一个不闭锁和抗畸变的四边形厚板元  

A locking-free and robust quadrilateral reissner plate element

作　　者：龙驭球[1] 陈晓明[1] 岑松[2] 

机构地区：[1]清华大学土木工程系,北京100084 [2]清华大学工程力学系,北京100084

出　　处：《计算力学学报》2005年第4期385-391,共7页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(10272063);高等学校博士点基金(2002003044);清华大学基础研究基金(JC2002003);高等学校全国优秀博士论文作者专项基金(200242)资助项目.

摘　　要：构造一个彻底消除剪切闭锁现象并且对网格畸变不敏感的四边形厚薄板通用单元RPAQ。在方法上有三个特点:第一,在厚板挠度和转角的试函数中,采用了合理匹配方案,从而在源头上彻底消除了剪切闭锁现象;第二,采用四边形面积坐标,以代替通常的等参坐标,从而使网格畸变时仍然保持高精度;第三,采用广义协调元做法,使协调条件的采用灵活多样,并保证单元的收敛性。进行了一系列数值例题测试,表明单元RPAQ能自动消除闭锁现象,在由薄板到厚板的不同情况下,在各种网格畸变的情况下,都能体现出良好的精度和数值稳定性。A locking-free and insensitive to mesh distortion quadrilateral thick/thin plate element named RPAQ was proposed in this paper. The formulation has three characteristics. At first, a reasonable matching form of test functions for deflection and rotation is adopted, thus the shear locking is eliminated automatically. Secondly, the quadrilateral area coordinate is adopted instead of isoparametric coordinate, so that the element can keep high accuracy for different meshes of distortion. At last, the generalized conforming theory is adopted, it makes that the conforming conditions can be selected flexibly and the element convergence is ensured. The results of numerical tests show that the element RPAQ is free from shear locking, insensitive to mesh distortion and very accurate and stable for both thin plate and thick plate.

关 键 词：有限元 四边形单元 中厚板 剪切闭锁 

分 类 号：O242.21[理学—计算数学]