Adaptive integration of cut finite elements and cells for nonlinear structural analysis.(English)Zbl 1481.74695

De Lorenzis, Laura (ed.) et al., Modeling in engineering using innovative numerical methods for solids and fluids. Papers based on the presentations at the CISM course, Udine, Italy, October 15–19, 2018. Cham: Springer. CISM Courses Lect. 599, 31-73 (2020).
Summary: Fictitious domain methods facilitate the discretization of boundary value problems by applying simple meshes containing finite elements or cells that do not conform to the geometry of the domain of interest. In this way, the effort of meshing complex domains is shifted to the numerical integration of those elements/cells that are cut by the boundary of the domain. In this chapter, we will first introduce a high-order fictitious domain method and then present adaptive methods that are suited for the numerical integration of broken elements and cells. Since the quadrature schemes presented in this chapter are quite general, they can be applied to the different versions of fictitious domain methods.
For the entire collection see [Zbl 1470.76007].

MSC:

 74S05 Finite element methods applied to problems in solid mechanics 74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) 74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 74K20 Plates
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