正交异性矩形板结构弯曲问题的解析解法

板结构为由若干板组成的结构。用解析法求解正交异性板结构的弯曲问题,必须建立一个正交异性矩形板弯曲的横向位移函数为变量的偏微分方程的一般解。这种解能求解任意边界和任意载荷的弯曲问题。对于结构中的每块板,有些边为单独的,可由边界条件来计算,而有些边与其它板边相连接,由连续性条件来计算。由这些条件组成的方程式可以求解一般解中的全部积分常数。以顶边简支底边固定承受静水压力的板结构水池为例,进行了分析计算。

The Analytical Method for the Bending Problem of Orthotropic Rectangular Plate Structure

A plate structure is a structure made up of several plates. To solve the bending problem of orthotropic plate, a general analytical solution of partial differential equation for transverse displacement function of orthotropic rectangular plates in bending must be worked out. It can be used to solve the bending problem for arbitrary boundaries and arbitrary load. For each plate; some edges are independent which can be calculated by boundary conditions, while some edges are connected by other plates which can be calculated by continuous conditions. With the equations made up of these conditions, it can be used to solve all the integral constants in general solutions. For example, a water tank under hydrostatic pressure with the edges simply supported at the top and fixed at the bottom has been calculated.