Abstract
In this contribution we provide benchmark problems in the field of computational solid mechanics. In detail, we address classical fields as elasticity, incompressibility, material interfaces, thin structures and plasticity at finite deformations. For this we describe explicit setups of the benchmarks and introduce the numerical schemes. For the computations the various participating groups use different (mixed) Galerkin finite element and isogeometric analysis formulations. Some programming codes are available open-source. The output is measured in terms of carefully designed quantities of interest that allow for a comparison of other models, discretizations, and implementations. Furthermore, computational robustness is shown in terms of mesh refinement studies. This paper presents benchmarks, which were developed within the Priority Programme of the German Research Foundation ‘SPP 1748 Reliable Simulation Techniques in Solid Mechanics—Development of Non-Standard Discretisation Methods, Mechanical and Mathematical Analysis’.
Highlights
Solving partial differential equations on complex geometries is perhaps one of the most important scientific achievement of the last decades
The convergence of the vertical displacement in z-direction at point P, uz(P), versus the degrees of freedom (DOF) of the discretization was investigated for the finite elements H1/ EI9, H1, H2, H1/P0, O2/P1, H1/E9 on regular meshes
To validate the extrapolated reference energy, the convergence of the solution is measured in the energy norm for p-refinement in a FE analysis and for h-refinement in an isogeometric analysis
Summary
Jörg Schröder1 · Thomas Wick2 · Stefanie Reese3 · Peter Wriggers4 · Ralf Müller5 · Stefan Kollmannsberger6 · Markus Kästner7 · Alexander Schwarz1 · Maximilian Igelbüscher1 · Nils Viebahn1 · Hamid Reza Bayat3 · Stephan Wulfinghoff12 · Katrin Mang2 · Ernst Rank6 · Tino Bog6 · Davide D’Angella6 · Mohamed Elhaddad6 · Paul Hennig7 · Alexander Düster8 · Wadhah Garhuom8 · Simeon Hubrich8 · Mirjam Walloth9 · Winnifried Wollner9 · Charlotte Kuhn10 · Timo Heister
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