Research On The Application Of Gradient Recovery Technology In Solving Linear Elastic Problems

The linear finite element method is a common method to solve linear elastic model problem,but when the Poisson’s ratio parameter in the model is close to0.5,the accuracy of the method will be reduced,which is called ”volume locking ”.In order to solve this problem,this paper uses the gradient restoration technique to reconstruct the derivation operator in the variational form of the linear elasticity equation,and to restore the partial derivative of the linear basis function to the continuous piecewise linear finite element function space,thus constructing a new linear elastic discrete matrix and replace the original linear element discrete matrix to find the numerical solution of the displacement.Finally,the linear finite element method based on gradient recovery is realized based on FEALPy software,and the two-dimensional and three-dimensional arbitrary finite element methods are also realized.Two-dimensional numerical examples show that the linear finite element method based on gradient restoration can overcome the volume locking effectively.However,a three-dimensional numerical example shows that the linear finite element method based on gradient restoration needs further improvement.At the same time,increasing the number of the finite element basis function can also reduce the impact of volume locking,and verify that the object no longer has volume locking when the degree is greater than or equal to 4.