Locking-free finite element methods for shells
Douglas N. Arnold,Franco Brezzi +1 more
Reads0
Chats0
TLDR
A new family of finite element methods for the Naghdi shell model, one method associated with each nonnegative integer k, based on a nonstandard mixed formulation, and the kth method employs triangular Lagrange finite elements of degree k+2 augmented by bubble functions ofdegree k + 3 for both the displacement and rotation variables.Abstract:
We propose a new family of finite element methods for the Naghdi shell model, one method associated with each nonnegative integer k. The methods are based on a nonstandard mixed formulation, and the kth method employs triangular Lagrange finite elements of degree k+2 augmented by bubble functions of degree k + 3 for both the displacement and rotation variables, and discontinuous piecewise polynomials of degree k for the shear and membrane stresses. This method can be implemented in terms of the displacement and rotation variables alone; as the minimization of an altered energy functional over the space mentioned. The alteration consists of the introduction of a weighted local projection into part, but not all, of the shear and membrane energy terms of the usual Naghdi energy. The relative error in the method, measured in a norm which combines the H I norm of the displacement and ro tation fields and an appropriate norm of the shear and membrane stress fields, converges to zero with order k+1 uniformly with respect to the shell thickness for smooth solutions, at least under the assumption that certain geometrical coefficients in the Nagdhi model are replaced by piecewise constants.read more
Citations
More filters
Reference EntryDOI
Models and finite elements for thin-walled structures
TL;DR: In this paper, the authors provide an overview of modeling and discretization aspects in finite element analysis of thin-walled structures, focusing on nonlinear finite element formulations for large displacements and rotations in the context of elastostatics.
Journal ArticleDOI
Fundamental considerations for the finite element analysis of shell structures
TL;DR: In this paper, the authors present fundamental considerations regarding the finite element analysis of shell structures and propose appropriate shell analysis test cases for numerical evaluations, which are applicable to both categories of shell behaviour and the rate of convergence in either case should be optimal.
Journal ArticleDOI
Asymptotic analysis of linearly elastic shells. II. Justification of flexural shell equations
TL;DR: In this paper, the authors considered a family of linearly elastic shells of thickness 2π, all having the same middle surfaceS = ϕ(ϖ)⊂R3, where ϕ⊆R2 is a bounded and connected open set with a Lipschitz-continuous boundary, and ϕ∈l3 (ϖ;R3).
Journal ArticleDOI
Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations
TL;DR: In this article, the static and free vibration analysis of laminated shells is performed by radial basis functions collocation, according to a sinusoidal shear deformation theory (SSDT).
Journal ArticleDOI
A minimal stabilisation procedure for mixed finite element methods.
Franco Brezzi,Michel Fortin +1 more
TL;DR: A general framework is presented that permits to introduce a minimal stabilising term and hence a minimal perturbation with respect to the original problem and in which the stabilising terms is introduced to cure coercivity problems.
References
More filters
Book
The finite element method
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Book
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
TL;DR: This paper presents the results of an analysis of the "Stream Function-Vorticity-Pressure" Method for the Stokes Problem in Two Dimensions and its applications to Mixed Approximation and Homogeneous Stokes Equations.
Book
Mixed and Hybrid Finite Element Methods
Franco Brezzi,Michel Fortin +1 more
TL;DR: Variational Formulations and Finite Element Methods for Elliptic Problems, Incompressible Materials and Flow Problems, and Other Applications.