Elasticity of initially stressed bodies with voids. Weak solutions
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Marin Marin (1999)
Rendiconti del Seminario Matematico della Università di Padova
István Ecsedi, Ákos József Lengyel (2015)
Curved and Layered Structures
This paper presents a derivation of the Rayleigh- Betti reciprocity relation for layered curved composite beams with interlayer slip. The principle of minimum of potential energy is also formulated for two-layer curved composite beams and its applications are illustrated by numerical examples. The solution of the presented problems are obtained by the Ritz method. The applications of the Rayleigh-Betti reciprocity relation proven are illustrated by some examples.
Marco Bonacini (2013)
ESAIM: Control, Optimisation and Calculus of Variations
In the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer...
Marian Bocea, Irene Fonseca (2002)
ESAIM: Control, Optimisation and Calculus of Variations
3D-2D asymptotic analysis for thin structures rests on the mastery of scaled gradients bounded in Here it is shown that, up to a subsequence, may be decomposed as where carries all the concentration effects, i.e. is equi-integrable, and captures the oscillatory behavior, i.e. in measure. In addition, if is a recovering sequence then nearby
Marian Bocea, Irene Fonseca (2010)
ESAIM: Control, Optimisation and Calculus of Variations
3D-2D asymptotic analysis for thin structures rests on the mastery of scaled gradients bounded in Here it is shown that, up to a subsequence, may be decomposed as where carries all the concentration effects, i.e. is equi-integrable, and captures the oscillatory behavior, i.e. in measure. In addition, if is a recovering sequence then nearby
Igor Brilla (1990)
Aplikace matematiky
The paper deals with the analysis of generalized von Kármán equations which desribe stability of a thin circular viscoelastic clamped plate of constant thickness under a uniform compressible load which is applied along its edge and depends on a real parameter. The meaning of a solution of the mathematical problem is extended and various equivalent reformulations of the problem are considered. The structural pattern of the generalized von Kármán equations is analyzed from the point of view of nonlinear...
Giovambattista Amendola, Adele Manes (1986)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
In this work we prove that the thermoelastic equilibrium problem in the context of the linear theory for thermoelastic incompressible solids has one and only one solution.
Nazarov, S.A. (2004)
Journal of Mathematical Sciences (New York)
Martin Kružík, Johannes Zimmer (2010)
ESAIM: Control, Optimisation and Calculus of Variations
Rate-independent problems are considered, where the stored energy density is a function of the gradient. The stored energy density may not be quasiconvex and is assumed to grow linearly. Moreover, arbitrary behaviour at infinity is allowed. In particular, the stored energy density is not required to coincide at infinity with a positively 1-homogeneous function. The existence of a rate-independent process is shown in the so-called energetic formulation.
Shao-Yuan Huang, Ping-Han Hsieh (2023)
Czechoslovak Mathematical Journal
We study the exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems where , , is a bifurcation parameter, is an evolution parameter, and is either or . We prove that the corresponding bifurcation curve is -shape. Thus, the exact multiplicity of positive solutions can be obtained.
Elgindi, M.B.M. (1994)
International Journal of Mathematics and Mathematical Sciences
Bonetti, Elena, Bonfanti, Giovanna (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Amassad, Amina, Fabre, Caroline (2002)
International Journal of Mathematics and Mathematical Sciences
Daniel Coutand (1999)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Daniel Coutand (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
A justification of the two-dimensional nonlinear “membrane” equations for a plate made of a Saint Venant-Kirchhoff material has been given by Fox et al. [9] by means of the method of formal asymptotic expansions applied to the three-dimensional equations of nonlinear elasticity. This model, which retains the material-frame indifference of the original three dimensional problem in the sense that its energy density is invariant under the rotations of , is equivalent to finding the critical points...
Elgindi, M.B.M., Yen, D.H.Y. (1992)
International Journal of Mathematics and Mathematical Sciences
Sergio Conti, Georg Dolzmann, Bernd Kirchheim (2007)
Annales de l'I.H.P. Analyse non linéaire
Marius Cocu, Rémi Rocca (2000)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Marius Cocu, Rémi Rocca (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
We consider a two dimensional elastic body submitted to unilateral contact conditions, local friction and adhesion on a part of his boundary. After discretizing the variational formulation with respect to time we use a smoothing technique to approximate the friction term by an auxiliary problem. A shifting technique enables us to obtain the existence of incremental solutions with bounds independent of the regularization parameter. We finally obtain the existence of a quasistatic solution...
Josip Tambača, Igor Velčić (2010)
ESAIM: Control, Optimisation and Calculus of Variations
In this paper we give an existence theorem for the equilibrium problem for nonlinear micropolar elastic body. We consider the problem in its minimization formulation and apply the direct methods of the calculus of variations. As the main step towards the existence theorem, under some conditions, we prove the equivalence of the sequential weak lower semicontinuity of the total energy and the quasiconvexity, in some variables, of the stored energy function.
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