The hp‐d‐adaptive finite cell method for geometrically nonlinear problems of solid mechanics

By Dominik Schillinger, Alexander Düster, Ernst Rank. 2012

146 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/432462bf3c6703396b517968663deced5d0848a2

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Isogeometric Collocation: Cost Comparison with Galerkin Methods and Extension to Adaptive Hierarchical NURBS Discretizations (2013, methodology): “Of particular importance in this respect is the observation that, unlike standard FEM, the higher modes of IGA basis functions do not diverge with increasing degree, but achieve almost spectral accuracy that improves with degree [8,9].”
An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces (2012, methodology): “Construction of adaptive hierarchical approximation spaces In the following, we will derive step by step a hierarchical scheme for local refinement of Bsplines in one dimension, which combines concepts from B-spline subdivision, the hp-d adaptive approach [36, 70, 71] and existing hierarchical refin”
The multi-level hp-method for three-dimensional problems: Dynamically changing high-order mesh refinement with arbitrary hanging nodes (2016, unknown): “(a) No refinement (p = 4, 4,131 unknowns) (b) hp-d-refinement [50, 63] (p = 4, k = 6, 10,257 unknowns)”
On utilizing topology optimization to design support structure to prevent residual stress induced build failure in laser powder bed metal additive manufacturing (2019, methodology): “It has been successfully applied to solve a wide-range of problems, such as non-linear analysis [58], transport problem in porous media [59], biomechanical analysis [56, 60], etc.”
Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method (2012, methodology): “For a treatment within the framework of the p-version and B-spline version of the Finite Cell Method, see [34] and [52], respectively.”
Local enrichment of the finite cell method for problems with material interfaces (2013, methodology): “Moreover, the stress distribution near the weak discontinuity becomes excessively oscillatory, especially in large strain analysis [28,29].”
An efficient integration technique for the voxel‐based finite cell method (2012, unknown): “In combination with a locally restricted octree generation that turns out to be an efficient and fast voxelization approach, the true domain is accurately identified [9, 21, 22].”
The p-Version of the Finite Element and Finite Cell Methods (2017, methodology): “Encyclopedia of Computational Mechanics Second Edition, Edited by Erwin Stein, René de Borst and Thomas J.R. Hughes. © 2017 John Wiley & Sons, Ltd. DOI: 10.1002/9781119176817.ecm2003g polynomial degree of elements on a fixed mesh results in a rate of convergence in energy norm that is faster than if”
Towards the stabilization of the low density elements in topology optimization with large deformation (2013, background): “It is an important to remark that it can be possible to avoid the use of the relaxation function by using elements that are insensitive to mesh distortion with the appropriate constitutive model [37].”