Numerical integration for nonlinear problems of the finite cell method using an adaptive scheme based on moment fitting

Hubrich, Simeon; Düster, Alexander

doi:10.1016/j.camwa.2018.11.030

Cited by 43 publications

(38 citation statements)

References 29 publications

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“…These schemes reduce the integration error either by decomposing the integration domain into boundary-conforming integration cells [23,24], or by modifying the quadrature weights, e.g. using moment-fitting equations [25].…”

Section: The Finite Cell Methodsmentioning

confidence: 99%

Direct structural analysis of domains defined by point clouds

Kudela

Kollmannsberger

Almaç

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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This contribution presents a method that aims at the numerical analysis of solids represented by oriented point clouds. The proposed approach is based on the Finite Cell Method, a highorder immersed boundary technique that computes on a regular background grid of finite elements and requires only inside-outside information from the geometric model. It is shown that oriented point clouds provide sufficient information for these point-membership classifications. Further, we address a tessellation-free formulation of contour integrals that allows to apply Neumann boundary conditions on point clouds without having to recover the underlying surface. Two-dimensional linear elastic benchmark examples demonstrate that the method is able to provide the same accuracy as those computed with conventional, continuous surface descriptions, because the associated error can be controlled by the density of the cloud. Three-dimensional examples computed on point clouds of historical structures show how the method can be employed to establish seamless connections between digital shape measurement techniques and numerical analyses.

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Section: The Finite Cell Methodsmentioning

confidence: 99%

Direct structural analysis of domains defined by point clouds

Kudela

Kollmannsberger

Almaç

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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“…Since its introduction, the FCM has been successfully applied in various fields, e.g. applications to elastic and plastic problems in small and large strain [19,20,[23][24][25][26][27][28][29][30][31][32][33], homogenization of heterogeneous and cellular materials as well as foams [34][35][36][37][38][39][40], topology optimization [41,42], problems including material interfaces [43][44][45][46][47], contact problems [40,[48][49][50][51][52][53][54], multi-physic problems [55][56][57][58][59][60][61][62], fracture simulation [63,64], or simulation of wave propagation [65][66][67]…”

Section: Motivationmentioning

confidence: 99%

The hierarchical finite cell method for nonlinear problems: Moment fitting quadratures, basis function removel, and remeshing

Hubrich¹

2021

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In this thesis, several approaches are discussed in order to further enhance the performance of the finite cell method (FCM). Thereby, novel moment fitting quadrature schemes are introduced that allow to reduce the effort of the numerical integration process significantly. Further, a basis function removal scheme is proposed to improve the conditioning behavior of the resulting equation system. Finally, an innovative remeshing strategy is presented that overcomes the problem of severely distorted elements for simulations with large deformations. Contents 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Goal and scope of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Basic elements of continuum mechanics 6 2.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Motion and deformation . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.2 Strain measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Equilibrium and stress measures . . . . . . . . ....

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“…Consider, for example, problems of elastoplasticity, where the moment fitting method turned out to be less robust as compared to the adaptive Gauss integration based on spacetrees. In situations like this, it was observed that the Newton-Raphson method, applied to solve the algebraic set of nonlinear equations resulting from the discretization of the linearized weak form, failed more often when the moment fitting method was used, see Hubrich and Düster (2019). Elastoplastic material models introduce an additional difficulty which is attributed to the evolving elastoplastic front representing a material interface intersecting the cells.…”

Section: Adaptive Moment Fittingmentioning

confidence: 99%

“…Material interfaces require a special treatment of the trial and test function of the spatial discretization as well as of the integration based on moment fitting. The robustness of the overall nonlinear solution process based on the finite cell method becomes even more fragile when considering problems of finite strains and cells that are filled with a small fraction of material only, see Schillinger et al (2012), Taghipour et al (2018), Hubrich and Düster (2019). Then, the deformation of broken cells can become quite large, leading to a failure of the nonlinear computation.…”

Section: Adaptive Moment Fittingmentioning

confidence: 99%

“…Employing the standard Gauss-Legendre points which might even be located in the fictitious domain turned out to be a good approach. In Hubrich and Düster (2019), a new idea to circumvent the solution of the linear system was suggested together with an adaptive version to improve the robustness of the moment fitting for strongly nonlinear problems of finite strain elastoplasticity.…”

Section: Introductionmentioning

confidence: 99%

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