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Luca Granieri (2010)
ESAIM: Control, Optimisation and Calculus of Variations
We provide an approximation of Mather variational problem by finite dimensional minimization problems in the framework of Γ-convergence. By a linear programming interpretation as done in [Evans and Gomes, ESAIM: COCV 8 (2002) 693–702] we state a duality theorem for the Mather problem, as well a finite dimensional approximation for the dual problem.
C. Lederman (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
B. Miara, L. Trabucho (1992)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
W. El Alem, A. El Hami, R. Ellaia (2010)
Mathematical Modelling of Natural Phenomena
In this paper, a new hybrid simulated annealing algorithm for constrained global optimization is proposed. We have developed a stochastic algorithm called ASAPSPSA that uses Adaptive Simulated Annealing algorithm (ASA). ASA is a series of modifications to the basic simulated annealing algorithm (SA) that gives the region containing the global solution of an objective function. In addition, Simultaneous Perturbation Stochastic Approximation (SPSA)...
Castrenze Polizzotto (1998)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
The concept of reduced plastic dissipation is introduced for a perfectly plastic rate-independent material not obeyng the associated normality rule and characterized by a strictly convex plastic potential function. A maximum principle is provided and shown to play the role of variational statement for the nonassociative constitutive equations. The Kuhn-Tucker conditions of this principle describe the actual material behaviour as that of a (fictitious) composite material with two plastic constituents,...
Michele Ciarletta, Edoardo Scarpetta (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
In the context of the linear, dynamic problem for elastic bodies with voids, a minimum principle in terms of mechanical energy is stated. Involving a suitable (Reiss type) function in the minimizing functional, the minimum character achieved in the Laplace-transform domain is preserved when going back to the original time domain. Initial-boundary conditions of quite general type are considered.
Werner Horn, Jan Sokołowski (2005)
Control and Cybernetics
Xu Guo, Kang Zhao, Michel Wang (2005)
Control and Cybernetics
P.G. Ciarlet (1990)
Numerische Mathematik
Véronique Lods (1994)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Pablo V. Négron Marrero (1990/1991)
Numerische Mathematik
Patrick Penzler, Martin Rumpf, Benedikt Wirth (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear deformations and nonlinear hyperelastic constitutive laws. A weighted sum of the structure compliance, its weight, and its surface area are minimized. The resulting nonlinear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. Indeed, there exist different definitions for the compliance: the change in potential energy of the...
Patrick Penzler, Martin Rumpf, Benedikt Wirth (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear deformations and nonlinear hyperelastic constitutive laws. A weighted sum of the structure compliance, its weight, and its surface area are minimized. The resulting nonlinear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. Indeed, there exist different definitions for the compliance: the change in potential energy of the...
Patrick Penzler, Martin Rumpf, Benedikt Wirth (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear deformations and nonlinear hyperelastic constitutive laws. A weighted sum of the structure compliance, its weight, and its surface area are minimized. The resulting nonlinear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. Indeed, there exist different definitions for the compliance: the change in potential energy of the...
E. Bécache, T. Ha Duong (1994)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Casarino, Valentina, Percivale, Danilo (1996)
Journal of Convex Analysis
Claudia Comi, Umberto Perego (1991)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
The elastoplastic rate problem is formulated as an unconstrained saddle point problem which, in turn, is obtained by the Lagrange multiplier method from a kinematic minimum principle. The finite element discretization and the enforcement of the min-max conditions for the Lagrangean function lead to a set of algebraic governing relations (equilibrium, compatibility and constitutive law). It is shown how important properties of the continuum problem (like, e.g., symmetry, convexity, normality) carry...
Michal Křížek (1982)
Aplikace matematiky
The tetrahedral stress element is introduced and two different types of a finite piecewise linear approximation of the dual elasticity problem are investigated on a polyhedral domain. Fot both types a priori error estimates in -norm and in -norm are established, provided the solution is smooth enough. These estimates are based on the fact that for any polyhedron there exists a strongly regular family of decomprositions into tetrahedra, which is proved in the paper, too.
Patrick Le Tallec, Saloua Mani (1998)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Luis Trabucho (2002)
International Journal of Applied Mathematics and Computer Science
The subject of topology optimization has undergone an enormous practical development since the appearance of the paper by Bendso e and Kikuchi (1988), where some ideas from homogenization theory were put into practice. Since then, several engineering applications as well as different approaches have been developed successfully. However, it is difficult to find in the literature some analytical examples that might be used as a test in order to assess the validity of the solutions obtained with different...
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