无网格方法在平面粘弹性力学问题中的应用

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。

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

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 transformation 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.