We present a novel further development of overlapping finite elements. The formulation of the enhanced elements is based on the earlier published elements but has an important new ingredient which renders the enhanced formulation more effective with respect to the evaluation of the element matrices and the solution of the governing finite element equations. The novel ingredient is that the elements are no longer based on a function used in meshless solution schemes; hence the elements provide more generality and ease of use. We first give the formulation which is applicable to two- and three-dimensional analyses of solids, give new insights, and then present an evaluation considering the required numerical integration, geometric distortion-insensitivity and the conditioning of the resulting finite element equations. In the study of the element characteristics, we also give some illustrative example solutions that show the performance of the elements in linear static analyses of two- and three-dimensional solids.

我们提出了重叠有限元的进一步发展。增强单元的公式基于较早发布的单元，但具有一个重要的新成分，它使增强公式在单元矩阵的评估和控制有限元方程的求解方面更加有效。新的成分是元素不再基于无网格解决方案中使用的函数；因此这些元素提供了更多的通用性和易用性。我们首先给出适用于固体二维和三维分析的公式，给出新的见解，然后考虑所需的数值积分、几何畸变不敏感性和所得有限元方程的条件进行评估。