Method of relaxation applied to optimization of discrete systems.
Modeling and optimization of non-symmetric plates
Modellazione e calcolo di strutture in materiale non resistente a trazione
Si affronta il problema del calcolo dello stato tensionale in strutture costituite da materiale non resistente a trazione ed elastico lineare a compressione. Si formula la legge costitutiva e se ne fornisce l'espressione esplicita nel caso di stati tensionali monoassiali, biassiali e triassiali. Si imposta quindi il problema dell'equilibrio elastico e si discute sulla condizione da imporre ai carichi affinché venga assicurata l'esistenza della soluzione. Si sviluppa la formulazione agli elementi...
Multi-phase structural optimization via a level set method
We consider the optimal distribution of several elastic materials in a fixed working domain. In order to optimize both the geometry and topology of the mixture we rely on the level set method for the description of the interfaces between the different phases. We discuss various approaches, based on Hadamard method of boundary variations, for computing shape derivatives which are the key ingredients for a steepest descent algorithm. The shape gradient obtained for a sharp interface involves jump...
Non unicità dell'energia libera per materiali viscoelastici
La non unicità dell'energia libera per un materiale viscoelastico di tipo «rate» viene provata mediante la determinazione di un controesempio.
Nonsmooth optimal design problems for the Kirchhoff plate with unilateral conditions
Note critiche sui carichi di collasso dei continui bidimensionali isotropi
Nei continui bidimensionali isotropi in fase fessurata si dimostra, nella sola ipotesi che le linee di rottura rappresentino univocamente il meccanismo di collasso, la impossibilità di ottenere un moltiplicatore ottimale del carico. La configurazione reale può essere definita considerando anche la capacità deformativa del continuo in esame.
Note on a mixed variational principle in finite elasticity
In the present context the variation is performed keeping the deformed configuration fixed while a suitable material stress tensor and the material coordinates are required to vary independently. The variational principle turns out to be equivalent to an equilibrium problem of placements and tractions prescribed at the boundary of a body of finite extent.
Numerical minimization of eigenmodes of a membrane with respect to the domain
In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.
Numerical minimization of eigenmodes of a membrane with respect to the domain
In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.
On a problem of potential wells.
On an unconventional variational method for solving the problem of linear elasticity with Neumann or periodic boundary conditions
A new variational formulation of the linear elasticity problem with Neumann or periodic boundary conditions is presented. This formulation does not require any quotient spaces and is advisable for finite element approximations.
On computer aided shape optimization
On numerical solution of weight minimization of elastic bodies weakly supporting tension
Shape optimization of a two-dimensional elastic body is considered, provided the material is weakly supporting tension. The problem generalizes that of a masonry dam subjected to its weight and to the hydrostatic pressure. A part of the boundary has to be found so as to minimize a given cost functional. The numerical realization using a penalty method and finite element technique is presented. Some typical results are shown.
On Reissner's variational theorem for boundary values in linear elasticity
On the mechanical behaviour of laminated curved beams: a simple model which takes into account the warping effects
A mechanical one-dimensional model which describes the dynamical behaviour of laminated curved beams is formulated. It is assumed that each lamina can be regarded as a Timoshenko's beam and that the rotations of the cross sections can differ from one lamina to another. The relative displacements at the interfaces of adjacent laminae are assumed to be zero. Consequently the model includes a shear deformability, due to the warping of the cross beam section consequent to the variability of the laminae...
On the membrane approximation for thin elastic shells in the hyperbolic case.
We consider the variational formulation of the problem of elastic shells in the membrane approximation, when the medium surface is hyperbolic. It appears that the corresponding bilinear form behaves as some kind of two-dimensional elasticity without shear rigidity. This amounts to saying that the membrane behaves rather as a net made of elastic strings disposed along the asymptotic curves of the surface than as an elastic two-dimensional medium. The mathematical and physical reasons of this behavior...
On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions
A control of the system of nonlinear Kármán's equations for a thin elastic plate with clamped edge is considered. The transversal loading plays the role of the control variable. The set of admissible controls is chosen in a way guaranteeing the unique solvability of the state function with respect to the control variable is proved. A disscussion of uniqueness of the optimal control and some necessary conditions of optimality are presented.
On the optimal control problem governed by the equations of von Kármán. II. Mixed boundary conditions
A control of the system of Kármán's equations for a thin elastic plate is considered. Existence of an optimal transversal load and optimal stress function, respectively, is proven. The set of admissible functions is chosen in a way guaranteeing the unique solvability of the state problem. The differentiability of the state function with respect to the control variable, uniqueness of the optimal control and some necessary conditions of optimality are discussed.
On the optimal control problem governed by the equations of von Kármán. III. The case of an arbitrary large perpendicular load
We shall deal with an optimal control problem for the deffection of a thin elastic plate. We consider the perpendicular load on the plate as the control variable. In contrast to the papers [1], [2], arbitrarily large loads are edmitted. As the unicity of a solution of the state equation is not guaranteed, we consider the cost functional defined on the set of admissible controls and states, and the state equation plays the role of the constraint. The existence of an optimal couple (i.e., control...