Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics

DOI10.1002/nme.5967zbMATH Open1548.74824MaRDI QIDQ6555434

C. Kadapa

Publication date: 14 June 2024

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

zbMATH Keywords

Bernstein polynomialsconnecting rodBézier elementsexplicit elastodynamics\textbf{B}-bar formulation

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Computer-aided design (modeling of curves and surfaces) (65D17)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Isogeometric collocation for elastostatics and explicit dynamics
• An edge-based smoothed tetrahedron finite element method (ES-T-FEM) for 3D static and dynamic problems
• Fifteen node tetrahedral elements for explicit methods in nonlinear solid dynamics
• A nonconforming rotated \(Q_{1}\) approximation on tetrahedra
• Mixed stabilized finite element methods in nonlinear solid mechanics. I: Formulation
• Mixed stabilized finite element methods in nonlinear solid mechanics. II: Strain localization
• Development of a stabilised Petrov-Galerkin formulation for conservation laws in Lagrangian fast solid dynamics
• A smoothed finite element method for mechanics problems
• A new family of stable elements for nearly incompressible elasticity based on a mixed Petrov-Galerkin finite element formulation
• Higher order stabilized finite element method for hyperelastic finite deformation
• Mixed linear/linear simplicial elements for incompressible elasticity and plasticity.
• A stabilised Petrov-Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics
• Explicit finite deformation analysis of isogeometric membranes
• A first order hyperbolic framework for large strain computational solid dynamics. I: Total Lagrangian isothermal elasticity
• Mixed stabilized finite element methods in nonlinear solid mechanics. III: compressible and incompressible plasticity
• On numerically accurate finite element solutions in the fully plastic range
• A stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations.
• A stabilized mixed finite element method for finite elasticity. Formulation for linear displacement and pressure interpolation
• A stabilised immersed framework on hierarchical b-spline grids for fluid-flexible structure interaction with solid-solid contact
• Implicit finite incompressible elastodynamics with linear finite elements: a stabilized method in rate form
• A stabilised immersed boundary method on hierarchical B-spline grids
• Isogeometric analysis with Bézier tetrahedra
• Adaptive isogeometric analysis with hierarchical box splines
• A stabilised immersed boundary method on hierarchical b-spline grids for fluid-rigid body interaction with solid-solid contact
• Isogeometric unstructured tetrahedral and mixed-element Bernstein-Bézier discretizations
• A velocity/stress mixed stabilized nodal finite element for elastodynamics: analysis and computations with strongly and weakly enforced boundary conditions
• Isogeometric triangular Bernstein-Bézier discretizations: automatic mesh generation and geometrically exact finite element analysis
• Subdivision based mixed methods for isogeometric analysis of linear and nonlinear nearly incompressible materials
• 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)
• B-bar FEMs for anisotropic elasticity
• A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: a dynamic variational multiscale approach
• The inf-sup test
• A stabilized nodally integrated tetrahedral
• A Stabilized Mixed Finite Element Method for Nearly Incompressible Elasticity
• Assumed-deformation gradient finite elements with nodal integration for nearly incompressible large deformation analysis
• Generalization of selective integration procedures to anisotropic and nonlinear media
• Triangles and tetrahedra in explicit dynamic codes for solids
• A new family of explicit time integration methods for linear and non‐linear structural dynamics
• Tetrahedral composite finite elements
• Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes
• Isogeometric Analysis
• Mean‐strain 10‐node tetrahedron with energy‐sampling stabilization
• F‐bar‐based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking
• Stabilized finite element method for viscoplastic flow: Formulation and a simple progressive solution strategy
• Mean-strain 10-node tetrahedron with energy-sampling stabilization for nonlinear deformation
• A dynamic variational multiscale method for viscoelasticity using linear tetrahedral elements

Related Items (1)

Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity

This page was built for publication: Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics