双向变刚度矩形板弯曲问题的精确解

Exact Solution on a Problem of Bending of Double-Direction Rectangular Elastic Plates of Variable Rigidity

本文研究了任意分布载荷作用下两对简支另两边任意支承的双向线性变刚度矩形板的弯曲问题。通过引入高等超越函数(指数积分,正弦和余弦积分等),得到了问题的一般解。最终将问题转化为求解两组积分常数的线性代数方程组。并以四边简求板为例求出了所有积分常数,从而得到问题的精确Levy解。

In this paper, the problem of bending of double-direction rectangularplates of variable rigidity with two opposite edges simply supported andother two edges arbitrarily supported under arbitrarily distributed loadsis discussed in detail. By means of higher transcendental functions(exponential integral, sine and cosine integral), the general solutions ofthe problem are obtained. Finally, the problem is turned into how tosolve the linear algebraic equations with two systems of unknown integralconstants. Taking the rectangular plates with four sides simply supportedas an example, all integral constants are obtained, thus giving out theexact Levy-type solutions of the problem.