Buckling and Free Vibration of Plates Resting on Elastic Foundation Using a New Strain Based Finite Element

Résumé

This paper presents a new four-node strain-based finite element (SBQ12) formulated within the framework of Reissner-Mindlin plate theory for the dynamic and stability analysis of isotropic plates resting on elastic foundations.The independent approximation of the bending and transverse shear strains in the proposed element is efficient in eliminating the shear locking and enhancing the numerical accuracy and stability for thin and thick plates.In this study, the strain-based finite element is used to investigate the free vibration and linear buckling of plates on Winkler, Pasternak and Kerr elastic foundations.The SBQ12 element is extensively validated for square and rectangular plates with different boundary conditions (all edges simply supported (SSSS), all edges clamped (CCCC), two opposite edges simply supported, two opposite edges clamped (SCSC), and two opposite edges simply supported, two opposite edges free (SFSF), etc.), thickness ratios (a/h ranging from 5 to 1000), and aspect ratios.The numerical results show excellent agreement with the analytical and reference solutions, with maximum relative errors generally less than 3.5% for free vibration analyses and 4% for buckling analyses in the majority of cases tested.Particular attention is given to the influence of foundation stiffness parameters on natural frequencies and critical buckling loads.The obtained results confirm the accuracy, reliability, and computational efficiency of the proposed element.Overall, the developed SBQ12 element proves to be a robust and highly accurate tool for the analysis of isotropic plate structures resting on elastic foundations, offering a valuable contribution to computational mechanics.

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