Discontinuous Petrov-Galerkin method with optimal test functions for thin-body problems in solid mechanics
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Publication:646364
DOI10.1016/j.cma.2010.10.018zbMath1225.74100OpenAlexW2063665081MaRDI QIDQ646364
Jamie A. Bramwell, Leszek F. Demkowicz, Antti H. Niemi
Publication date: 16 November 2011
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.2010.10.018
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Finite element methods applied to problems in solid mechanics (74S05) Shells (74K25)
Related Items (20)
Nonstandard finite element methods. Abstracts from the workshop held January 10--16, 2021 (hybrid meeting) ⋮ A discontinuous Petrov-Galerkin methodology for adaptive solutions to the incompressible Navier-Stokes equations ⋮ Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: quasi-optimal test space norm ⋮ A robust DPG method for convection-dominated diffusion problems. II: Adjoint boundary conditions and mesh-dependent test norms ⋮ The DPG method for the Stokes problem ⋮ Locking-free finite element method for a bending moment formulation of Timoshenko beams ⋮ On perfectly matched layers for discontinuous Petrov-Galerkin methods ⋮ Penalty \(\mathrm{C}^0 8\)-node quadrilateral and 20-node hexahedral elements for consistent couple stress elasticity based on the unsymmetric finite element method ⋮ Approximation properties of primal discontinuous Petrov-Galerkin method on general quadrilateral meshes ⋮ An ultraweak formulation of the Kirchhoff–Love plate bending model and DPG approximation ⋮ An Overview of the Discontinuous Petrov Galerkin Method ⋮ Automatically adaptive, stabilized finite element method via residual minimization for heterogeneous, anisotropic advection-diffusion-reaction problems ⋮ Natural frequency analysis of shells of revolution based on hybrid dual-mixed \(hp\)-finite element formulation ⋮ Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model ⋮ Discrete energy behavior of a damped Timoshenko system ⋮ A locking-free DPG scheme for Timoshenko beams ⋮ The DPG methodology applied to different variational formulations of linear elasticity ⋮ Dual-mixed \(hp\)-version axisymmetric shell finite element using NURBS mid-surface interpolation ⋮ An ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximation ⋮ Finite element analysis of a bending moment formulation for the vibration problem of a non-homogeneous Timoshenko beam
Cites Work
- A class of discontinuous Petrov-Galerkin methods. III: Adaptivity
- Singularities in shell theory: anisotropic error estimates and numerical simulations
- Approximate symmetrization and Petrov-Galerkin methods for diffusion- convection problems
- An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable
- An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in two space variables
- Mixed Petrov-Galerkin methods for the Timoshenko beam problem
- Stability, convergence, and accuracy of a new finite element method for the circular arch problem
- Petrov-Galerkin formulations of the Timoshenko beam problem
- A new family of stable elements for nearly incompressible elasticity based on a mixed Petrov-Galerkin finite element formulation
- Discretization by finite elements of a model parameter dependent problem
- The discontinuous Petrov-Galerkin method for elliptic problems
- Approximation of shell layers using bilinear elements on anisotropically refined rectangular meshes
- Analysis of the DPG Method for the Poisson Equation
- A Family of ${C}^0$ Finite Elements For Kirchhoff Plates I: Error Analysis
- Asymptotic Analysis of the Boundary Layer for the Reissner–Mindlin Plate Model
- Fourier mode analysis of layers in shallow shell deformations
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