Numerical Approximation for Elastic Shell Bending Problems by Boundary Element Method

分析弹性扁壳的弯曲问题有两种方法。一种是应力函数法，另一种是位移法。在本研究中，我们发展了基于位移法的弹性扁壳线弯曲问题的边界元求解程序。本文的研究成果概括如下：1.建立了问题的边界积分方程组，推导了问题的边界积分方程组，并构造了相应的基本解。2.数值求解程序的建议为了对边界积分方程组进行数值求解，我们提出了一种利用常量单元的有效求解方法。3.对具有两种曲率的简支和固定边界条件的扁球壳在均布载荷和集中载荷作用下进行了数值计算。将计算结果与傅里叶级数解进行了比较。

There exist two approaches for analyzing bending problems of elastic shallow shells. One is the stress function method and the other is the displacement method. In this research we developed the boundary element solution procedure based on the displacement approach for numerical solutions of linear bending problems of elastic shallow shells.The research results obtained in this research project are summarized as follows:1. Boundary Integral Equation Formulation of Problems The boundary integral equations of the problems were derived and the related fundamental solution was constructed. 2. Proposal for Numerical Solution Procedure In order to numerically the system of boundary integral equations, we proposed an effective solution procedure with use of the constant element. 3. Performance of Numerical Calculation Numerical calculations were performed for shallow spherical shells with two kinds of curvature of simply supported or fixed boundary condition subjected to uniformly distributed or concentrated load. The results were compared with Fourier-series solutions.