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COLLOQUIA PATAVINA

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Twist-Kirchhoff model for plate bending problems

Donatella Marini
Universita' di Pavia

18.1.2011



Abstract


We introduce a new framework for the development of thin plate finite elements, the “twist-Kirchhoff theory.” A family of quadrilateral plate elements is derived that takes advantage of the special structure of this new theory.  Particular attention is focused on the lowest-order member of the family, an eight degree-of-freedom, four-node quadrilateral element with mid-side rotations whose stiffness matrix is exactly computed with one-point Gaussian quadrature.  We prove a convergence theorem for it and various error estimates for the rectangular configuration.  These are also generalized to the higher-order elements in the family.  Numerical tests corroborate the theoretical results.