Papers by Danilo Percivale
Abstract. In this paper we study the asymptotic behavior, as h-> oo, of the minimum points of ... more Abstract. In this paper we study the asymptotic behavior, as h-> oo, of the minimum points of the functionals where f(x, #) is periodic in xand convex in ~:, and u is vector valued. A convergence theorem is stated without uniform coerciveness assumptions.
Rendiconti Lincei - Matematica e Applicazioni
We characterize the solution to the Newton minimal resistance problem in a specific class of holl... more We characterize the solution to the Newton minimal resistance problem in a specific class of hollow profiles, satisfying a q-concavity condition. We treat two-dimensional bodies and radially symmetric three-dimensional bodies.
Calculus of Variations and Partial Differential Equations
We consider the topic of linearization of finite elasticity for pure traction problems. We charac... more We consider the topic of linearization of finite elasticity for pure traction problems. We characterize the variational limit for the approximating sequence of rescaled nonlinear elastic energies. We show that the limiting minimal value can be strictly lower than the minimal value of the standard linear elastic energy if a strict compatibility condition for external loads does not hold. The results are provided for both the compressible and the incompressible case.
This note provides a variational description of the mechanical effects of flexural stiffening of ... more This note provides a variational description of the mechanical effects of flexural stiffening of a 2D plate glued to an elastic-brittle or an elastic-plastic reinforcement. The reinforcement is assumed to be linear elastic outside possible free plastic yield lines or free crack. Explicit Euler equations and a compliance identity are shown for the reinforcement of a 1D beam.
We provide an approximation result for the pure traction problem of linearized elasticity in term... more We provide an approximation result for the pure traction problem of linearized elasticity in terms of local minimizers of finite elasticity, under the constraint of vanishing average curl for admissible deformation maps. When suitable rotations are included in the constraint, the limit is shown to be the linear elastic equilibrium associated to rotated loads.
Bollettino Della Unione Matematica Italiana, 2009
ABSTRACT
We obtain linear elasticity as $\Gamma$-limit of finite elasticity under incompressibility assump... more We obtain linear elasticity as $\Gamma$-limit of finite elasticity under incompressibility assumption and Dirichlet boundary conditions. The result is shown for a large class of energy densities for rubber-like materials.
Zeitschrift für angewandte Mathematik und Physik
We consider pure traction problems, and we show that incompressible linearized elasticity can be ... more We consider pure traction problems, and we show that incompressible linearized elasticity can be obtained as variational limit of incompressible finite elasticity under suitable conditions on external loads.
Calculus of Variations and Partial Differential Equations
We study an old variational problem formulated by Euler as Proposition 53 of his Scientia Navalis... more We study an old variational problem formulated by Euler as Proposition 53 of his Scientia Navalis by means of the direct method of the calculus of variations. Precisely, through relaxation arguments, we prove the existence of minimizers. We fully investigate the analytical structure of the minimizers in dependence of the geometric parameters and we identify the ranges of uniqueness and non-uniqueness.
Asymptotic Analysis
... Auteur(s) / Author(s). ANZELLOTTI G. (1) ; BALDO S. (1) ; PERCIVALE D. ; Affiliation(s) du ou... more ... Auteur(s) / Author(s). ANZELLOTTI G. (1) ; BALDO S. (1) ; PERCIVALE D. ; Affiliation(s) du ou des auteurs / Author(s) Affiliation(s). (1) Univ. ... Placa elástica. ; Localisation / Location. INIST-CNRS,Cote INIST : 21721, 35400004718426.0050. Nº notice refdoc (ud4) : 4179945. ...
ESAIM: Control, Optimisation and Calculus of Variations
We characterize the solution to the Newton minimal resistance problem in a class of radial q-conc... more We characterize the solution to the Newton minimal resistance problem in a class of radial q-concave profiles. We also give the corresponding result for one-dimensional profiles. Moreover, we provide a numerical optimization algorithm for the general nonradial case.
Archive for Rational Mechanics and Analysis
A limit elastic energy for pure traction problem is derived from re-scaled nonlinear energy of an... more A limit elastic energy for pure traction problem is derived from re-scaled nonlinear energy of an hyperelastic material body subject to an equilibrated force field. We show that the strains of minimizing sequences associated to re-scaled non linear energies weakly converge, up to subsequences, to the strains of minimizers of a limit energy, provided an additional compatibility condition is fulfilled by the force field. The limit energy is different from classical energy of linear elasticity; nevertheless the compatibility condition entails the coincidence of related minima and minimizers. A strong violation of this condition provides a limit energy which is unbounded from below, while a mild violation may produce a limit energy with infinitely many extra minimizers which are not minimizers of standard linear elastic energy and whose strains are not uniformly bounded. A relevant consequence of this analysis is that a rigorous validation of linear elasticity fails for compressive force fields that do not fulfil such compatibility condition. Contents 10 4. Limit problem and Linear Elasticity 17 References 22
Journal of Optimization Theory and Applications
A new energy functional for pure traction problems in elasticity has been deduced in [23] as the ... more A new energy functional for pure traction problems in elasticity has been deduced in [23] as the variational limit of nonlinear elastic energy functional for a material body subject to an equilibrated force field: a sort of Gamma limit with respect to the weak convergence of strains when a suitable small parameter tends to zero. This functional exhibits a gap that makes it different from the classical linear elasticity functional. Nevertheless a suitable compatibility condition on the force field ensures coincidence of related minima and minimizers. Here we show some relevant properties of the new functional and prove stronger convergence of minimizing sequences for suitable choices of nonlinear elastic energies. DRAFT Contents 1. Introduction 1 2. Structural properties of functional F 5 3. Preliminary variational convergence results 8 4. Strong convergence of minimizing sequences of F h 13 References 15
SIAM Journal on Mathematical Analysis
Some variational problems for a Föppl-von Kármán plate subject to general equilibrated loads are ... more Some variational problems for a Föppl-von Kármán plate subject to general equilibrated loads are studied. The existence of global minimizers is proved under the assumption that the out-of-plane displacement fulfils homogeneous Dirichlet condition on the whole boundary while the in-plane displacement fulfils nonhomogeneous Neumann condition. If the Dirichlet condition is prescribed only on a subset of the boundary, then the energy may be unbounded from below over the set of admissible configurations, as shown by several explicit conterexamples: in these cases the analysis of critical points is addressed through an asymptotic development of the energy functional in a neighborhood of the flat configuration. By a Γ-convergence approach we show that critical points of the Föpplvon Kármán energy can be strongly approximated by uniform Palais-Smale sequences of suitable functionals: this property leads to identify relevant features for critical points of approximating functionals, e.g. buckled configurations of the plate. Eventually we perform further analysis as the plate thickness tends to 0, by assuming that the plate is prestressed and the energy functional depends only on the transverse displacement around the given prestressed state: by this approach, first we identify suitable exponents of plate thickness for load scaling, then we show explicit asymptotic oscillating minimizers as a mechanism to relax compressive states in an annular plate. Contents 3. Scaling Föppl-von Kármán energy 4. Prestressed plates: oscillating versus flat equilibria. References
2016 IEEE 55th Conference on Decision and Control (CDC), 2016
We address the optimal allocation of the capacity of a single server to buffers with different ar... more We address the optimal allocation of the capacity of a single server to buffers with different arrival flows and priority. The well-posedness is studied in a general setting with a state equation having a lower semicontinuous, nonlinear r.h.s. and a linear discounted cost function. The solution of the problem given by a discontinuous feedback control is presented by referring to a two-buffer system under the assumption of the perfect knowledge of the inflow rates. Such an assumption is relaxed by using an output feedback control scheme, for which a reduced-order practical observer is proposed to estimate the unknown inflow rates. Ultimate boundedness is proved for such a setup by using a different control law that takes into account the loss of observability at steady state. The effectiveness of the resulting approach is shown by means of simulations.
IMA Journal of Applied Mathematics, 2016
Set Valued Analysis, 2002
Uploads
Papers by Danilo Percivale