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The existence of a solution and a numerical method for the Timoshenko nonlinear wave system

Jemal Peradze (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The initial boundary value problem for a beam is considered in the Timoshenko model. Assuming the analyticity of the initial conditions, it is proved that the problem is solvable throughout the time interval. After that, a numerical algorithm, consisting of three steps, is constructed. The solution is approximated with respect to the spatial and time variables using the Galerkin method and a Crank–Nicholson type scheme. The system of equations obtained by discretization is solved by a version of...

The existence of a solution and a numerical method for the Timoshenko nonlinear wave system

Jemal Peradze (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The initial boundary value problem for a beam is considered in the Timoshenko model. Assuming the analyticity of the initial conditions, it is proved that the problem is solvable throughout the time interval. After that, a numerical algorithm, consisting of three steps, is constructed. The solution is approximated with respect to the spatial and time variables using the Galerkin method and a Crank–Nicholson type scheme. The system of equations obtained by discretization is solved by a version...

The nonlinear membrane model : a Young measure and varifold formulation

Med Lamine Leghmizi, Christian Licht, Gérard Michaille (2005)

ESAIM: Control, Optimisation and Calculus of Variations

We establish two new formulations of the membrane problem by working in the space of W Γ 0 1 , p ( Ω , 𝐑 3 ) -Young measures and W Γ 0 1 , p ( Ω , 𝐑 3 ) -varifolds. The energy functional related to these formulations is obtained as a limit of the 3 d formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing sequences...

The nonlinear membrane model: a Young measure and varifold formulation

Med Lamine Leghmizi, Christian Licht, Gérard Michaille (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We establish two new formulations of the membrane problem by working in the space of W Γ 0 1 , p ( Ω , 𝐑 3 ) -Young measures and W Γ 0 1 , p ( Ω , 𝐑 3 ) -varifolds. The energy functional related to these formulations is obtained as a limit of the 3d formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing...

The Singularity Expansion Method applied to the transient motions of a floating elastic plate

Christophe Hazard, François Loret (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we propose an original approach for the simulation of the time-dependent response of a floating elastic plate using the so-called Singularity Expansion Method. This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles...

Currently displaying 541 – 560 of 684