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Regularity and optimal control of quasicoupled and coupled heating processes

Jiří Jarušek (1996)

Applications of Mathematics

Sufficient conditions for the stresses in the threedimensional linearized coupled thermoelastic system including viscoelasticity to be continuous and bounded are derived and optimization of heating processes described by quasicoupled or partially linearized coupled thermoelastic systems with constraints on stresses is treated. Due to the consideration of heating regimes being “as nonregular as possible” and because of the well-known lack of results concerning the classical regularity of solutions...

Relaxed hyperelastic curves

Ahmet Yücesan, Gözde Özkan, Yasemín Yay (2011)

Annales Polonici Mathematici

We define relaxed hyperelastic curve, which is a generalization of relaxed elastic lines, on an oriented surface in three-dimensional Euclidean space E³, and we derive the intrinsic equations for a relaxed hyperelastic curve on a surface. Then, by examining relaxed hyperelastic curves in a plane, on a sphere and on a cylinder, we show that geodesics are relaxed hyperelastic curves in a plane and on a sphere. But on a cylinder, they are relaxed hyperelastic curves only in special cases.

Reliable solutions of problems in the deformation theory of plasticity with respect to uncertain material function

Ivan Hlaváček (1996)

Applications of Mathematics

Maximization problems are formulated for a class of quasistatic problems in the deformation theory of plasticity with respect to an uncertainty in the material function. Approximate problems are introduced on the basis of cubic Hermite splines and finite elements. The solvability of both continuous and approximate problems is proved and some convergence analysis presented.

Remarks on Carleman estimates and exact controllability of the Lamé system

Oleg Yu. Imanuvilov, Masahiro Yamamoto (2002)

Journées équations aux dérivées partielles

In this paper we established the Carleman estimate for the two dimensional Lamé system with the zero Dirichlet boundary conditions. Using this estimate we proved the exact controllability result for the Lamé system with with a control locally distributed over a subdomain which satisfies to a certain type of nontrapping conditions.

Remarks on materials with memory

Victor Mizel (1992)

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

The mistaken notion that consistency with fading memory should require uniqueness is refuted by citation of the sources. Indeed, insistence on uniqueness would exclude many examples from non-linear elasticity and would exclude materials capable of exhibiting hysteresis.

Remarks on the theory of elasticity

Sergio Conti, Camillo de Lellis (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In compressible Neohookean elasticity one minimizes functionals which are composed by the sum of the L 2 norm of the deformation gradient and a nonlinear function of the determinant of the gradient. Non–interpenetrability of matter is then represented by additional invertibility conditions. An existence theory which includes a precise notion of invertibility and allows for cavitation was formulated by Müller and Spector in 1995. It applies, however, only if some L p -norm of the gradient with p > 2 is controlled...

Residual a posteriori error estimators for contact problems in elasticity

Patrick Hild, Serge Nicaise (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the unilateral contact problem in linear elasticity. We define two a posteriori error estimators of residual type to evaluate the accuracy of the mixed finite element approximation of the contact problem. Upper and lower bounds of the discretization error are proved for both estimators and several computations are performed to illustrate the theoretical results.

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