矩形截面梁受五次多项式作用的应力函数解答

Section of stress function for a rectangular beam subjected to any quintic polynomial pressure

针对矩形截面悬臂梁受任意五次多项式分布载荷作用的情况,采用逆解法,构造一个既满足双调和方程,又满足边界条件的应力函数,并且运用此应力函数求解出了该情况下的各应力分量.此外,将该理论应用于一个工程实例中,理论计算与实验结果比较吻合.克服了矩形截面悬臂梁受五次多项式分布载荷作用时选取应力函数的盲目性,为选取矩形截面悬臂梁在更复杂载荷下的应力函数奠定了基础.

With regard to the rectangular beam subjected to any quintic polynomial distributed load, a uniform stress function which meets both the biharmonic equations and boundary conditions was constructed in this paper by the inverse method. Furthermore, the analytic solution of it on its surface was deduced. When this theory was applied to an engineering example, the experimental results were in accord with the theoretic calculation. This theory overcomes the blindness of choosing the stress function and paves the way for the solution of the beam with randomly uneven pressure.