Alternative integration algorithms for three-dimensional mortar contact

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• 作者：C. Wilking ; M. Bischoff
• 关键词：Contact ; Mortar method ; Mortar integral ; Numerical integration ; Quadrilateral integration cell
• 刊名：Computational Mechanics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：59
• 期：2
• 页码：203-218
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics; Computational Science and Engineering; Classical and Continuum Physics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0924
• 卷排序：59

文摘

In this paper, a new approach is proposed to improve efficiency of the integration procedure for mortar integrals within finite element mortar methods for contact. Appropriate approaches subdivide polygonal integration segments into triangular integration cells where well-established quadrature rules can be applied for numerical integration. Here, a subdivision of segments into quadrilateral integration cells is proposed and investigated in detail. By this procedure, the numerical effort is decreased because the number of integration cells is smaller and less quadrature points are needed. In all the aforementioned methods, necessary projections of integration points result in rational polynomials in the integrand. Thus, an exact numerical integration is impossible. Using quadrilateral integration cells additionally involves non-constant Jacobian determinants which further increases the polynomial degree of the integrand. Numerical experiments indicate, that the resulting increase in the error is small enough to be acceptable in consideration of the gained speed-up.