000012630 001__ 12630
000012630 005__ 20160920162634.0
000012630 04107 $$aeng
000012630 046__ $$k2016-09-05
000012630 100__ $$aSteeger, K.
000012630 24500 $$aA comparative study of the consistency of Galerkin-type and least-squares finite element formulations for bifurcation problems

000012630 24630 $$n6.$$pInsights and Innovations in Structural Engineering, Mechanics and Computation
000012630 260__ $$bTaylor and Francis Group, London, UK
000012630 506__ $$arestricted
000012630 520__ $$2eng$$aThe computation of reliable results using finite elements is a major engineering goal. Under the assumption of a linear theory many stable and reliable (standard and mixed) finite elements have been developed. Unfortunately, in the nonlinear regime, e.g. applying these elements in the field of incompressible, hyperelastic materials, problems can occur. A typical example is the detection of stability points using mixed Galerkin finite elements, compare e.g. (Auricchio, Beirão da Veiga, Lovadina,& Reali 2005), (Auricchio, Beirão da Veiga, Lovadina, & Reali 2010) and (Auricchio, Beirão da Veiga, Lovadina, Reali, Taylor, & Wriggers 2013). In this contribution we analyze, amongst others, the consistency of Galerkin-type and least-squares finite element formulations for structural stability problems in the framework of hyperelasticity. Basis for the least-squares element formulation is a div-grad first order system consisting of the equilibrium condition, the constitutive equation and a stress symmetry condition all written in a residual form, compare also (Schwarz, Steeger, & Schröder 2014). The sum of squared L2 (B ) -norms of the residuals leads to the basic functional which has to be minimized, see also (Jiang 1998). For the approximation of the displacement and the stress field we use independent interpolations. In order to show the performance of the proposed method a boundary value problem will be analyzed.

000012630 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000012630 653__ $$a

000012630 7112_ $$aSixth International Conference on Structural Engineering, Mechanics and Computation$$cCape Town, South Africa$$d2016-09-05 / 2016-09-07$$gSEMC2016
000012630 720__ $$aSteeger, K.$$iSchröder, J.
000012630 8560_ $$ffischerc@itam.cas.cz
000012630 8564_ $$s473356$$uhttps://invenio.itam.cas.cz/record/12630/files/078.pdf$$yOriginal version of the author's contribution as presented on CD, 078.pdf.
000012630 962__ $$r12552
000012630 980__ $$aPAPER