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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 106
PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by:
Paper 213

A Hierarchic High-Order C1 Quadrilateral Plate Finite Element

L.J.F. Ferreira and M.L. Bittencourt

Department of Mechanical Design, Faculty of Mechanical Engineering, University of Campinas, Sao Paolo, Brazil

Full Bibliographic Reference for this paper
L.J.F. Ferreira, M.L. Bittencourt, "A Hierarchic High-Order C1 Quadrilateral Plate Finite Element", in , (Editors), "Proceedings of the Twelfth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 213, 2014. doi:10.4203/ccp.106.213
Keywords: high-order, Kirchhoff, p-FEM, plate elements..

Summary
The Kirchhoff model is the simplest plate theory. In stress analysis of plate structures, finite elements have been used with acceptable accuracy and good performance. The Bogner-fox-Schmit plate finite element is a C1 element that ensures continuity of displacements and rotations between two elements. To improve the convergence rate and accuracy, a hierarchical Kirchhoff plate finite element is developed. The enrichment procedure adds edge and face functions for each order p increased. The tensor product of Hermite cubic polynomials defines the vertex shape functions. The edge and face functions are given in terms of Hermite and Jacobi polynomials. The C1 continuity is ensured because each new function has zero value at the vertex nodes of the edges. Some problems of plate structures under simple loads were solved to evaluate the performance of the p-version element. We compared the results with analytic solutions using error in energy and L2 norm. The results showed excellent accuracy and fast convergence rate when increasing the polynomial order for regular meshes.

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