非线性粘弹性梁弯曲问题的新算法  

A new method for bending problems of nonlinear viscoelastic beam

作　　者：张锋伟[1] 张能辉[2] 占海艺[2] 

机构地区：[1]甘肃农业大学机电工程系,甘肃兰州730070 [2]上海大学力学系,上海200436

出　　处：《兰州大学学报（自然科学版）》2002年第2期37-41,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：上海市教育发展基金 (99A0 1);上海市博士后基金 (1999年度 )资助项目

摘　　要：首先从松弛型的非线性 L eaderman本构关系出发 ,利用线性几何假设 ,建立了非线性粘弹性梁弯曲问题的数学模型 ;其次 ,利用 L aplace变换法证明了非线性粘弹性梁问题与非线性弹性梁问题之间存在着某些对应关系 .对应关系为粘弹性梁的求解提供了一种新的思路 ,利用这些关系可直接从相应弹性问题获得粘弹性问题的部分响应 ,与传统的时域有限差分法相比 。In this paper, firstly, based on the Leaderman constitutive relations in nonlinear viscoelasticity and the linear geometrical assumption, a mathematical model for bending problems of nonlinear viscoelastic beams is set up. Secondly, the Laplace transformation method is used to prove that some relations exist between solutions for bending problems of viscoelastic and elastic beams. The corresponding relations provide a new method for solving viscoelastic problems. Part of responses of viscoelastic problems could be obtained directly from the corresponding elastic ones by these relations. Compared with the traditional finite difference method in the time domain, the computational time is greatly shortened.

关 键 词：非线性粘弹性梁 弯曲问题 对应关系 积分型本构理论 粘弹性力学 Laplace变换法 非线性Leaderman本构关系 

分 类 号：O345[理学—固体力学]