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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 19
Edited by: B.H.V. Topping
Paper IV.6

Hierarchical 2-D Equilibrium Finite Elements based on Chebyshev Interpolation Functions

J.A. Teixeira de Freitas

Departmenta de Engenharia Civil, Universidade Tecnica de Lisboa, Lisbon, Portugal

Full Bibliographic Reference for this paper
J.A. Teixeira de Freitas, "Hierarchical 2-D Equilibrium Finite Elements based on Chebyshev Interpolation Functions", in B.H.V. Topping, (Editor), "Developments in Computational Engineering Mechanics", Civil-Comp Press, Edinburgh, UK, pp 115-120, 1993. doi:10.4203/ccp.19.4.6
An equilibrium finite element formulation is used to illustrate the application of Chebyshev stress functions in the solution of 2-D linear elastostatic problems. The interpolation functions and the interpolation criteria are so chosen as to ensure that the governing system is symmetric and all the intervening structural operators are defined by boundary integral expressions. A family of 2-D Chebyshev polynomials is used to simulate the basic stress flow in the structural domain. Singular stress points or points associated with steep stress gradients are modeled using (weakly) singular Chebyshev rational functions. Taylor series are adopted in the independent interpolation of the displacements on the boundary of the structure. The hierarchic enrichment of the interpolation sets yields convergent results. Numerical testing shows that the static boundary conditions are accurately modeled with a relatively low number of interpolation functions and at the expense of low computation costs.

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