Elastostatic Problems (elastostatic + problem)

Distribution by Scientific Domains

Kinds of Elastostatic Problems

  • linear elastostatic problem


  • Selected Abstracts


    Nonparametric probabilistic approach of uncertainties for elliptic boundary value problem

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6-7 2009
    Christian 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]


    Scaled boundary finite-element analysis of a non-homogeneous axisymmetric domain subjected to general loading

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2003
    James P. Doherty
    Abstract The scaled boundary finite-element method is derived for elastostatic problems involving an axisymmetric domain subjected to a general load, using a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co-ordinate system. The method is particularly well suited to modelling unbounded problems, and the formulation allows a power-law variation of Young's modulus with depth. The efficiency and accuracy of the method is demonstrated through a study showing the convergence of the computed solutions to analytical solutions for the vertical, horizontal, moment and torsion loading of a rigid circular footing on the surface of a homogeneous elastic half-space. Computed solutions for the vertical and moment loading of a smooth rigid circular footing on a non-homogeneous half-space are compared to analytical ones, demonstrating the method's ability to accurately model a variation of Young's modulus with depth. Copyright © 2003 John Wiley & Sons, Ltd. [source]


    Exact transformation of a wide variety of domain integrals into boundary integrals in boundary element method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2008
    M. R. Hematiyan
    Abstract In this paper, a sufficient condition for transforming domain integrals into boundary integral is described. The transformation is accomplished by Green's and Gauss' theorems. It is shown that a wide range of domain integrals including some integrals in boundary element method satisfy this sufficient condition and can be simply transformed into boundary. Although emphasis is made on potential and elastostatic problems, this method can also be used for many other applications. Using the present method, a wide range of 2D and 3D domain integrals over simply or multiply connected regions can be transformed exactly into the boundary. The resultant boundary integrals are numerically evaluated using an adaptive version of the Simpson integration method. Several examples are provided to show the efficiency and accuracy of the present method. Copyright © 2007 John Wiley & Sons, Ltd. [source]


    Dual analysis by a meshless method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2002
    Marc Duflot
    Abstract A meshless method to solve elastostatic problems based on an equilibrium model is presented. This means that the equilibrium and constitutive equations are satisfied a priori and that the approximation only concerns the compatibility equations. The application of this method together with the classical displacement meshless method leads to upper and lower bounds on the energy. The difference between these bounds gives a global error estimation on the solution. Copyright © 2002 John Wiley & Sons, Ltd. [source]


    A fictitious energy approach for shape optimization

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2010
    M. 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]


    Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2010
    Haim Waisman
    Abstract This paper investigates the extended finite element method (XFEM)-GA detection algorithm proposed by Rabinovich et al. (Int. J. Numer. Meth. Engng 2007; 71(9):1051,1080; Int. J. Numer. Meth. Engng 2009; 77(3):337,359) on elastostatic problems with different types of flaws. This algorithm is designed for non-destructive assessment of structural components. Trial flaws are modeled using the XFEM as the forward problem and genetic algorithms (GAs) are employed as the optimization method to converge to the true flaw location and size. The main advantage of the approach is that XFEM alleviates the need for re-meshing the domain at every new iteration of the inverse solution process and GAs have proven to be robust and efficient optimization techniques in particular for this type of problems. In this paper the XFEM-GA methodology is applied to elastostatic problems where flaws are considered as straight cracks, circular holes and non-regular-shaped holes. Measurements are obtained from strain sensors that are attached to the surface of the structure at specific locations and provide the target solution to the GA. The results show convergence robustness and accuracy provided that a sufficient number of sensors are employed and sufficiently large flaws are considered. Copyright © 2009 John Wiley & Sons, Ltd. [source]


    An a posteriori error estimator for the p - and hp -versions of the finite element method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2005
    J. 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]


    A variational r -adaption and shape-optimization method for finite-deformation elasticity

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004
    P. Thoutireddy
    Abstract This paper is concerned with the formulation of a variational r -adaption method for finite-deformation elastostatic problems. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system. This is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis. Energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes. We derive general expressions for the configurational forces for isoparametric elements and non-linear, possibly anisotropic, materials under general loading. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of a semi-infinite crack in linear and non-linear elastic bodies; and the optimization of the shape of elastic inclusions. Copyright © 2004 John Wiley & Sons, Ltd. [source]


    Use of the tangent derivative boundary integral equations for the efficient computation of stresses and error indicators

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2002
    K. H. Muci-Küchler
    Abstract In this work, a new global reanalysis technique for the efficient computation of stresses and error indicators in two-dimensional elastostatic problems is presented. In the context of the boundary element method, the global reanalysis technique can be viewed as a post-processing activity that is carried out once an analysis using Lagrangian elements has been performed. To do the reanalysis, the functional representation for the displacements is changed from Lagrangian to Hermite, introducing the nodal values of the tangential derivatives of those quantities as additional degrees of freedom. Next, assuming that the nodal values of the displacements and the tractions remain practically unchanged from the ones obtained in the analysis using Lagrangian elements, the tangent derivative boundary integral equations are collocated at each functional node in order to determine the additional degrees of freedom that were introduced. Under this scheme, a second system of equations is generated and, once it is solved, the nodal values of the tangential derivatives of the displacements are obtained. This approach gives more accurate results for the stresses at the nodes since it avoids the need to differentiate the shape functions in order to obtain the normal strain in the tangential direction. When compared with the use of Hermite elements, the global reanalysis technique has the attraction that the user does not have to give as input data the additional information required by this type of elements. Another important feature of the proposed approach is that an efficient error indicator for the values of the stresses can also be obtained comparing the values for the stresses obtained through the use of Lagrangian elements and the global reanalysis technique. Copyright © 2001 John Wiley & Sons, Ltd. [source]


    On generalized stochastic perturbation-based finite element method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2006
    Marcin 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]