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A comparison of solvers for linear complementarity problems arising from large-scale masonry structures

Mark Ainsworth, L. Angela Mihai (2006)

Applications of Mathematics

We compare the numerical performance of several methods for solving the discrete contact problem arising from the finite element discretisation of elastic systems with numerous contact points. The problem is formulated as a variational inequality and discretised using piecewise quadratic finite elements on a triangulation of the domain. At the discrete level, the variational inequality is reformulated as a classical linear complementarity system. We compare several state-of-art algorithms that have...

A discretization method for the problem of a membrane constrained by elastic obstacle

Aldo Maceri (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questo lavoro sono dati alcuni modelli matematici per il problema di contatto tra una membrana ed un suolo od ostacolo elastico. Viene costruita una approssimazione lineare a tratti della soluzione e, tramite una disequazione variazionale discreta, se ne dà il corrispondente teorema di convergenza.

A finite element analysis for elastoplastic bodies obeying Hencky's law

Ivan Hlaváček (1981)

Aplikace matematiky

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 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 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...

A two well Liouville theorem

Andrew Lorent (2005)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we analyse the structure of approximate solutions to the compatible two well problem with the constraint that the surface energy of the solution is less than some fixed constant. We prove a quantitative estimate that can be seen as a two well analogue of the Liouville theorem of Friesecke James Müller. Let H = σ 0 0 σ - 1 for σ > 0 . Let 0 < ζ 1 < 1 < ζ 2 < . Let K : = S O 2 S O 2 H . Let u W 2 , 1 Q 1 0 be a C 1 invertible bilipschitz function with Lip u < ζ 2 , Lip u - 1 < ζ 1 - 1 . There exists positive constants 𝔠 1 < 1 and 𝔠 2 > 1 depending only on σ , ζ 1 , ζ 2 such that if ϵ 0 , 𝔠 1 and u satisfies the...

A Two Well Liouville Theorem

Andrew Lorent (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we analyse the structure of approximate solutions to the compatible two well problem with the constraint that the surface energy of the solution is less than some fixed constant. We prove a quantitative estimate that can be seen as a two well analogue of the Liouville theorem of Friesecke James Müller.
Let H = σ 0 0 σ - 1 for σ > 0 . Let 0 < ζ 1 < 1 < ζ 2 < . Let K : = S O 2 S O 2 H . Let u W 2 , 1 Q 1 0 be a invertible bilipschitz function with Lip u < ζ 2 , Lip u - 1 < ζ 1 - 1 . 
There exists positive constants 𝔠 1 < 1 and 𝔠 2 > 1 depending only on σ, ζ 1 , ζ 2 such that if ϵ 0 , 𝔠 1 and u satisfies...

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