非均匀弹性地基圆板轴对称弯曲的一般解
The General Solution for Axial Symmetrical Bending of Nonhomogeneous Circular Plates Resting on an Elastc Foundation
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摘要: 本文在阶梯折算法的基础上,提出一个新的方法——精确解析法,得到了非均匀弹性地基圆板弯曲的一般解.文中导出了在任意轴对称载荷和边界条件下求解非均匀弹性地基圆板和中心带孔圆板弯曲的一般公式,并给出一致收敛于精确解的证明.文中得到的一般解可直接计算无弹性地基圆板的弯曲问题.问题最后归结为求解一个二元一次代数方程.文末给出算例,算例表明无论内力和位移均可得到满意的结果.Abstract: In this paper,a new method,the exact analytic method,is presented on the basis of step reduction method.By this method,the general solution for the bending of nonhomogenous circular plates and circular plates with a circular hole at the center resting,on an elastfc foundation is obtained under arbitrary axial symmetrical loads' and boundary conditions.The uniform convergence of the solution is proved.This general solution can also he applied directly to the bending of circular plates without elastic foundation.Finally,it is only necessary to solve a set of binary linear algebraic equation.Numerical examples are given at the end of this paper which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.
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