两对边简支单向变刚度矩形板的弯曲问题

本文通过做未知函数变换，将两对边简支单向变刚度矩形板在任意横向分布载荷作用下的弯曲问题归结为求解第二类的Ｖｏｌｔｅｒｒａ积分方程。对上述积分方程，建议了二次样条函数的近似解法，求得了问题的渐近解析解。为了检验方法的有效性并说明其应用，对线性变厚度的形做了数值计算，所得结果和精确解符合得很好。

Bending Problems of Rectangular Plates of Unidirectionally Varying Stiffness with Two Opposite Edges Simply Supported

Making the transformation of an unknown function, the bending problems of rectangular plates of unidirectionally varying stiffness with two opposite edges simply supported under any normal load distribution are reduced to solving the Volterra integral equations of the second kind. The approximate method of quadratic spline functions is proposed for the abovementioned integral equations. And the approximate analytic solutions of the problems are obtained. To verify the effectiveness of the method and to illustrate its application. a numerical example of linearly varying thickness is given. which agrees well with the exact solution.