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Linear Elastostatic Problems (linear + elastostatic_problem)
Selected AbstractsNonparametric probabilistic approach of uncertainties for elliptic boundary value problemINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6-7 2009Christian SoizeArticle first published online: 2 FEB 200 Abstract The paper is devoted to elliptic boundary value problems with uncertainties. Such a problem has already been analyzed in the context of the parametric probabilistic approach of system parameters uncertainties or for random media. Model uncertainties are induced by the mathematical,physical process, which allows the boundary value problem to be constructed from the design system. If experiments are not available, the Bayesian approach cannot be used to take into account model uncertainties. Recently, a nonparametric probabilistic approach of both the model uncertainties and system parameters uncertainties has been proposed by the author to analyze uncertain linear and non-linear dynamical systems. Nevertheless, the use of this concept that has to be developed for dynamical systems cannot directly be applied for elliptic boundary value problem, for instance, for a linear elastostatic problem relative to an elastic bounded domain. We then propose an extension of the nonparametric probabilistic approach in order to take into account model uncertainties for strictly elliptic boundary value problems. The theory and its validation are presented. Copyright © 2009 John Wiley & Sons, Ltd. [source] A fictitious energy approach for shape optimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2010M. Scherer Abstract This paper deals with shape optimization of continuous structures. As in early works on shape optimization, coordinates of boundary nodes of the FE-domain are directly chosen as design variables. Convergence problems and problems with jagged shapes are eliminated by a new regularization technique: an artificial inequality constraint added to the optimization problem limits a fictitious total strain energy that measures the shape change of the design with respect to a reference design. The energy constraint defines a feasible design space whose size can be varied by one parameter, the upper energy limit. By construction, the proposed regularization is applicable to a wide range of problems; although in this paper, the application is restricted to linear elastostatic problems. Copyright © 2009 John Wiley & Sons, Ltd. [source] An a posteriori error estimator for the p - and hp -versions of the finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2005J. E. Tarancón Abstract An a posteriori error estimator is proposed in this paper for the p - and hp -versions of the finite element method in two-dimensional linear elastostatic problems. The local error estimator consists in an enhancement of an error indicator proposed by Bertóti and Szabó (Int. J. Numer. Meth. Engng. 1998; 42:561,587), which is based on the minimum complementary energy principle. In order to obtain the local error estimate, this error indicator is corrected by a factor which depends only on the polynomial degree of the element. The proposed error estimator shows a good effectivity index in meshes with uniform and non-uniform polynomial distributions, especially when the global error is estimated. Furthermore, the local error estimator is reliable enough to guide p - and hp -adaptive refinement strategies. Copyright © 2004 John Wiley & Sons, Ltd. [source] On generalized stochastic perturbation-based finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2006Marcin Kami Abstract Generalized nth order stochastic perturbation technique, that can be applied to solve some boundary value or boundary initial problems in computational physics and/or engineering with random parameters is proposed here. This technique is demonstrated in conjunction with the finite element method (FEM) to model 1D linear elastostatics problem with a single random variable. The symbolic computer program is employed to perform computational studies on convergence of the first two probabilistic moments for simple unidirectional tension of a bar. These numerical studies verify the influence of coefficient of variation of the random input and, at the same time, of the perturbation parameter on the first two probabilistic moments of the final solution vector. Copyright © 2005 John Wiley & Sons, Ltd. [source] | ||||||||||