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A locking-free finite element method for the buckling problem of a non-homogeneous Timoshenko beam

Carlo Lovadina, David Mora, Rodolfo Rodríguez (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

A locking-free finite element method for the buckling problem of a non-homogeneous Timoshenko beam

Carlo Lovadina, David Mora, Rodolfo Rodríguez (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

A mathematical model of suspension bridges

Gabriela Liţcanu (2004)

Applications of Mathematics

We prove the existence of weak T-periodic solutions for a nonlinear mathematical model associated with suspension bridges. Under further assumptions a regularity result is also given.

A mixed finite element method for plate bending with a unilateral inner obstacle

Ivan Hlaváček (1994)

Applications of Mathematics

A unilateral problem of an elastic plate above a rigid interior obstacle is solved on the basis of a mixed variational inequality formulation. Using the saddle point theory and the Herrmann-Johnson scheme for a simultaneous computation of deflections and moments, an iterative procedure is proposed, each step of which consists in a linear plate problem. The existence, uniqueness and some convergence analysis is presented.

A model problem for boundary layers of thin elastic shells

Philippe Karamian, Jacqueline Sanchez-Hubert, Évarisite Sanchez Palencia (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a model problem (with constant coefficients and simplified geometry) for the boundary layer phenomena which appear in thin shell theory as the relative thickness ε of the shell tends to zero. For ε = 0 our problem is parabolic, then it is a model of developpable surfaces. Boundary layers along and across the characteristic have very different structure. It also appears internal layers associated with propagations of singularities along the characteristics. The special structure of...

A nonlinear model of a turbine blade by asymptotic analysis

José Rodríguez (2002)

International Journal of Applied Mathematics and Computer Science

In this paper we obtain a limit model for a turbine blade fixed to a 3D solid. This model is a three-dimensional linear elasticity problem in the 3D part of the piece (the rotor) and a two-dimensional problem (the nonlinear shallow shell equations) in the 2D part (the turbine blade), with junction conditions in the part of the turbine blade fixed to the rotor. To obtain this model, we perform an asymptotic analysis, starting with the nonlinear three-dimensional elasticity equations on all the pieces...

Currently displaying 21 – 40 of 684