基于ANSYS的三维近不可压缩问题的有限元分析  

Finite Element Analysis for 3D Nearly Incompressible Elasticity Problems Based on ANSYS Software

作　　者：周磊[1] 肖映雄[1] 王彪[1] 

机构地区：[1]湘潭大学土木工程与力学学院,湖南湘潭411105

出　　处：《昆明理工大学学报（自然科学版）》2014年第5期117-125,共9页Journal of Kunming University of Science and Technology(Natural Science)

基　　金：国家自然科学基金项目(10972191);湖南省自然科学基金项目(14JJ2063)

摘　　要：有限元方法是数值求解三维弹性问题的一类重要的离散化方法.在实际工程中,有相当多的材料(如橡胶、塑料等)呈现出近不可压缩(泊松比ν→0.5)的性质,利用常规有限元进行求解时会出现体积闭锁(Locking)现象,需要采用某些特殊的方法.本文基于ANSYS平台系统研究了六面体网格剖分下高阶单元法、减缩积分法及基于u/p格式的混合高阶元法对求解混合边界条件的三维近不可压缩问题的有效性和鲁棒性(robustness).数值结果表明:这三种协调有限元法均能有效地克服三维弹性材料的Locking现象,其中混合高阶元法最为精确,计算所得位移值均随网格尺寸变小而稳定地收敛于理论解.Finite element （FE） method is one of the most efficient numerical methods for the solution of three - dimensional elasticity problems. In practical engineering, there are many materials such as rubber and plastic, which show nearly incompressibility material property, i. e. , Poisson＇s ratio t, is close to 0.5. The volume loc- king phenomenon will happen when the commonly used finite elements are applied to the solution of this nearly incompressibility problems. Thus, we need to use some Some special methods are required to handle the prob- lem. In this paper, based on the ANSYS software, we make some systematic studies are carried out on for the ef- ficiency and robustness of high - order FE method, reduced integration and mixed higher - order FE method based on the u/p scheme by using hexahedral mesh for 3 D nearly incompressible problems with mixed boundary conditions. The numerical results have been shownshow that the aforementioned methods can effectively overcome the locking phenomenon of 3 D elastic materials in which mixed high -order FE method is the most accurate, and the calculated displacements stably converge to the theoretical solution with the decrease of the mesh size.

关 键 词：三维弹性问题 闭锁现象 高次元 混合元 减缩积分 

分 类 号：O343.3[理学—固体力学]