A Family of Mixed Finite Elements for the Elasticity Problem.
A finite element analysis for elastoplastic bodies obeying Hencky's law
Using the Haar-Kármán principle, approximate solutions of the basic boundary value problems are proposed and studied, which consist of piecewise linear stress fields on composite triangles. The torsion problem is solved in an analogous manner. Some convergence results are proven.
A finite element analysis for the Signorini problem in plane elastostatics
A finite element discretization of the contact between two membranes
From the fundamental laws of elasticity, we write a model for the contact between two membranes and we perform the analysis of the corresponding system of variational inequalities. We propose a finite element discretization of this problem and prove its well-posedness. We also establish a priori and a posteriori error estimates.
A finite element discretization of the contact between two membranes
From the fundamental laws of elasticity, we write a model for the contact between two membranes and we perform the analysis of the corresponding system of variational inequalities. We propose a finite element discretization of this problem and prove its well-posedness. We also establish a priori and a posteriori error estimates.
A Finite Element Lumped Mass Scheme for Solving Eigenvalue Problems of Circular Arches.
A Finite Element Lumped Mass Scheme for Solving Eigenvalue Problems of Circular Arches.
A finite element method for stiffened plates
The aim of this paper is to analyze a low order finite element method for a stiffened plate. The plate is modeled by Reissner-Mindlin equations and the stiffener by Timoshenko beams equations. The resulting problem is shown to be well posed. In the case of concentric stiffeners it decouples into two problems, one for the in-plane plate deformation and the other for the bending of the plate. The analysis and discretization of the first one is straightforward. The second one is shown to have a solution...
A finite element method for stiffened plates
The aim of this paper is to analyze a low order finite element method for a stiffened plate. The plate is modeled by Reissner-Mindlin equations and the stiffener by Timoshenko beams equations. The resulting problem is shown to be well posed. In the case of concentric stiffeners it decouples into two problems, one for the in-plane plate deformation and the other for the bending of the plate. The analysis and discretization of the first one is straightforward. The second one is shown to have a solution...
A finite element solution for plasticity with strain-hardening
A Finite-Difference Approximation for the Eigenvalue of the Clamped Plate.
A frictionless contact problem for viscoelastic materials.
A full discretization of the time-dependent Navier-Stokes equations by a two-grid scheme
We study a two-grid scheme fully discrete in time and space for solving the Navier-Stokes system. In the first step, the fully non-linear problem is discretized in space on a coarse grid with mesh-size H and time step k. In the second step, the problem is discretized in space on a fine grid with mesh-size h and the same time step, and linearized around the velocity uH computed in the first step. The two-grid strategy is motivated by the fact that under suitable assumptions, the contribution of uH...
A Galerkin spectral approximation in linearized beam theory
A Galerkin-parameterization method for the optimal control of smart microbeams.
A Generalization of the Schwarz Alternating Method to an Arbitrary Number of Subdomains.
A generalization to nonlinear hardening of the first shakedown theorem for discrete elastic-plastic structural models
In the plastic constitutive laws the yield functions are assumed to be linear in the stresses, but generally non-linear in the internal variables which are non-decreasing measures of the contribution to plastic strains by each face of the yield surface. The structural models referred to for simplicity are aggregates of constant-strain finite elements. Influence of geometry changes on equilibrium are allowed for in a linearized way (the equilibrium equation contains a bilinear term in the displacements...
A geometrically nonlinear analysis of laminated composite plates using a shear deformation theory
A shear deformation theory is developed to analyse the geometrically nonlinear behaviour of layered composite plates under transverse loads. The theory accounts for the transverse shear (as in the Reissner Mindlin plate theory) and large rotations (in the sense of the von Karman theory) suitable for simulating the behaviour of moderately thick plates. Square and rectangular plates are considered: the numerical results are obtained by a finite element computational procedure and are given for various...
A hybrid finite element method to compute the free vibration frequencies of a clamped plate
A locking-free finite element method for the buckling problem of a non-homogeneous Timoshenko beam
The aim of this paper is to develop a finite element method which allows computing the buckling coefficients and modes of a non-homogeneous Timoshenko beam. Studying the spectral properties of a non-compact operator, we show that the relevant buckling coefficients correspond to isolated eigenvalues of finite multiplicity. Optimal order error estimates are proved for the eigenfunctions as well as a double order of convergence for the eigenvalues using classical abstract spectral approximation theory...