Schwarz, Alexander; Schröder, Jörg:
Least-squares mixed finite elements with applications to anisotropic elasticity and viscoplasticity
2007
In: Proceedings in Applied Mathematics and Mechanics, Jg. 7 (2007), Heft 1, Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007, S. 4040043 - 4040044
Artikel/Aufsatz in Zeitschrift / Fach: Bauwissenschaften
Titel:
Least-squares mixed finite elements with applications to anisotropic elasticity and viscoplasticity
Autor(in):
Schwarz, Alexander im Online-Personal- und -Vorlesungsverzeichnis LSF anzeigen; Schröder, Jörg im Online-Personal- und -Vorlesungsverzeichnis LSF anzeigen
Erscheinungsjahr
2007
Erschienen in:
Proceedings in Applied Mathematics and Mechanics, Jg. 7 (2007), Heft 1, Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007, S. 4040043 - 4040044
ISSN
DOI

Abstract:

The objective of this work is to discuss a least-squares finite element method with applications to physically nonlinear and anisotropic constitutive equations at small strains. The L2-norm minimization of the residuals of the given first order system of differential equations leads to a functional, which is a two field formulation in the displacements and the stresses, see e.g. Cai & Starke [1]. These functionals provide the foundation for the formulations of the related least-squares mixed finite elements. A main focus of the presentation lies on the extension of plane elasticity to anisotropic or nonlinear material behavior. In this context transversely isotropic elasticity and viscoplasticity is considered. Finally a numerical example is presented.