A mass lumping scheme for the 10-node tetrahedral element

Abstract

In the dynamic analysis with explicit time integration scheme, a lumped mass matrix (LMM) is always preferable than the consistent mass matrix (CMM), since the solving of large scale simultaneous algebraic equations can be avoided if a LMM is employed. In this study, a mass lumping scheme which is suitable for the 10-node tetrahedral element is proposed. A series of numerical examples show that the natural frequencies assessed from the proposed LMM are very close to those from CMM. In addition, the dynamic responses of structure predicted by the proposed LMM are in very good agreement with those from CMM if an implicit time integration scheme is adopted. More importantly, the proposed LMM is less sensitive to mesh distortion than the CMM. The proposed LMM can supersede the CMM at any cases.