拉压不同模量弹性问题 - 上海大学学报.PDF

第 20 卷 第 5 期 （自然科学版） Vol. 20 No. 5 2014年10月 JOURNAL OF SHANGHAI UNIVERSITY (NATURAL SCIENCE) Oct. 2014 DOI: 10.3969/j.issn.1007-2861.2013.07.034 拉压不同模量弹性问题 1 1,2 赵慧 , 叶志明 (1. 上海大学 土木工程系, 上海 200072; 2. 上海大学 上海市应用数学和力学研究所, 上海 200072) 摘摘摘要要要: 拉压不 同模量弹性体具有材料非线性特征, 不 同模量本构关系受到材料本身及结构各 点的应力、应变状态等 因素的综合影响. 总结了近年来对不 同模量本构关系的研究工作, 阐述 了多种形式 的不 同模量弹性 问题有 限元求解方法 的改进, 简述 了拉压不 同模量 问题解析法取 得的研究成果, 并介绍了不同模量理论中尚待解决 的问题. 关关关键键键词词词 : 不同模量; 弹性理论; 本构关系; 有限元法; 解析法 中中中图图图分分分类类类号号号 : TB 301 文文文献献献标标标志志志码码码 : A 文文文章章章编编编号号号 : 1007-2861(2014)05-0550-09 Elastic Bodies with Different Modules in Tension and Compression 1 1,2 ZHAO Hui-ling , YE Zhi-ming (1. Department of Civil Engineering, Shanghai University, Shanghai 200072, China; 2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China) Abstract: Elastic bodies having different modules in tension and compression exhibit nonlinear behaviors. The constitutive equations of an elastic body with different modules depend on the material itself, and also on the stress and strain state of each point in the body. Recent achievements of research on the constitutive equations are presented. Also discussed are the improvements in the finite element method (FEM) employed to solve different module problems. Analytical methods of the elastic body with different modules are introduced. Problems to be solved next are outlined. Key words: different module; elasticity theory; co