Studies in the Form of Finite Element Mass Matrices for BEAMS, Plates and Shells

摘要

A variety of different mass matrices are presented for beam and plate elements,and the resulting eigenvalues are compared which were obtained from each of the different mass matrices. From the results, it is clear that no one mass matrix formulation gives the correct results for natural frequencies. For beam elements, it was found that the consistent mass matrices give more accurate results, for the examples tested, than did the diagonal mass matrices. Noting that for the axial and torsional modes, the modified consistent mass matrix, whose axial and torsional terms are the average of the consistent and HRZ diagonal terms, gave the most accurate results. Whereas with the bending modes, the consistent and modified consistent mass matrices both give the most accurate results, remembering that the modified consistent has the same bending term as the consistent mass matrix. With the plate elements, the diagonal mass matrices seemed to produce the better values, even the lumped diagonal mass matrix, which has no rotational terms gave results that are as good as and sometimes better than the consistent mass matrices. Yet all plate element mass matrices needed high numbers of elements to produce accurate results.