矩形板结构的弯曲问题

采用一般解析解法，先根据矩形薄板弯曲问题的微分方程来求得各种类型的解，如双正弦级数、单正弦级数和代数多项式的解，然后选取其中能满足四个边和四个角的全部边界以及各种载荷作用的解的组合作为每块板的一般解．然后可以用来求解板结构计算中的所有积分常数．作为算例考虑了一个静水压力作用下的水池．本文的解为精确解，理论简单，便于实际应用。

The Problem of Bending of Rectangular Plate Structure

A plate structure is a structure made of several plates. For each plate, some edges are independent and can be calculated by boundary conditions, while some edges are connected by other plates and can be solved by continuous conditions. In this paper, According to the differential equation of rectangular thin plates during bending, we obtained cases of solutions,such as double sine series, single sine series and algebraic polynomials. Then,we chosed a lot of solutions which could satisfy all the boundaries of the four edges and the four corners and arbitrary loading to establish a general solution for a plate, so as to solve all the integral constants in plate structure calculations. The analytical solution for a water tank under hydrostatic pressure proved to be accurate. The theory in this paper is simple and easy for practical use.