矩形截面梁受n次函数作用时应力函数的选取

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

针对矩形截面悬臂梁受任意n次多项式分布载荷作用的情况,采用逆解法,构造了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,还把此理论应用于工程实例中,理论计算与实验结果比较吻合。此理论克服了矩形截面悬臂梁受任意n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 polynomial of degree n distributed load, a uniform stress function which meets both the biharmonic equations and boundary conditions is constructed by the inverse method. Furthermore, the analytic solution of the stress components is deduced by the stress function. When this theory is applied to an engineering example, the experimental results are in accordance with the theoretical calculation. This theory overcomes the blindness of choosing the stress function for the rectangular beamsubjected to arbi- trary polynomial of degree n, and paves the way for the solution of the beam with randomly uneven pressure of the cantilever beam of rectangular section.