弹性力学的杂交自然单元法  

THE HYBRID NATURAL ELEMENT METHOD FOR ELASTICITY

作　　者：董轶[1] 马永其[1,2] 冯伟[1] 

机构地区：[1]上海大学上海市应用数学和力学研究所,上海200072 [2]上海大学力学系,上海200444

出　　处：《力学学报》2012年第3期568-575,共8页Chinese Journal of Theoretical and Applied Mechanics

摘　　要：为了解决自然单元法无法直接求解节点应力以及应力解精度不高的问题,将应力杂交的思想引入自然单元法中,与弹性问题的Hellinger-Reissner变分原理结合,提出了弹性问题的杂交自然单元法.算例表明:杂交自然单元法的计算结果与解析解吻合,证明该方法是可行的;在求解应力方面,杂交自然单元法比自然单元法有着更高的计算精度,而且可以直接求解出节点的应力.Because for the inaccurate stress solution and poor ability to solve the stress of node, the traditional natural element method （NEM） are rarely used to solve the complex questions. In this paper, the hybrid finite element method was introduced into NEM to be the hybrid natural element method （HNEM）. On the basis of HNEM and Hellinger-Reissner principle, the HNEM for elasticity is present. Compare with NEM, the HNEM has more precision solution of stress and can solve the stress of node directly.

关 键 词：自然单元法 杂交自然单元法 弹性 应力 Hellinger-Reissner变分原理 

分 类 号：O34[理学—固体力学]