两端固定深梁的自重应力

Stresses in Deep Beams with Both Ends Fixed to Dead Weight

本文讨论两端固定深梁在自重作用下的应力分析问题,利用体积应变函数将耦联的控制偏微分方程组解耦成为非耦联的,然后利用有限积分变换法求解所得非耦联的控制偏微分方程,从而得到给定问题的解答。文中所述方法可用以求解具有其它边界条件和载荷的深梁的应力分析问题。文末对两端固定深梁的自重应力进行了数值计算,并与有限元素法的结果进行了比较,二者吻合良好。

This paper deals with stress analysis of deep beams with both ends fixed and subjected to dead weight. First of all by making use of dilatation function the coupled governing differential equations are made uncoupled. Then the finite integral transform method is used to solve the uncoupled governing differential equations obtained. Finally the analytical solution which satisfies all governing differential equations and boundary conditions to the given problem is obtained. The technique proposed in this paper can be used to determine stresses in deep beams with other boundary conditions and loads. At the end of the paper the numerical results of a deep beam with both ends fixed and subjected to dead weight are obtained and compared with the results obtained from the finite element method. The comparison shows that both results have good agreement.