Numerical homogenization of heterogeneous and cellular materials utilizing the finite cell method

Düster, Alexander; Sehlhorst, Hans-Georg; Rank, Ernst

doi:10.1007/s00466-012-0681-2

Cited by 85 publications

(67 citation statements)

References 37 publications

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“…We prove in Lemma 1 that, under a simple assumption, problem (2.7) converges to a limit as α → 0. We introduce the kernel of a ap 9) and its orthogonal space…”

Section: Convergence Of Discrete Problems With Respect To the Penalizmentioning

confidence: 99%

“…Nonlinear problems such 1 as geometrically nonlinearity [23] or elastoplasticity [1,3] have been addressed as well. The FCM has also been successfully applied to the numerical homogenization of materials with complicated microstructures [9] or to topology optimization [6,14] in structural mechanics. Instead of classical hierarchic shape functions [25] NURBS, which have become very popular thanks to the isogeometric analysis [10], can also be successfully used within the FCM, see [22,17].…”

Section: Introductionmentioning

confidence: 99%

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Theoretical and Numerical Investigation of the Finite Cell Method

2015

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We present a detailed analysis of the convergence properties of the finite cell method which is a fictitious domain approach based on high order finite elements. It is proved that exponential type of convergence can be obtained by the finite cell method for Laplace and Lamé problems in one, two as well three dimensions. Several numerical examples in one and two dimensions including a wellknown benchmark problem from linear elasticity confirm the results of the mathematical analysis of the finite cell method.

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“…We prove in Lemma 1 that, under a simple assumption, problem (2.7) converges to a limit as α → 0. We introduce the kernel of a ap 9) and its orthogonal space…”

Section: Convergence Of Discrete Problems With Respect To the Penalizmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Theoretical and Numerical Investigation of the Finite Cell Method

2015

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“…Technical improvements include the weak imposition of boundary and coupling conditions [47,48], local refinement schemes [49][50][51][52][53], and improved quadrature rules for intersected elements [39,40,54]. Furthermore, the FCM has been successfully applied for large deformation analysis [55,56], thermoelasticity [57], homogenization [58], bone mechanics [59], topology optimization [60], and elastodynamics and wave propagation [61][62][63]. A concise summary of the FCM and related developments and applications can be found in the recent review article by Schillinger and Ruess [46].…”

Section: Introductionmentioning

confidence: 99%

The tetrahedral finite cell method for fluids: Immersogeometric analysis of turbulent flow around complex geometries

et al. 2016

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We present a tetrahedral finite cell method for the simulation of incompressible flow around geometrically complex objects. The method immerses such objects into non-boundary-fitted meshes of tetrahedral finite elements and weakly enforces Dirichlet boundary conditions on the objects' surfaces. Adaptively-refined quadrature rules faithfully capture the flow domain geometry in the discrete problem without modifying the non-boundary-fitted finite element mesh. A variational multiscale formulation provides accuracy and robustness in both laminar and turbulent flow conditions. We assess the accuracy of the method by analyzing the flow around an immersed sphere for a wide range of Reynolds numbers. We show that quantities of interest such as the drag coefficient, Strouhal number and pressure distribution over the sphere are in very good agreement with reference values obtained from standard boundary-fitted approaches. We place particular emphasis on studying the importance of the geometry resolution in intersected elements. Aligning with the immersogeometric concept, our results show that the faithful representation of the geometry in intersected elements is critical for accurate flow analysis. We demonstrate the potential of our proposed method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor. KeywordsImmersed method, Complex geometry, Immersogeometric finite elements, Geometric accuracy in intersected elements, Weakly enforced boundary conditions, Tetrahedral finite cell method AbstractWe present a tetrahedral finite cell method for the simulation of incompressible flow around geometrically complex objects. The method immerses such objects into non-boundary-fitted meshes of tetrahedral finite elements and weakly enforces Dirichlet boundary conditions on the objects' surfaces. Adaptively-refined quadrature rules faithfully capture the flow domain geometry in the discrete problem without modifying the non-boundary-fitted finite element mesh. A variational multiscale formulation provides accuracy and robustness in both laminar and turbulent flow conditions. We assess the accuracy of the method by analyzing the flow around an immersed sphere for a wide range of Reynolds numbers. We show that quantities of interest such as the drag coefficient, Strouhal number and pressure distribution over the sphere are in very good agreement with reference values obtained from standard boundary-fitted approaches. We place particular emphasis on studying the importance of the geometry resolution in intersected elements. Aligning with the immersogeometric concept, our results show that the faithful representation of the geometry in intersected elements is critical for accurate flow analysis. We demonstrate the potential of our proposed method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor.

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“…The image-based finite cell method has been used for e.g. the analysis of metal foams [14], the validation of in vitro bone experiments [15], and trabecular bone micro-structures [11] (see [13] for an overview).…”

Section: Introductionmentioning

confidence: 99%