A characterization of families of function sets described by constraints on the gradient
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Antonio Corbo Esposito, Riccardo De Arcangelis (1994)
Annales de l'I.H.P. Analyse non linéaire
Peter Wall (1997)
Applications of Mathematics
In this paper we study a unidirectional and elastic fiber composite. We use the homogenization method to obtain numerical results of the plane strain bulk modulus and the transverse shear modulus. The results are compared with the Hashin-Shtrikman bounds and are found to be close to the lower bounds in both cases. This indicates that the lower bounds might be used as a first approximation of the plane strain bulk modulus and the transverse shear modulus. We also point out the connection with the...
Vincenzo Nesi, Enrico Rogora (2007)
ESAIM: Control, Optimisation and Calculus of Variations
The theory of compensated compactness of Murat and Tartar links the algebraic condition of rank-r convexity with the analytic condition of weak lower semicontinuity. The former is an algebraic condition and therefore it is, in principle, very easy to use. However, in applications of this theory, the need for an efficient classification of rank-r convex forms arises. In the present paper, we define the concept of extremal 2-forms and characterize them in the rotationally invariant jointly...
Usal, Melek (2010)
Mathematical Problems in Engineering
El Hajji, Mohamed (2000)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Giacinto Porco, Giuseppe Spadea, Raffaele Zinno (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
A shear deformation theory is developed to analyse the geometrically nonlinear behaviour of layered composite plates under transverse loads. The theory accounts for the transverse shear (as in the Reissner Mindlin plate theory) and large rotations (in the sense of the von Karman theory) suitable for simulating the behaviour of moderately thick plates. Square and rectangular plates are considered: the numerical results are obtained by a finite element computational procedure and are given for various...
Dario Benedetto, Emanuele Caglioti, Mario Pulvirenti (1999)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Dario Benedetto, Emanuele Caglioti, Mario Pulvirenti (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
In this short note we correct a conceptual error in the heuristic derivation of a kinetic equation used for the description of a one-dimensional granular medium in the so called quasi-elastic limit, presented by the same authors in reference[1]. The equation we derived is however correct so that, the rigorous analysis on this equation, which constituted the main purpose of that paper, remains unchanged.
P.G. Ciarlet (1990)
Numerische Mathematik
Milena Radnović (2003)
Publications de l'Institut Mathématique
Jindřich Nečas, Miloš Štípl (1976)
Aplikace matematiky
Let us have the system of partial differential equations of the linear elasticity. We show that the solution of this system with a bounded boundary condition is not generally bounded (i.e., the displacement vector is not bounded). This example is a modification of that given by E. De Giorgi [1].
Jean-François Babadjian, Marco Barchiesi (2009)
Annales de l'I.H.P. Analyse non linéaire
Gilbert, R.P., Panchenko, A. (1999)
Zeitschrift für Analysis und ihre Anwendungen
Piotr Bogusław Mucha, Piotr Rybka (2009)
Banach Center Publications
In this note we analyze equilibria of static Stefan type problems with crystalline/singular weighted mean curvature in the plane. Our main goal is to improve the meaning of variational solutions so that their properties allow us to call them almost classical solutions. The idea of our approach is based on a new definition of a composition of multivalued functions.
Andreas Prohl (1999)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Andreas Prohl (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
The minimization of nonconvex functionals naturally arises in materials sciences where deformation gradients in certain alloys exhibit microstructures. For example, minimizing sequences of the nonconvex Ericksen-James energy can be associated with deformations in martensitic materials that are observed in experiments[2,3]. — From the numerical point of view, classical conforming and nonconforming finite element discretizations have been observed to give minimizers with their quality being highly dependent...
Massoudi, Mehrdad (2005)
Mathematical Problems in Engineering
G. F. Dell'Antonio, R. Figari, E. Orlandi (1986)
Annales de l'I.H.P. Physique théorique
Ferdinando Auricchio, Carlo Lovadina, Alexandre L. Madureira (2004)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
In this paper, we derive and analyze a Reissner-Mindlin-like model for isotropic heterogeneous linearly elastic plates. The modeling procedure is based on a Hellinger-Reissner principle, which we modify to derive consistent models. Due to the material heterogeneity, the classical polynomial profiles for the plate shear stress are replaced by more sophisticated choices, that are asymptotically correct. In the homogeneous case we recover a Reissner-Mindlin model with as shear correction factor....
Ferdinando Auricchio, Carlo Lovadina, Alexandre L. Madureira (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
In this paper, we derive and analyze a Reissner-Mindlin-like model for isotropic heterogeneous linearly elastic plates. The modeling procedure is based on a Hellinger-Reissner principle, which we modify to derive consistent models. Due to the material heterogeneity, the classical polynomial profiles for the plate shear stress are replaced by more sophisticated choices, that are asymptotically correct. In the homogeneous case we recover a Reissner-Mindlin model with 5/6 as shear correction...
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