Abstract
The classical method of Trefftz consists of minimizing the energy error over the finite-energy solutions of the equilibrium equations. The method of Reissner [4] (also [3]) is equivalent. Analysis of the methods and of their coupling with domain methods requires an alternative formulation of the theory of elasticity. The three-dimensional case is considered (similar results hold in two dimensions). The elastic body occupies a region Ω with Lipschitz boundary Γ.
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References
Grannell, J.J.: Boundary-Galerkin and hybrid finite element methods in elasticity. Preprint MPJG-874, University College Cork 1987.
Grannell, J.J., Dwyer, J.: Singular problems in anisotropic elasticity — an edge-function method. ICES-88 These proceedings.
Hlavacek, I.: On Reissner’s variational theorem for boundary values in linear elasticity. Aplikace Matematiky 16 (1971) 109–124.
Reissner, E.; On some variational theorems in elasticity; Problems of continuum mechanics — contributions in honour of N.I. Muskhelishvili (1961) 370–381.
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© 1988 Springer-Verlag Berlin Heidelberg
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Grannell, J.J. (1988). On Boundary-Galerkin and Hybrid Finite Element Methods in Elasticity. In: Atluri, S.N., Yagawa, G. (eds) Computational Mechanics ’88. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61381-4_6
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DOI: https://doi.org/10.1007/978-3-642-61381-4_6
Publisher Name: Springer, Berlin, Heidelberg
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