Free vibration of plates by the high accuracy quadrature element method. (English) Zbl 1235.74124

Summary: A highly accurate and rapidly converging hybrid approach is presented for the Quadrature Element Method (QEM) solution of plate free vibration problems. The hybrid QEM essentially consists of a collocation method in conjunction with a Galerkin finite element technique, to combine the high accuracy of the Differential Quadrature Method (DQM) for the efficient solution of differential equations with the generality of the finite element formulation. This results in superior accuracy with fewer degrees of freedom than conventional FEM or FDM. A series of numerical tests is conducted to assess the performance of the quadrature plate element in free vibration problems. Anisotropic and stepped thickness plates are investigated as well as mixed boundary conditions and point supports at the edges. In all cases, the results obtained are quite accurate.


74H45 Vibrations in dynamical problems in solid mechanics
74K20 Plates
74S30 Other numerical methods in solid mechanics (MSC2010)
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