CAJ | 학술논문

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．
유한원방법시수치구해삼유탄성문제적일류중요적리산화방법．재실제공정중，유상당다적재료（여상효、소료등）정현출근불가압축（박송비ν0.5）적성질，이용상규유한원진행구해시회출현체적폐쇄（Locking）현상，수요채용모사특수적방법．본문기우ANSYS평태계통연구료륙면체망격부분하고계단원법、감축적분법급기우u/p격식적혼합고계원법대구해혼합변계조건적삼유근불가압축문제적유효성화로봉성（robustness）．수치결과표명：저삼충협조유한원법균능유효지극복삼유탄성재료적Locking현상，기중혼합고계원법최위정학，계산소득위이치균수망격척촌변소이은정지수렴우이론해．
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 ratioνis 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 3D 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.