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Novel quadrilateral elements based on explicit Hermite polynomials for bending of Kirchhoff–Love plates

  • Alireza Beheshti
Original Paper

Abstract

The contribution addresses the finite element analysis of bending of plates given the Kirchhoff–Love model. To analyze the static deformation of plates with different loadings and geometries, the principle of virtual work is used to extract the weak form. Following deriving the strain field, stresses and resultants may be obtained. For constructing four-node quadrilateral plate elements, the Hermite polynomials defined with respect to the variables in the parent space are applied explicitly. Based on the approximated field of displacement, the stiffness matrix and the load vector in the finite element method are obtained. To demonstrate the performance of the subparametric 4-node plate elements, some known, classical examples in structural mechanics are solved and there are comparisons with the analytical solutions available in the literature.

Keywords

Plate bending FEM Kirchhoff–Love model Hermite polynomials 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of GuilanRashtIran

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