Spurious reflection of elastic waves in nonuniform meshes of constant and linear strain unite elements

A change in finite element size causes spurious reflection of elastic waves passing through a finite element grid when the wavelength is less than about 10-times the largest element in the grid. Extending the previously published study in which the phenomenon was analyzed for the case of constant strain finite elements, the higher-order elements with linear strain distribution are studied herein. Similarly to the previous study, it is found that the consistent mass matrix gives less spurious wave reflection than the lumped mass matrix; however the advantage is smaller for the higher-order elements. For the lumped mass matrix, there is little difference in spurious wave reflection between the constant strain and linear strain elements. The phenomenon of spurious wave reflection is less pronounced when the higher-order elements are used in conjunction with the consistent mass matrix. These results are obtained from exact analytical solutions in complex variables for a planar wave with a planar wave front propagating along grid lines through an infinite grid which is uniform in each half plane.