二维黏弹性力学问题的无网格自然单元法  

A Meshless Natural Element Method for 2D Viscoelastic Problems

作　　者：陈莘莘[1] 钟斌[1] 

机构地区：[1]华东交通大学土木建筑学院,南昌330013

出　　处：《应用数学和力学》2017年第5期605-612,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11462006;21466012)~~

摘　　要：基于无网格自然单元法,建立了求解二维黏弹性力学问题的一条新途径.基于弹性-黏弹性对应原理和Laplace(拉普拉斯)变换技术,首先将黏弹性问题转换成Laplace域内与弹性力学问题相同的形式,然后推导出基于自然单元法分析黏弹性问题的基本公式.作为一种新兴的无网格数值计算方法,自然单元法的实质是一种基于自然邻近插值的Galerkin(伽辽金)法.相对于其他无网格法,自然单元法的形函数具有插值性和支持域各向异性等特点.算例结果证明了所提分析方法的有效性.Based on the meshless natural element method, a new algorithm was proposed to solve 2D viscoelastic problems. According to the elastic-viscoelastic correspondence principle and the Laplace transform technique, the viscoelastic problem was transformed into an elastic problem in the Laplace space and then the basic formula of the natural element method for the analysis of viscoelastic problems were derived. As a recently developed meshless method, the natural element method （NEM） is essentially a Galerkin method based on natural neighbour in- terpolation. Compared to most other meshless methods, the shape function employed in the NEM has interpolation property and its support domain is anisotropic. Some numerical exam- ples verify the effectiveness of the developed method.

关 键 词：无网格法 自然单元法 黏弹性 对应原理 LAPLACE变换 

分 类 号：O39[理学—工程力学] TB12[理学—力学]