# 三维近不可压缩弹性问题的罚函数有限元分析Penalty Function Finite Element Analysis for Nearly Incompressible Elasticity Problems in Three Dimensions

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The locking phenomenon will appear when the commonly used finite elements are applied to the solution of nearly incompressible problems in three dimensions. It is necessary to use some special methods. The penalty function conforming finite element method is an effective method to overcome this locking phenomenon since it is simple for the realization of the resulting program and easy to determine the penalty number and it also does not change the functional stationary value properties. In this paper, the computing format of penalty function finite element method is carefully derived, the conditions for success of the resulting method is analyzed and the effective-ness and robustness of this method are finally verified by some numerical experiments for nearly incompressible elasticity problems. The quality of the mesh used in three-dimensional finite ele-ment analysis has a great effect on the accuracy and computational efficiency. If the isotropic grids can be used in the practical calculations, the method will have better convergence.

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