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The Singularity Expansion Method applied to the transient motions of a floating elastic plate

Christophe Hazard, François Loret (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we propose an original approach for the simulation of the time-dependent response of a floating elastic plate using the so-called Singularity Expansion Method. This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles...

The unbonded contact problem of a rectangular plate resting on an elastic foundation

Luigi Ascione, Renato S. Olivito, Giuseppe Spadea (1983)

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

In questo lavoro viene analizzato il problema di equilibrio statico di una piastra rettangolare in contatto unilaterale e senza attrito con un mezzo elastico. Si esaminano i due modelli di fondazione alla Winkler e di semispazio elastico. Il problema viene risolto mediante discretizzazione agli elementi finiti utilizzando un approccio di tipo «penalty». La rapida convergenza del metodo e la sua efficienza sono dimostrate dagli esempi studiati, che riguardano sia piastre quadrate che rettangolari...

Unconditionally stable mid-point time integration in elastic-plastic dynamics

Alberto Corigliano, Umberto Perego (1990)

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

The dynamic analysis of elastoplastic systems discretized by finite elements is dealt with. The material behaviour is described by a rather general internal variable model. The unknown fields are modelled in terms of suitable variables, generalized in Prager's sense. Time integrations are carried out by means of a generalized mid-point rule. The resulting nonlinear equations expressing dynamic equilibrium of the finite step problem are solved by means of a Newton-Raphson iterative scheme. The unconditional...

Variational inequalities in plasticity with strain-hardening - equilibrium finite element approach

Zdeněk Kestřánek (1986)

Aplikace matematiky

The incremental finite element method is applied to find the numerical solution of the plasticity problem with strain-hardening. Following Watwood and Hartz, the stress field is approximated by equilibrium triangular elements with linear functions. The field of the strain-hardening parameter is considered to be piecewise linear. The resulting nonlinear optimization problem with constraints is solved by the Lagrange multipliers method with additional variables. A comparison of the results obtained...

Variational-hemivariational inequalities in nonlinear elasticity. The coercive case

Panagiotis D. Panagiotopoulos (1988)

Aplikace matematiky

Existence of a solution of the problem of nonlinear elasticity with non-classical boundary conditions, when the relationship between the corresponding dual quantities is given in terms of a nonmonotone and generally multivalued relation. The mathematical formulation leads to a problem of non-smooth and nonconvex optimization, and in its weak form to hemivariational inequalities and to the determination of the so called substationary points of the given potential.

Von Kármán equations. III. Solvability of the von Kármán equations with conditions for geometry of the boundary of the domain

Július Cibula (1991)

Applications of Mathematics

Solvability of the general boundary value problem for von Kármán system of nonlinear equations is studied. The problem is reduced to an operator equation. It is shown that the corresponding functional of energy is coercive and weakly lower semicontinuous. Then the functional of energy attains absolute minimum which is a variational solution of the problem.

Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side

Ivan Hlaváček, Michal Křížek (1992)

Applications of Mathematics

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 own weight and to the hydrostatic presure. Existence of an optimal shape is proved. Using a penalty method and finite element technique, approximate solutions are proposed and their convergence is analyzed.

Weight minimization of elastic bodies weakly supporting tension. II. Domains with two curved sides

Ivan Hlaváček, Michal Křížek (1992)

Applications of Mathematics

Extending the results of the previous paper [1], the authors consider elastic bodies with two design variables, i.e. "curved trapezoids" with two curved variable sides. The left side is loaded by a hydrostatic pressure. Approximations of the boundary are defined by cubic Hermite splines and piecewise linear finite elements are used for the displacements. Both existence and some convergence analysis is presented for approximate penalized optimal design problems.

Young-measure approximations for elastodynamics with non-monotone stress-strain relations

Carsten Carstensen, Marc Oliver Rieger (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Microstructures in phase-transitions of alloys are modeled by the energy minimization of a nonconvex energy density . Their time-evolution leads to a nonlinear wave equation with the non-monotone stress-strain relation plus proper boundary and initial conditions. This hyperbolic-elliptic initial-boundary value problem of changing types allows, in general, solely Young-measure solutions. This paper introduces a fully-numerical time-space discretization of this equation in a corresponding very...

Young-Measure approximations for elastodynamics with non-monotone stress-strain relations

Carsten Carstensen, Marc Oliver Rieger (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Microstructures in phase-transitions of alloys are modeled by the energy minimization of a nonconvex energy density ϕ. Their time-evolution leads to a nonlinear wave equation with the non-monotone stress-strain relation plus proper boundary and initial conditions. This hyperbolic-elliptic initial-boundary value problem of changing types allows, in general, solely Young-measure solutions. This paper introduces a fully-numerical time-space discretization of this equation in a corresponding...

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