Abstract
Abstract An assumed-stress hybrid 4-node plate element is developed based on the Hellinger-Reissner variational principle modified with a generalized least-squares operator for accurate vibration and wave propagation response of Reissner-Mindlin plates. The least-squares operator is proportional to a weighted integral of a differential operator acting on the residual of the steady-state equations of motion for Reissner-Mindlin plates. Through judicious selection of the design parameters inherent in the least-squares modification, this formulation provides a consistent framework for enhancing the accuracy of mixed Reissner-Mindlin plate elements that have no shear locking or spurious modes. Improved methods are designed such that the complex wave-number finite element dispersion relations closely match the analytical relations for all wave angle directions. For uniform meshes, optimal methods are designed to achieve zero dispersion error along given wave directions. Comparisons of finite element dispersion relations demonstrate the superiority of the new hybrid least-squares plate element over the underlying hybrid element, and standard Galerkin elements based on selectively reduced integration. Numerical experiments validate these conclusions.
Published Version
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