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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)...
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...
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...
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...
We consider the problem of placing a Dirichlet region made by n small balls of given radius in a given domain subject to a force f in order to minimize the compliance of the configuration. Then we let n tend to infinity and look for the Γ-limit of suitably scaled functionals, in order to get informations on the asymptotical distribution of the centres of the balls. This problem is both linked to optimal location and shape optimization problems.
Four optimal design problems and a weight minimization problem are considered for elastic plates with small bending rigidity, resting on a unilateral elastic foundation, with inner rigid obstacles and a friction condition on a part of the boundary. The state problem is represented by a variational inequality and the design variables influence both the coefficients and the set of admissible state functions. If some input data are allowed to be uncertain a new method of reliable solutions is employed....
In addition to the optimal design and worst scenario problems formulated in a previous paper [3], approximate optimization problems are introduced, making use of the finite element method. The solvability of the approximate problems is proved on the basis of a general theorem of [3]. When the mesh size tends to zero, a subsequence of any sequence of approximate solutions converges uniformly to a solution of the continuous problem.
Optimal design problems in mechanics can be mathematically formulated as optimal control tasks. The minimum principle is employed in solving such problems. This principle allows us to write down optimal design problems as Multipoint Boundary Value Problems (MPBVPs). The dimension of MPBVPs is an essential restriction that decides on numerical difficulties. Optimal control theory does not give much information about the control structure, i.e., about the sequence of the forms of the right-hand sides...
We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset of a reference domain, and the complement of is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure , which is the total work of the pressure and...
We present, analyze, and implement a new method for the design of
the stiffest structure subject to a pressure load or a given field
of internal forces. Our structure is represented as a subset S of
a reference domain, and the complement of S is made of two other
“phases”, the “void” and a fictitious “liquid” that exerts a
pressure force on its interface with the solid structure. The
problem we consider is to minimize the compliance of the structure
S, which is the total work of the pressure...
Free material optimization solves an important problem of structural engineering, i.e. to find the stiffest structure for given loads and boundary conditions. Its mathematical formulation leads to a saddle-point problem. It can be solved numerically by the finite element method. The convergence of the finite element method can be proved if the spaces involved satisfy suitable approximation assumptions. An example of a finite-element discretization is included.
The paper is a continuation of a previous work of the same authors dealing with homogenization processes for some energies of integral type arising in the modeling of rubber-like elastomers. The previous paper took into account the general case of the homogenization of energies in presence of pointwise oscillating constraints on the admissible deformations. In the present paper homogenization processes are treated in the particular case of fixed constraints set, in which minimal coerciveness hypotheses...
The paper is a continuation of a previous work of the same authors
dealing with homogenization processes for some energies
of integral type arising in the modeling of rubber-like elastomers.
The previous paper took into account the general case of the
homogenization of energies in presence of pointwise oscillating
constraints on the admissible deformations.
In the present paper homogenization processes are treated in the
particular case of fixed constraints set, in which minimal
coerciveness hypotheses...
A design optimization problem for an elastic beam with a unilateral elastic foundation is analyzed. Euler-Bernoulli's model for the beam and Winkler's model for the foundation are considered. The state problem is represented by a nonlinear semicoercive problem of 4th order with mixed boundary conditions. The thickness of the beam and the stiffness of the foundation are optimized with respect to a cost functional. We establish solvability conditions for the state problem and study the existence of...
We minimize, with respect to shape, the moment of inertia of a turbine having the given lowest eigenfrequency of the torsional oscillations. The necessary conditions of optimality in conjunction with certain physical parameters admit a unique optimal design.
We minimize, with respect to shape, the moment of inertia of a
turbine having the given
lowest eigenfrequency of the torsional oscillations. The necessary
conditions of optimality in conjunction with certain
physical parameters admit a unique optimal design.
A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for...
The gradient based topological optimization tools introduced during the last ten years tend naturally to modify the topology of a domain by creating small holes inside the domain. Once these holes have been created, they usually remain unchanged, at least during the topological phase of the optimization algorithm. In this paper, a new asymptotic expansion is introduced which allows to decide whether an existing hole must be removed or not for improving the cost function. Then, two numerical examples...
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