简支双层叠合梁的变形计算

DEFORMATION COMPUTATION OF SIMPLIFIED SUPPORTED DOUBLE COMPOSITE BEAM

考虑小变形假设,利用梁挠度近似微分方程、积分方程理论和数值方法,研究简支双层光滑接触叠合梁的变形计算问题。通过上、下梁变形的协调条件,给出双层梁之间相互作用分布力系满足的第一类沃尔特拉积分方程及其精确解,直接利用上、下梁之间分布力满足的积分方程和梁挠度近似微分方程,推出上、下梁截面转角函数的解析表示式,对梁的变形和应力计算提出简明的求解方法。算例结果说明方法的可行性,其结论可为复合梁的强度设计和刚度校核提供理论参考。

Considering of small deformation, approximate differential equation of beam deflection and integration equation theory and numerical method are used to study the deformation computation problem of simplified supported double composite beams which has a smooth interface. Considering the deflection equation of compatibility between the upper and lower beams, the first kind of Voherra integral equation which the distributing force between the upper and lower beam satisfy and its exact solution are obtained, and the beam section rotation angle analytical solutions of the upper and lower beams are also obtained with the direct uses of the integral equation of the distributing force and the approximate differential equation, the concise method of computing the deformation and the stress of beam are put forward, and the results of given example show the feasibility of the method here, the conclusions given here have theoretical references to the strength design and the stiffness check.