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发布时间：2019-03-11

论文类型：期刊论文

发表时间：2017-10-26

发表刊物：INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

收录刊物：EI、SCIE、Scopus

卷号：112

期号：4

页面范围：303-337

ISSN号：0029-5981

关键字：finite element methods; quasi-conforming; Reissner-Mindlin plate theory; fundamental analytical solutions; Hellinger-Reissner variational principle

摘要：This paper presents a novel formulation based on Hellinger-Reissner variational principle in the framework of quasi-conforming method for static and free vibration analysis of Reissner-Mindlin plates. The formulation starts from polynomial approximation of stresses, which satisfy the equilibrium equations of Reissner-Mindlin plate theory. Then the stress matrix is treated as the weighted function to weaken the strain-displacement equations after the strains are derived by using the constitutive equations. Finally, the string-net functions are introduced to calculate strain integration. As examples, two new plate bending elements, a 4-node quadrilateral element QC-P4-11 beta and a 3-node triangular element QC-P3-7 beta,are proposed. Several benchmark examples are demonstrated to show the performance of the elements, and the results obtained are compared with other available ones. Numerical results have proved that both elements possess excellent precision. In particular, the quadrilateral element performs well even when the element shape degenerates into a triangle or concave quadrangle. Copyright (C) 2017 John Wiley & Sons, Ltd.