On the spectral properties of grid operators for FEM schemes in elasticity theory. Two-dimensional schemes

The spectra of grid operators in some finite element method (FEM) schemes for solving twodimensional problems of elasticity theory were investigated. It was revealed that, for a number of classical FEM schemes, a mutual influence between the spectra of volumetric and shear deformations may occur, which can lead to undesirable effects such as volumetric and shear locking. The analysis of the spectral errors in the FEM schemes demonstrated the effectiveness of the reduced integration technique and underscored the importance of fulfilling the group properties of grid differential operators that ensure consistent approximation of partial derivatives. A number of numerical schemes with improved spectral properties were described. The results were illustrated by the solutions of model problems.