Summary
Stress function-based solution procedures in elasticity require the knowledge of those stress functions that give zero complementary strain energy. In the two-dimensional case, the structure of the zero-energy first-order stress functions is as simple as that of the zero-energy displacements, and the number of the zero-energy modes is three [1]. This paper investigates the more complicated three-dimensional case and, considering a possible set of six independent first-order stress functions, derives the zero-energy stress functions in polynomial form. It is pointed out that the number of the zero-energy stress function modes in the three-dimensional case is infinite.
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References
Fraeijs de Veubeke, B. M.: Stress function approach. Proc. of the World Congress on Finite Element Methods in Structural Mechanics, pp. J.1–J.51. Bournemouth, UK 1975.
Fraeijs de Veubeke, B. M.: Diffusive equilibrium models. Lecture Notes for the International Research Seminar on `The theory and application of finite element methods'. University of Calgary, Alberta, Canada 1973.
Geradin, M. (ed.): B. M. Fraeijs de Veubeke memorial volume of selected papers. Alphen aan den Rijn: Sijthoff & Noordhoff 1980.
B. M. Fraeijs de Veubeke A. Millard (1976) ArticleTitleDiscretization of stress fields in the finite element method J. Franklin Institute 302 389–412 Occurrence Handle0352.73061 Occurrence Handle10.1016/0016-0032(76)90032-6 Occurrence Handle455773
B. M. Fraeijs de Veubeke (1972) ArticleTitleA new variational principle for finite elastic displacements Int. J. Engng. Sci. 10 745–763 Occurrence Handle10.1016/0020-7225(72)90079-1 Occurrence Handle459170
E. Bertóti (2000) ArticleTitleDual-mixed hp finite element methods using first-order stress functions and rotations Comput. Mech. 26 39–51 Occurrence Handle0980.74057 Occurrence Handle10.1007/s004660000148 Occurrence Handle1780142
E. Bertóti (2002) ArticleTitleDual-mixed p and hp finite element methods for elastic membrane problems Int. J. Numer. Meth. Engng. 53 3–29 Occurrence Handle01742269 Occurrence Handle10.1002/nme.389
I. Kozák G. Szeidl (1980) ArticleTitleThe field equations and the boundary conditions with force stresses and couple stresses in the linearized theory of micropolar elastostatics Acta Tech. Acad. Sci. Hungaricae 91 57–80 Occurrence Handle0479.73004
E. Bertóti (1994) ArticleTitleIndeterminacy of first order stress functions and the stress- and rotation-based formulation of linear elasticity Comput. Mech. 14 249–265 Occurrence Handle0809.73018 Occurrence Handle10.1007/BF00370076 Occurrence Handle1285211
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Bertóti, E. On the stress function approach in three-dimensional elasticity. Acta Mechanica 190, 197–204 (2007). https://doi.org/10.1007/s00707-006-0432-6
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DOI: https://doi.org/10.1007/s00707-006-0432-6