The finite cell method for three-dimensional problems of solid mechanics

By Alexander Düster, Jamshid Parvizian, Zheng-jun Yang, Ernst Rank. 2008

551 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ba0eec06e0053e857bb5ba2dab5fb416bc7928be

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Local enrichment of the finite cell method for problems with material interfaces (2013, methodology): “The refinement has been made synergetically, thus taking advantage of the adaptive integration of the original FCM formulation [16].”
The p-Version of the Finite Element and Finite Cell Methods (2017, methodology): “Afterwards we present the FCM as a highorder immersed boundary method, taking advantage of the previous formulation and discussion of the p-version.”
An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces (2012, methodology): “ICES REPORT 12-05 January 2012 An Isogeometric Design-through-analysis Methodology based on Adaptive Hierarchical Refinement of NURBS, Immersed Boundary Methods, and T-spline CAD Surfaces by”
Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method (2012, methodology): “The high-order basis originally applied in the FCM [28, 29] uses a regular mesh of elements of the p-version of the finite element method, introduced by Szabó and Babuška [30,31,49,50].”
Simulation Methods for Guided Wave-Based Structural Health Monitoring: A Review (2015, methodology): “Düster and Parvzian [69, 192] introduced the finite cell method (FCM) and several extensions were presented by Schillinger et al.”
The hp‐d‐adaptive finite cell method for geometrically nonlinear problems of solid mechanics (2012, methodology): “Generalizing the concept of hierarchical overlays in two and three dimensions FCM for 2D and three-dimensional (3D) problems of solid mechanics [25, 26] uses the so-called trunk space of the p-version of the FE [27, 28] over a structured finite cell mesh.”
A Cut Finite Element Method with Boundary Value Correction for the Incompressible Stokes Equations (2017, methodology): “…has increased signiﬁcantly during the last few years; among recent contributions we mention the ﬁnite cell method of Parvizian, D¨uster, et al. [14,23]; the least squares stabilized Lagrange multiplier methods of Haslinger and Renard [18], Tur et al. [25], and Baiges et al. [2]; the…”
Tensor-based methods for numerical homogenization from high-resolution images (2013, background): “Finally, non-conforming approaches can be considered (see [13, 54] among others): these approaches allows to avoid meshing issues.”
An immersogeometric variational framework for fluid–structure interaction: application to bioprosthetic heart valves (2014, unknown): “[105] describe a method of automatically generating more accurate quadrature rules for finite cell computations by dividing cut elements into sub-cells and applying standard quadrature rules within the sub-cells.”
The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models (2015, methodology): “The quadtree approach can be easily adjusted to one or three dimensions using binary trees or octrees, respectively [49, 144, 145].”
An efficient integration technique for the voxel‐based finite cell method (2012, unknown): “In [21], a sub-cell strategy is introduced that allows to arbitrarily densify the quadrature points within C thus supporting adaptive integration on various granularity levels.”