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| Block diagonal and higher order mass matrices for Hermite beam elements |
| Received:September 09, 2023 Revised:October 20, 2023 |
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| DOI：10.7511/jslx20230909002 |
| KeyWord:Hermite beam element vibration frequency lumped mass matrix block diagonal mass matrix higher order mass matrix |
| Author | Institution |
| 王东东 |
厦门大学 土木工程系 福建省滨海土木工程数字仿真重点实验室, 厦门 |
| 吴振宇 |
厦门大学 土木工程系 福建省滨海土木工程数字仿真重点实验室, 厦门 |
| 侯松阳 |
厦门大学 土木工程系 福建省滨海土木工程数字仿真重点实验室, 厦门 |
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| Abstract: |
| 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.However, 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. |
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