Convergence Studies of Dynamic Analysis by Using the Finite Element Method With Lumped Mass Matrix

The convergence rates of the natural frequencies and the dynamic response of plates obtained when using the 12-degree-of-freedom, non-conforming rectangular plate element with the lumped mass formulation are studied for particular problems. Finite element solutions for a square plate with all edges simply supported are derived in explicit form by using the double U-transformation method. It has been found that the convergence rate of the natural frequencies for the lumped mass discretization is the same as that for a consistent mass formulation and is dependent on the Poisson ratio μ. The finite element solutions of the dynamic response with arbitrary excitation may similarly be derived. It is shown that the rate of convergence is dependent on the type of loading.