Mixed Finite Element Methods - Theory and Discretization
This contribution is concerned with the formulation of mixed finite elements discretization schemes for nonlinear problems of solid mechanics. Thus continuum mechanics for solids is described in the first section to provide the necessary background for the numerical method. This includes necessary kinematical relations as well as the balance laws with their weak forms and the constitutive equations. The second section then describes mixed discretization schemes which can be applied to simulate nonlinear elastic problems including finite deformations.
KeywordsMixed Finite Element Mixed Finite Element Method Nonlinear Elastic Problem Mixed Finite Element Discretization Element Discretization Scheme
Unable to display preview. Download preview PDF.
- K. J. Bathe. Finite Element Procedures. Prentice-Hall, Englewood Cliffs, New Jersey, 1996.Google Scholar
- P. Chadwick. Continuum Mechanics, Concise Theory and Problems. Dover Publications, Mineola, 1999.Google Scholar
- B. M. Fraeijs de Veubeke. Stress function approach. In World Congress on the Finite Element Method in Structural Mechanics, pages 1–51. Bournmouth, 1975.Google Scholar
- L. E. Malvern. Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, Englewood Cliffs, New Jersey, 1969.Google Scholar
- R. W. Ogden. Non-Linear Elastic Deformations. Ellis Horwood and John Wiley, Chichester, 1984.Google Scholar
- T. H. H. Pian. Derivation of element stiffness matrices by assumed stress distributions. AIAA-J. 2, 7:1333–1336, 1964.Google Scholar
- C. Truesdell and W. Noll. The nonlinear field theories of mechanics. In S. Flügge, editor, Handbuch der Physik III/3. Springer, Berlin, Heidelberg, Wien, 1965.Google Scholar
- C. Truesdell and R. Toupin. The classical field theories. In Handbuch der Physik III/1. Springer, Berlin, Heidelberg, Wien, 1960.Google Scholar
- E. L. Wilson, R. L. Taylor, W. P. Doherty, and J. Ghaboussi. Incompatible Displacements Models. In Numerical and Computer Models in Structural Mechanics, Fenves S. J., Perrone N., Robinson A. R. and Schnobrich W. C. (Eds.), New York, 1973. Academic Press. 43–57.Google Scholar
- P. Wriggers. Nichtlineare Finite Elemente. Springer, Berlin, 2001.Google Scholar
- P. Wriggers. Nonlinear Finite Elements. Springer, Berlin, Heidelberg, New York, 2008.Google Scholar
- O. C. Zienkiewicz and R. L. Taylor. The Finite Element Method, 4th Ed., volume 1. McGraw Hill, London, 1989.Google Scholar