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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 quasi-Newton algorithm based on a reduced model for fluid-structure interaction problems in blood flows

Jean-Frédéric Gerbeau, Marina Vidrascu (2003)

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

We propose a quasi-Newton algorithm for solving fluid-structure interaction problems. The basic idea of the method is to build an approximate tangent operator which is cost effective and which takes into account the so-called added mass effect. Various test cases show that the method allows a significant reduction of the computational effort compared to relaxed fixed point algorithms. We present 2D and 3D fluid-structure simulations performed either with a simple 1D structure model or with shells...

A Quasi-Newton Algorithm Based on a Reduced Model for Fluid-Structure Interaction Problems in Blood Flows

Jean-Frédéric Gerbeau, Marina Vidrascu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose a quasi-Newton algorithm for solving fluid-structure interaction problems. The basic idea of the method is to build an approximate tangent operator which is cost effective and which takes into account the so-called added mass effect. Various test cases show that the method allows a significant reduction of the computational effort compared to relaxed fixed point algorithms. We present 2D and 3D fluid-structure simulations performed either with a simple 1D structure model or with...

Buckling of anisotropic shells. I

Anukul De (1983)

Aplikace matematiky

The formulation of differential equations of buckling problem of anisotropic cylindrical shell is presented here. The solution for anisotropic cylindrical shells without shear load in case of two way compression is found out from the differential equations formulated. The corresponding results for isotropic case are deduced as a particular case.

Buckling of anisotropic shells. II

Anukul De (1983)

Aplikace matematiky

The object of this paper is to find the solution of the differential equation of the buckling problem of anisotropic cylindrical shells with shear load in case of torsion of a long tube. The critical values of the shear load and the total torque are also found. The corresponding results for the isotropic case are deduced as a special case.

Buckling of beam-column problem of anisotropic cylindrical shells

Anukul De (1986)

Aplikace matematiky

The object of this paper is to formulate the differential equations in the beamcolumn problem of the buckling of anisotropic cylindrical shells, placed between the plates of a testing machine subject to an axial load P and a radial load H of sufficient magnitude to bring the expansion without constraint of the edges produced by P to zero deflection. The solution is obtained with necessary boundary conditions and the corresponding results for the isotropic case are deduced.

Exact controllability of shells in minimal time

Paola Loreti (2001)

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

We prove an exact controllability result for thin cups using the Fourier method and recent improvements of Ingham type theorems, given in a previous paper [2].

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