Transverse vibration of mindlin plates on two-parameter foundations by analytical trapezoidal p-elements

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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  • Andrew Y.T. Leung
  • Bin Zhu


Original languageEnglish
Pages (from-to)1140-1145
Journal / PublicationJournal of Engineering Mechanics
Issue number11
Publication statusPublished - Nov 2005


An analytical trapezoidal hierarchical element for the transverse vibration of Mindlin plates resting on two-parameter foundations is presented. Legendre orthogonal polynomials are used as enriching shape functions to avoid the shear-locking problem and to improve considerably the computational efficiency. Element matrices are integrated in closed form eliminating the numerical integration errors conventionally found. With the C0 continuity requirement, the element can be used to analyze any triangular and polygonal plates without difficulty, while the Kirchhoff p-version elements requiring C1 continuity are not as versatile. The computed natural frequencies for rectangular, skew, trapezoidal, triangular, annular, and polygonal plates on two-parameter foundations show that the convergence of the proposed element is very fast compared to the conventional linear finite elements with respect to the number of degrees of freedom used. Many numerical examples are given. Journal of Engineering Mechanics © ASCE.

Research Area(s)

  • Finite element method, Foundations, Plates, Vibration