Locking-free finite element methods for linear and nonlinear elasticity in 2D and 3D ⋆
نویسندگان
چکیده
The uniform convergence of finite element approximations based on a modified Hu-Washizu formulation for the nearly incompressible linear elasticity is analyzed. We show the optimal and robust convergence of the displacement-based discrete formulation in the nearly incompressible case with the choice of approximations based on quadrilateral and hexahedral elements. These choices include bases that are well known, as well as newly constructed bases. Starting from a suitable threefield problem, we extend our α-dependent three-field formulation to geometrically nonlinear elasticity with Saint-Venant Kirchhoff law. Additionally, an α-dependent three-field formulation for a general hyperelastic material model is proposed. A range of numerical examples using different material laws for small and large strain elasticity is presented.
منابع مشابه
Coupling Nonlinear Element Free Galerkin and Linear Galerkin Finite Volume Solver for 2D Modeling of Local Plasticity in Structural Material
This paper introduces a computational strategy to collaboratively develop the Galerkin Finite Volume Method (GFVM) as one of the most straightforward and efficient explicit numerical methods to solve structural problems encountering material nonlinearity in a small limited area, while the remainder of the domain represents a linear elastic behavior. In this regard, the Element Free Galerkin met...
متن کاملNonlinear Finite Element Analysis of Bending of Straight Beams Using hp-Spectral Approximations
Displacement finite element models of various beam theories have been developed using traditional finite element interpolations (i.e., Hermite cubic or equi-spaced Lagrange functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation φ and/or shear strain γxz, or in the integral form u...
متن کاملNon Uniform Rational B Spline (NURBS) Based Non-Linear Analysis of Straight Beams with Mixed Formulations
Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, tota...
متن کاملA Comparative Study of Least-Squares and the Weak-Form Galerkin Finite Element Models for the Nonlinear Analysis of Timoshenko Beams
In this paper, a comparison of weak-form Galerkin and least-squares finite element models of Timoshenko beam theory with the von Kármán strains is presented. Computational characteristics of the two models and the influence of the polynomial orders used on the relative accuracies of the two models are discussed. The degree of approximation functions used varied from linear to the 5th order. In ...
متن کاملModified Fixed Grid Finite Element Method in the Analysis of 2D Linear Elastic Problems
In this paper, a modification on the fixed grid finite element method is presented and used in the solution of 2D linear elastic problems. This method uses non-boundary-fitted meshes for the numerical solution of partial differential equations. Special techniques are required to apply boundary conditions on the intersection of domain boundaries and non-boundary-fitted elements. Hence, a new met...
متن کامل