Josef Malík (1998)
Applications of Mathematics
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The main goal of the paper is to give a variational formulation of the behaviour of bolt systems in rock mass. The problem arises in geomechanics where bolt systems are applied to reinforce underground openings by inserting steel bars or cables. After giving a variational formulation, we prove the existence and uniqueness and some other properties.
Ivan Hlaváček (1998)
Applications of Mathematics
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We apply the method of reliable solutions to the bending problem for an elasto-plastic beam, considering the yield function of the von Mises type with uncertain coefficients. The compatibility method is used to find the moments and shear forces. Then we solve a maximization problem for these quantities with respect to the uncertain input data.
Oanh Chau, Dumitru Motreanu, Mircea Sofonea (2002)
Applications of Mathematics
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We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution...
Isabel N. Figueiredo, Georg Stadler (2009)
ESAIM: Control, Optimisation and Calculus of Variations
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The purpose of this paper is to derive and study a new asymptotic model for the equilibrium state of a thin anisotropic piezoelectric plate in frictional contact with a rigid obstacle. In the asymptotic process, the thickness of the piezoelectric plate is driven to zero and the convergence of the unknowns is studied. This leads to two-dimensional Kirchhoff-Love plate equations, in which mechanical displacement and electric potential are partly decoupled. Based on this model numerical...
Jindřich Nečas, Luděk Trávníček (1980)
Aplikace matematiky
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An abstract theory of evolutionary variational inequalities and its applications to the traction boundary value problems of elastoplasticity are studied, using the penalty method to prove the existence of a solution.