Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method

By Dominik Schillinger, Martin Ruess, Nils Zander, Yuri Bazilevs, Alexander Düster, Ernst Rank. 2012

204 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ca0adcae33f546306af4ff245e21a0ba073a5cab

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

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”
Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion (2014, methodology): “This is contrary to the approach presented in [17, 40, 41], where all sub-cells are integrated with the full number of Gauss-points.”
A gradient-based shape optimization scheme using an interface-enriched generalized FEM (2015, background): “A subset of the non-conforming finite element mesh is also shown. approaches such as the finite cell method [41] [42] [43], where integration over bi-material cells is performed using adaptive composite Gaussian quadrature schemes wherein the integration sub-cells do not conform to the interface.”
Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis (2014, background): “However, the higher-order continuity of splines leads to a superior per-degree-of-freedom accuracy with respect to C finite elements, an observation that has been made many times before [12, 43, 87, 88].”
The non-symmetric Nitsche method for the parameter-free imposition of weak boundary and coupling conditions in immersed finite elements (2016, methodology): “For example, immersed finite element concepts have been employed to resolve multi-phase flow interfaces [7, 31], to deal with trimmed CAD surfaces [17, 50, 61, 65] and image based geometries [62, 68, 69], to prevent mesh updating and mesh distortion [10, 15, 21, 55], or to handle fluid–structure int”
Comparison of different higher order finite element schemes for the simulation of Lamb waves (2012, unknown): “[64].”
Local enrichment of the finite cell method for problems with material interfaces (2013, methodology): “The FCM has successfully been applied to various types of problems such as homogenization [18], topology optimization [19], biomechanics [20–24], geometrically nonlinear problems [25], elastoplasticity [26] and thin-walled structures [27].”
A parameter-free variational coupling approach for trimmed isogeometric thin shells (2017, background): “This enables a smooth extension of the solution into the fictitious domain, so that the approximation of the solution in the physical domain is higher-order accurate and its gradients remain unaffected up to the geometric boundary [68].”
Imposition of essential boundary conditions in the material point method (2018, unknown): “p=1 vpr σij , with r p σij = ||σp ij − σe ij|| ||σe ij|| (30)”