Conforming versus non-conforming boundary elements in three-dimensional elastostatics
Conforming versus non-conforming boundary elements in three-dimensional elastostatics
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DOI：
10.1002/nme.1620231008
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发表时间：
1986-10
影响因子：
2.9
通讯作者：
G. Manolis;P. K. Banerjee
中科院分区：
文献类型：
--
作者：
G. Manolis;P. K. Banerjee
在这项工作中，我们提出了一个关键的比较两种基本的方式实现边界元法在三维弹性静力学。第一种方法是通过使用非协调单元，即从其周边移除配置节点的单元。用于边界力和位移配置的节点数不必与为了描述几何形状而沿单元周边沿着布置的节点数一致。第二种方法是沿着单元的周边沿着放置配置节点，通常与几何节点重合。这样就得到了单元间位移的连续性。在边界元法中使用非协调元的基本原因有两个。首先，简化的组装和解决方案的系统方程，其次，容易计算的“自由”和柯西主值项出现在积分方程。然而，边界元法的技术水平在过去的十年中已经发展到上述两个原因都不再是问题的程度。如下文所示，协调元比非协调元能产生更精确的结果，而且在系统方程的最终尺寸上具有相当大的经济性。
In this work, we present a critical comparison of two basic ways of implementing the boundary element method in three-dimensional elastostatics. The first way is by using non-conforming elements, i.e. elements which have the collocation nodes removed from their perimeter. The number of nodes used for the collocation of the boundary tractions and displacements need not coincide with the number of nodes placed along the perimeter of the element for the purpose of describing the geometry. The second way is by placing the collocation nodes along the perimeter of the element, usually in coincidence with the geometry nodes. Thus, interelement continuity of the displacements is obtained. The basic reasons for the use of non-conforming elements in the boundary element method are twofold. First, simplification in the assembly and solution of the system equations and, secondly, easy computation of the ‘free’ and Cauchy principal value terms appearing in the integral equations. The state of the art in the boundary element method, however, has advanced in the last decade to the point where both of the aforementioned reasons are no longer problematic. As will be shown in what follows, conforming elements are able to produce more accurate results than non-conforming ones with substantial economy in the final size of the system equations.