An Accurate Locking-free Quadrilateral Plate Element

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An Accurate Locking-free Quadrilateral Plate Element

更新时间：2023-11-28

- An Accurate Locking-free Quadrilateral Plate Element
- Advanced Engineering Sciences Vol. 38, Issue 1, Pages: 44-48(2006)
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- Published：2006，
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罗鲲,冯民富,王成.一个精确的免闭锁四边形板元[J].工程科学与技术,2006,38(1):44-48.

An Accurate Locking-free Quadrilateral Plate Element. [J]. Advanced Engineering Sciences 38(1):44-48(2006)
罗鲲,冯民富,王成.一个精确的免闭锁四边形板元[J].工程科学与技术,2006,38(1):44-48. DOI：

An Accurate Locking-free Quadrilateral Plate Element. [J]. Advanced Engineering Sciences 38(1):44-48(2006) DOI：

摘要

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。

Abstract

Abstract: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.

关键词

Mindlin-Reissner 板混合/杂交方法免闭锁能量优化条件

Keywords

Mindlin-Reissner platesMixed/hybrid methodslocking freeenergy optimization

references

Pifkaranta J,Suri M.Design principles and error analysis for reduced-shear plate-bending finite element[J].Numerische Mathematik,1996,75:223-266.

Bathe K J,Dvorkin E H.A four-node plate bending element based on Mindlin-Reissnerplate theory and mixed interpolation[J].International Journal for Numerical Methods in Engineering,1985,21:367-383.

Chen W J,Cheung Y K.Refined quadrilateral element based on Mindlin-Reissner plate theory[J].International Journal for Numerical Methods in Engineering,2000,47:605-627.

Xie X P,Zhou T X.Optimization of stress modes by energy compatibility for 4-node hybrid quadrilaterats[J].International Journal for Numerical Methods in Engineering,2004,59:293 -313.

Malkus D S,Hughes T J R.Mixed finite element methods-Reduced and selective integration techniques:A unification of concepts[J].Computer Methods in Applied Mechanics and Engineering,1978,15:63-81.

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四川大学数学学院四川

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