A triangular plate element with drilling degrees of freedom,for large rotation analyses of built-up plate/shell structures, based on the reissner variational principle and the von karman nonlinear theory in the Co-Rotational reference frame

Y. C. Cai, J. K. Paik, S. N. Atluri

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

This paper presents an elementary finite element method for geometrically nonlinear large rotation analyses of built-up plate/shellstructures comprising of thin members. The tangent stiffness matrix of the element in the updated Lagrangian co-rotational reference frame is developed, based on the von Karman nonlinear theory of plates,and the Reissner variational principle, allowing for unsymmetric stresses and drilling rotations, useful in the analysis of built-up plate and shell structure. The finite rotation of the co-rotational reference frame relative to a globally fixed Cartesian frame, is simplydetermined from the finite displacement vectors of the nodes of the element in the global reference frame, thus allowing for an elementary transformation of the tangent stiffness matrix from the updated co-rotational reference frame to the globally fixed Cartesian frame. The element employed here is a 3-node plate element with 6 degrees of freedom per node, including 1 drilling degree of freedom and 5 degrees of freedom [3 displacements, and the derivatives of the transverse displacement around two independent axes in the plane of the plate in the co-rotational reference frame]. The (18×18) tangent stiffness matrices of the plate element in the updated Lagrangian co-rotational reference frame are derived, based on the assumptins that: (1) the inplane stress resultants Nαβ (unsymmetric) are constant in each element; (2) the bending moments Mαβ (symmetric) are linear and C0 within each element; and (3)the transverse rotations θi (including the drillingdegrees of θ3) are linear and C0 within each element. When compared to the primal approach wherein C1 continuous trial functions for transverse displacements over eachelement are necessary, the trial functions for the transverse bending moments and the rotations are very simple in the current approach,and can be assumed to be linear within each element. The present (18×18) tangent stiffness matrices of the plate, based on the Reissner variational principle and the von Karman type simplified nolinear plate theory in the co-rotational reference frame, lead to analyses, which are much simpler and more physically-based, than many others in the literature for large rotation/deformation analysis of builtup plate/shell structures [such as component plates joined at an angle]. Numerical examples demonstrate the accuracy and robustness ofthe present method.

Original languageEnglish
Pages (from-to)273-312
Number of pages40
JournalCMES - Computer Modeling in Engineering and Sciences
Volume61
Issue number3
StatePublished - 2010

Keywords

  • Drilling degrees offreedom
  • Explicit tangent stiffness
  • Large deformation
  • Reissner variational principle
  • Thin plate/shell
  • Updated Lagrangian formulation

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