Hybrid-equilibrium elements with control of spurious kinematic modes
Abstract
A review is presented of a recent formulation of hybrid-equilibrium elements for modelling planar structural problems. The formulation is based on the use of polynomials of general degree to approximate internal stress fields and bounding side displacements. The existence of hyperstatic stress fields and spurious kinematic modes are considered algebraically for both primitive and macro-elements, the latter providing a means of controlling or removing the spurious modes in the former. Consideration is given to stress fields which are statically admissible, and to Trefftz stress fields which are both statically and kinematically admissible.
References
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[2] B.M. Fraeijs de Veubeke. Diffusive equilibrium models. In: M. Geradin, ed., B.M. Fraeijs de Veubeke Memorial Volume of Selected Papers, 569-628. Sijthoff and Noordhoff, 1980.
[3] J. Jirousek, A. Venkatesh. Generation of optimal assumed stress expansions for hybrid- stress elements. Computers and Structures, 32(6): 1413- 1417, 1989.
[4] E.A.W. Maunder. A reappraisal of compound equilibrium finite elements. In: M.A. Erki, J. Kirkhope, eds. , Proceedings of the 12th Canadian Congress of Applied Mechanics, 796- 797. Carleton University, 1989.
[5] E.A.W. Maunder, J.P. Moitinho de Almeida, A.C.A. Ramsay. A general formulation of equilibrium macroelements with control of spurious kinematic modes. Int. J. Num. Meth. in Eng., 39: 3175-3194, 1996.
[2] B.M. Fraeijs de Veubeke. Diffusive equilibrium models. In: M. Geradin, ed., B.M. Fraeijs de Veubeke Memorial Volume of Selected Papers, 569-628. Sijthoff and Noordhoff, 1980.
[3] J. Jirousek, A. Venkatesh. Generation of optimal assumed stress expansions for hybrid- stress elements. Computers and Structures, 32(6): 1413- 1417, 1989.
[4] E.A.W. Maunder. A reappraisal of compound equilibrium finite elements. In: M.A. Erki, J. Kirkhope, eds. , Proceedings of the 12th Canadian Congress of Applied Mechanics, 796- 797. Carleton University, 1989.
[5] E.A.W. Maunder, J.P. Moitinho de Almeida, A.C.A. Ramsay. A general formulation of equilibrium macroelements with control of spurious kinematic modes. Int. J. Num. Meth. in Eng., 39: 3175-3194, 1996.
Published
2023-06-19
Issue
pp. 587-605
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Ward Maunder, E. A., & Moitiniho de Almeida, J. P. (2023). Hybrid-equilibrium elements with control of spurious kinematic modes. Computer Assisted Methods in Engineering and Science, 4(3-4), 587-605. https://cames3.ippt.pan.pl/index.php/cames/article/view/1393
