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A model of seismic excitation

Piero Villaggio (2004)

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

The influence of a seismic wave on a building is customarily described as a force, a function of the time, whose explicit expression is prescribed. We here suggest a one-dimensional model able to relate this force to the sudden onset of a fault in the rock layer on which the building is built.

Homogenization of many-body structures subject to large deformations

Philipp Emanuel Stelzig (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We give a first contribution to the homogenization of many-body structures that are exposed to large deformations and obey the noninterpenetration constraint. The many-body structures considered here resemble cord-belts like they are used to reinforce pneumatic tires. We establish and analyze an idealized model for such many-body structures in which the subbodies are assumed to be hyperelastic with a polyconvex energy density and shall exhibit an initial brittle bond with their neighbors. Noninterpenetration...

Homogenization of many-body structures subject to large deformations

Philipp Emanuel Stelzig (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We give a first contribution to the homogenization of many-body structures that are exposed to large deformations and obey the noninterpenetration constraint. The many-body structures considered here resemble cord-belts like they are used to reinforce pneumatic tires. We establish and analyze an idealized model for such many-body structures in which the subbodies are assumed to be hyperelastic with a polyconvex energy density and shall exhibit an...

Locking-Free Finite Elements for Unilateral Crack Problems in Elasticity

Z. Belhachmi, J.-M. Sac-Epée, S. Tahir (2009)

Mathematical Modelling of Natural Phenomena

We consider mixed and hybrid variational formulations to the linearized elasticity system in domains with cracks. Inequality type conditions are prescribed at the crack faces which results in unilateral contact problems. The variational formulations are extended to the whole domain including the cracks which yields, for each problem, a smooth domain formulation. Mixed finite element methods such as PEERS or BDM methods are designed to avoid locking for nearly incompressible materials in plane elasticity....

On a 3D-Hypersingular Equation of a Problem for a Crack

Samko, Stefan (2011)

Fractional Calculus and Applied Analysis

MSC 2010: 45DB05, 45E05, 78A45We show that a certain axisymmetric hypersingular integral equation arising in problems of cracks in the elasticity theory may be explicitly solved in the case where the crack occupies a plane circle. We give three different forms of the resolving formula. Two of them involve regular kernels, while the third one involves a singular kernel, but requires less regularity assumptions on the the right-hand side of the equation.

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