Isogeometric collocation: Neumann boundary conditions and contact

By Laura De Lorenzis, John A. Evans, Thomas J. R. Hughes, Alessandro Reali. 2015

127 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6f3c65d760ac9f16522b6b8deb3339ba7beff84a

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In Computational Mechanics

In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

The variational collocation method (2016, background): “Isogeometric collocation has recently triggered a great interest in the computational mechanics community [14, 15, 16, 17, 18].”
Isogeometric collocation methods for the Reissner–Mindlin plate problem (2015, unknown): “However, we remark that it has been recently shown in [20] that such an approach may not be optimal in singular situations, in particular when non-uniform meshes are adopted.”
Isogeometric collocation using analysis-suitable T-splines of arbitrary degree (2016, methodology): “We also highlight that one of the drawbacks of NURBS-based IGA-C, recently observed in [40], is the fact that spurious oscillations in the numerical solution may arise in the case of problems characterized by reduced regularity, when Neumann boundary conditions are imposed in strong form and element”
Single-variable formulations and isogeometric discretizations for shear deformable beams (2015, methodology): “Isogeometric collocation has been recently proposed as a high-order, lowcost alternative to Galerkin-based isogeometric analysis [12,18–25].”
Isogeometric analysis: An overview and computer implementation aspects (2012, background): “There is ongoing research in developing efficient iterative solvers for the linear system resulting from collocation [12, 38], imposition of Neumann boundary conditions [75], and plate collocation formulations [65].”
Fast formation and assembly of finite element matrices with application to isogeometric linear elasticity (2019, methodology): “Firstly, collocating the strong form of the equations [4, 5, 21] is a 35 viable alternative to the Galerkin method that decreases the formation and assembly time by orders of magnitude at the expense of decreased accuracy per degree of freedom and sub-optimal convergence rates [42].”
Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams (2016, background): “Two important aspects in the development of isogeometric collocation, that are the imposition of Neumann boundary conditions and the contact constraints between multiple patches, are addressed in [32].”
Three-dimensional isogeometrically enriched finite elements for frictional contact and mixed-mode debonding (2015, background): “…contact Temizer (2014), large deformation contact using T-splines Dimitri et al. (2014a), thermomechanical Mortar contact Dittmann et al. (2014), isogeometric collocation for contact De Lorenzis et al. (2015), and modeling of solid and liquid membrane contact Sauer et al. (2014) and Sauer (2014).”
An isogeometric collocation method for frictionless contact of Cosserat rods (2017, methodology): “Of particular relevance for the present work are the investigations on straight Timoshenko beams [21] and spatial Timoshenko rods [22], Reissner–Mindlin plates [23], Bernoulli beams and Kirchhoff plates [24], and frictionless contact [25].”