无网格方法在平面粘弹性力学问题中的应用  

Application of Element-Free Galerkin Method on Plane Problems of Visco-Elasticity

作　　者：朱媛媛[1] 胡育佳[2] 程昌钧[2] 

机构地区：[1]上海师范大学计算机科学与技术系,上海200234 [2]上海大学上海市应用数学和力学研究所力学系,上海200072

出　　处：《力学季刊》2006年第3期404-412,共9页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金项目(50278051);上海市高校选拔培养优秀青年教师科技专项基金;上海师范大学科研启动基金

摘　　要：本文综合应用无网格方法(EFGM)、线性粘弹性与弹性力学之间的对应原理,Laplace变换和逆变换等方法求解了拟静态平面弹性和粘弹性力学问题。首先,利用Laplace变换和逆变换推导了平面问题的粘弹性本构关系,建立了拟静态粘弹性平面问题的边值问题;其次,利用粘弹性与弹性力学之间的对应原理得到了Laplace变换域中平面问题的基本方程,在Laplace变换域中建立了相应的泛函,并得到了用无网格方法离散的控制方程;同时,求解了几个拟静态弹性和粘弹性平面问题,给出了它们的表达式和数值结果;最后,采用Laplace逆变换和数值逆变换,得到了粘弹性力学平面问题在物理空间中的解,并比较了由解析解和无网格数值方法所得到的数值结果,可以看到它们是非常吻合的。说明本文方法的正确性和有效性。The elment-free Galerkin method （EFGM）, the correspondence principle between visco-elasticity and elasticity and Laplace transformation and its inverse transformation were syntheticalli applied to solve the quasi-static elastic and visco-elastic plane problems. First, the constitutive equations of visco-elastic plane problems were deduced and the corresponding boundary value problem was established by Laplace transformation and its inverse transformation. Secondly, the basic equations of visco-elastic plane problems and the governing equations for EFGM were all obtained in Laplace transformation region. The quasi-static elastic and visoelastic problems were solved and the expressions and numerical results of solutions were presented. Finally, using Laplace inverse transformation and numerical converse transforma- tion methods, the solutions of visco-elastic plane problems were obtained in physical space, comparison between the results obtained from FEGM with those obtained from FEM and/or analytical solutions points out almost identical. This means that the methods are correct and reliable.

关 键 词：拟静态粘弹性平面问题 Laplace变换和数值逆变换 无网格方法 背景网格 

分 类 号：O39[理学—工程力学] TB12[理学—力学]