Block diagonal and higher order mass matrices for Hermite beam elements
The lumped mass matrices of Hermite finite elements for Euler-Bernoulli beams are often constructed by the row sum technique via neglecting the rotational entries,or by the nodal quadrature.H owever,such lumped mass matrices of Hermite beam elements exhibit a sudden drop of accuracy in frequency calculation in case of free boundary conditions.In this study,based upon the numerical integration accuracy requirement,the gradient-enhanced nodal quadrature rules are developed for both cubic and quintic elements.These nodal quadrature rules lead to a block diagonal form of element mass matrices,while the assembled global mass matrix still preserves a desirable diagonal pattern except a few entries associated with the boundary nodes.The block diagonal mass matrices of cubic and quintic elements have an optimal convergence rate of 4 and a sub-optimal convergence rate of 6,respectively.Subsequently,through rationally mixing the consistent mass matrices and the mass matrices generated by the gradient-enhanced nodal quadrature rules with equal accuracy orders,superconvergent higher-order mass matrices are attained for cubic and quintic Hermite beam elements.The accuracy and robustness of the proposed block diagonal and higher-order mass matrices are systematically demonstrated by numerical results.
Hermite beam elementvibration frequencylumped mass matrixblock diagonal mass matrixhigher order mass matrix
万方数据
维普
