A consistent control of spurious singular modes in the 9-node Lagrange element for the laplace and mindlin plate equations

Abstract

When 2 × 2 quadrature is used with the 9-node Lagrange element, which is essential in C 0 plate elements to avoid locking, spurious singular modes appear on the element level which can lead to singularity or near-singularity of the global equations. Here these modes are controlled by a procedure that introduces additional generalized stresses and strains so that the spurious modes are eliminated and the consistency of the resulting finite difference equations is not impaired; hence the procedure passes the patch test. Applications to the diffusion and Mindlin plate equations are presented. Results show that h 3 convergence in the L 2-norm is almost retained.