the upper beamand the lower beam can maintain relatively stable contact;the analytical solution is consistent with the finite element solution,which verifies the correctness of the stress analytical solution in elastic theory.