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On quasistatic inelastic models of gradient type with convex composite constitutive equations

Krzysztof Chełmiński (2003)

Open Mathematics

This article defines and presents the mathematical analysis of a new class of models from the theory of inelastic deformations of metals. This new class, containing so called convex composite models, enlarges the class containing monotone models of gradient type defined in [1]. This paper starts to establish the existence theory for models from this new class; we restrict our investigations to the coercive and linear self-controlling case.

On semiconvexity properties of rotationally invariant functions in two dimensions

Miroslav Šilhavý (2004)

Czechoslovak Mathematical Journal

Let f be a function defined on the set 𝐌 2 × 2 of all 2 by 2 matrices that is invariant with respect to left and right multiplications of its argument by proper orthogonal matrices. The function f can be represented as a function f ˜ of the signed singular values of its matrix argument. The paper expresses the ordinary convexity, polyconvexity, and rank 1 convexity of f in terms of its representation f ˜ .

On Signorini problem for von Kármán equations. The case of angular domain

Jan Franců (1979)

Aplikace matematiky

The paper deals with the generalized Signorini problem. The used method of pseudomonotone semicoercive operator inequality is introduced in the paper by O. John. The existence result for smooth domains from the paper by O. John is extended to technically significant "angular" domains. The crucial point of the proof is the estimation of the nonlinear term which appears in the operator form of the problem. The substantial technical difficulties connected with non-smoothness of the boundary are overcome...

On some composite schemes of time integration in structural dynamics

Vala, Jiří (2019)

Programs and Algorithms of Numerical Mathematics

Numerical simulations of time-dependent behaviour of advances structures need the analysis of systems of partial differential equations of hyperbolic type, whose semi-discretization, using the Fourier multiplicative decomposition together with the finite element or similar techniques, leads to large sparse systems of ordinary differential equations. Effective and robust methods for numerical evaluation of their solutions in particular time steps are required; thus still new computational schemes...

On some viscoelastic models

Pasquale Renno (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Sia ℬ n un sistema linearmente viscoelastico, omogeneo ed isotropo, caratterizzato dalla funzione di memoria g n ⁢ ( t ) = ∑ k = 1 n B k ⁢ exp ⁡ ( - β k ⁢ t ) , tipica di numerosi polimeri solidi. Si dimostra che la soluzione fondamentale E n dell’operatore integrodifferenziale che descrive i moti di ℬ n è, in ogni punto del suo supporto, maggiorata da quella relativa ad un opportuno solido standard ℬ 1 Di conseguenza, è possibile applicare all’analisi qualitativa dei moti di ℬ n alcuni risultati stabiliti in [10], quali proprietà asintotiche, principi...

On symmetrically growing bodies.

Reuven Segev (1997)

Extracta Mathematicae

This work presents a setting for the formulation of the mechanics of growing bodies. By the mechanics of growing bodies we mean a theory in which the material structure of the body does not remain fixed. Material points may be added or removed from the body.

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