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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 39
ADVANCES IN FINITE ELEMENT TECHNOLOGY Edited by: B.H.V. Topping
Paper III.3
Formulation of Hybrid-Trefftz Displacement Elements J.A. Teixeira de Freitas and C. Cismasiu
Department of Civil Engineering, I.S.T., Technical University of Lisbon, Lisbon, Portugal J.A. Teixeira de Freitas, C. Cismasiu, "Formulation of Hybrid-Trefftz Displacement Elements", in B.H.V. Topping, (Editor), "Advances in Finite Element Technology", Civil-Comp Press, Edinburgh, UK, pp 195-202, 1996. doi:10.4203/ccp.39.3.3
Abstract
A displacement model of the hybrid-Trefftz finite element
formulation based on the independent approximation of
the displacements and tractions is presented. The finite
element equilibrium and compatibility equations represent
dual transformations and are described by boundary
integral arrays, independent from the structural constitutive
relations. Reciprocity is preserved in the finite
element elasticity equations, which are also found to be
described by boundary integral arrays when the displacement
approximation functions are constrained to solve
the Navier equations. As a consequence of this duality
and reciprocity, the resulting boundary integral governing
system is symmetric. The formulation is derived from
first-principles of Mechanics and the associated energy
theorems are recovered through mathematical programming
equivalence theory. Conditions for static and kinematic
admissibility of the finite element solutions are also
presented.
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