摘要
本文在文[1]的基础上提出了一个新的方法可用于求解任意变系数非线性常微分方程组.文中导出了任意轴对称载荷和不同边界条件下的非均匀弹性地基圆薄板大变形的一般解,并给出了收敛于精确解的证明.问题最后可归结为求解一个仅含有三个未知量的非线性代数方程组.该方法和其它方法比较,具有收敛范围大,计算简便迅速等特点.文末给出算例表明内力和位移均可得到满意的结果,验证了本文理论的正确性.
In this paper, a new method is presented based on [1]. It can be used to solve the arbitrary nonlinear system of differential equations with variable coefficients. By this method, the general solution for large deformation of nonhomogeneous circular plates resting on an elastic foundation is derived. The convergence of the solution is proved. Finally, it is only necessary to solve a set of nonlinear algebraic equations with three unknowns. The solution obtained by the present method has large convergence range and the computation is simpler and more rapid than other numerical methods. Numerical examples given at the end of this paper indicate that satisfactory results of stress resultants and displacements can be obtained by the present method. The correctness of the theory in this paper is confirmed
出处
《应用数学和力学》
EI
CSCD
北大核心
1992年第11期951-962,共12页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助的课题
关键词
非均匀圆板
弹性地基
大挠度
nonhomogeneous circular plate, clastic foundation, large deformation
