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论文摘要

一个精确的免闭锁四边形板元

An Accurate Locking-free Quadrilateral Plate Element

作者:罗鲲(四川大学 数学学院,四川 成都 610064);冯民富(四川大学 数学学院,四川 成都 610064);王成(唐山学院基础教学部,河北 唐山 063000)

Author:(School of Mathematics, Sichuan Univ., Chengdu 610064, China);(School of Mathematics, Sichuan Univ., Chengdu 610064, China);(Dept. of Foundation Sci., Tangshan College, Hebei Tangshan 063000, China)

收稿日期:2005-07-06          年卷(期)页码:2006,38(1):44-48

期刊名称:工程科学与技术

Journal Name:Advanced Engineering Sciences

关键字:Mindlin-Reissner 板;混合/杂交方法;免闭锁;能量优化条件

Key words:Mindlin-Reissner plates; Mixed/hybrid methods; locking free; energy optimization

基金项目:

中文摘要

基于Mindlin-Reissner 板的Hellinger Reissner变分原理,构造了一个高性能的免闭锁低阶板元。借助能量优化条件,构造了一个7参数的弯矩场,并假设单元内部的弯矩和剪力严格满足平衡方程。在一个简化插值算子的帮助下,得到一个高精度免闭锁的四边形杂交板元。数值结果表明,新板元对畸形网格具有很好的性能,而且在极薄板时是免闭锁的。

英文摘要

It is the purpose of this paper to design a high-performance locking-free low-order plate element, based on the Hellinger-Reissner variational principle of Mindlin-Reissner plates. By means of the energy optimization condition,we present a 7-parameter bending moment field, and assume that the equilibrium equations associating bending moments with shear forces are satisfied strictly within the elements. With the aid of a reduced interpolation operator, we obtain an accurate locking free quadrilateral hybrid element. The numerical experiments reveal that the proposed plate element possesses good properties despite distorted meshes, and is free of shear locking in the case of very thin plates.

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