Weak imposition of constraints for structural membranes in transient geometrically nonlinear isogeometric analysis on multipatch surfaces

DOI10.1016/j.cma.2019.01.023zbMath1441.74104OpenAlexW2912964995MaRDI QIDQ1988021

A. Apostolatos, Kai-Uwe Bletzinger, Roland Wüchner

Publication date: 16 April 2020

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2019.01.023

zbMATH Keywords

form-findingNURBS-based isogeometric analysisdomain-decomposition methodsmultipatch geometriesnon-matching parametrizationstransient nonlinear membrane analysis

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Finite element methods applied to problems in solid mechanics (74S05) Membranes (74K15) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (7)

Enhanced nodal gradient finite elements with new numerical integration schemes for 2D and 3D geometrically nonlinear analysis ⋮ Nitsche's method for non-conforming multipatch coupling in hyperelastic isogeometric analysis ⋮ A comparison of smooth basis constructions for isogeometric analysis ⋮ A unified adaptive approach for membrane structures: form finding and large deflection isogeometric analysis ⋮ Isogeometric multi-patch analyses for mixed thin shells in the framework of non-linear elasticity ⋮ An updated Lagrangian framework for isogeometric Kirchhoff-Love thin-shell analysis ⋮ Isogeometric continuity constraints for multi-patch shells governed by fourth-order deformation and phase field models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Nitsche embedded mesh method
• Isogeometric analysis and domain decomposition methods
• Isogeometric analysis of trimmed NURBS geometries
• Realization of an integrated structural design process: analysis-suitable geometric modelling and isogeometric analysis
• A perturbed Lagrangian formulation for the finite element solution of contact problems
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• Finite cell method. \(h\)- and \(p\)-extension for embedded domain problems in solid mechanics
• A discourse on the stability conditions for mixed finite element formulations
• Nitsche's method for coupling non-matching meshes in fluid-structure vibration problems
• Nitsche method for isogeometric analysis of Reissner-Mindlin plate with non-conforming multi-patches
• A parameter-free variational coupling approach for trimmed isogeometric thin shells
• Stabilized finite element schemes with LBB-stable elements for incompressible flows
• Isogeometric mortar methods
• Analysis in computer aided design: nonlinear isogeometric B-Rep analysis of shell structures
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
• Embedded structural entities in NURBS-based isogeometric analysis
• Integrated design and analysis of structural membranes using the isogeometric B-rep analysis
• Generalizations of the Lax-Milgram theorem
• Computational methods for form finding and optimization of shells and membranes
• A comparison of mortar and Nitsche techniques for linear elasticity
• Nitsche's method for two and three dimensional NURBS patch coupling
• Error-bounds for finite element method
• Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
• Deriving robust unfitted finite element methods from augmented Lagrangian formulations
• Domain Decomposition Methods and Kirchhoff-Love Shell Multipatch Coupling in Isogeometric Analysis
• Weakly enforced essential boundary conditions for NURBS-embedded and trimmed NURBS geometries on the basis of the finite cell method
• A Nitsche-type formulation and comparison of the most common domain decomposition methods in isogeometric analysis
• The weak substitution method - an application of the mortar method for patch coupling in NURBS-based isogeometric analysis
• On methods for stabilizing constraints over enriched interfaces in elasticity
• The Finite Element Method with Penalty
• Isogeometric Analysis
• A penalty-free Nitsche method for the weak imposition of boundary conditions in compressible and incompressible elasticity
• Stress-adapted numerical form finding of pre-stressed surfaces by the updated reference strategy
• A special stability problem for linear multistep methods

This page was built for publication: Weak imposition of constraints for structural membranes in transient geometrically nonlinear isogeometric analysis on multipatch surfaces