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Solid Mechanics (solid + mechanic)

Distribution by Scientific Domains
Engineering90%

Terms modified by Solid Mechanics

  • solid mechanic problem
    		•

    Selected Abstracts

    Coupling of Forming Process and Fatigue Design Computations: A Local Approach

    ADVANCED ENGINEERING MATERIALS, Issue 9 2009
    Matteo Luca Facchinetti
    The fatigue design of stamped parts is supposed to take into account for the forming process. In this paper, stamping of steel sheets is addressed by basic rules coming from elementary solid mechanics and plasticity. As an effective alternative to complex FE computations, such a pragmatic approach highlights how the forming process affects fatigue design and allows direct application in an industrial framework. [source]

    A three dimensional surface-to-surface projection algorithm for non-coincident domains,

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2003
    M. W. Heinstein
    Abstract A numerical procedure is outlined to achieve the least squares projection of a finite dimensional representation from one surface to another in three dimensions. Although the applications of such an algorithm are many, the specific problem considered is the mortar tying of dissimilarly meshed grids in large deformation solid mechanics. The algorithm includes a nearest neighbour search, a systematic subdivision of the surface of intersection into smooth subdomains (termed segments), and a robust numerical quadrature scheme for evaluation of the spatial integrals defining the mortar projection. The procedure outlined, while discussed for the mesh tying problem, is directly applicable to the study of contact-impact. Published in 2003 by John Wiley & Sons, Ltd. [source]

    Splitting elastic modulus finite element method and its application

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2001
    Dang Faning
    Abstract To establish the best precision FEM, the proportion of potential and complementary energy in the functional of the variational principles must be changeable. A new kind of variational principle in linear theory of solid mechanics, called the splitting elastic modulus variational principle, is introduced. Its distinctive feature is that the functional contains one arbitrary additional parameter, called splitting factor; the proportion of potential and complementary energy in the functional can be changed by the splitting factor. Finite element method, which is based on the new principle, is established. It is called splitting modulus FEM, its stiffness can be adjusted by properly selecting the splitting factors, some ill-conditioned problem can be conquered by it. The methods to choose the splitting factors, reduce the condition number of stiffness matrix and improve the precision of solutions are also discussed. The reason why the new method can transform the ill-conditioned problems into well-conditioned ones is analysed finally. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    A Cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problems

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2010
    Phong B. H. Le
    Abstract In this paper, high-order systems are reformulated as first-order systems, which are then numerically solved by a collocation method. The collocation method is based on Cartesian discretization with 1D-integrated radial basis function networks (1D-IRBFN) (Numer. Meth. Partial Differential Equations 2007; 23:1192,1210). The present method is enhanced by a new boundary interpolation technique based on 1D-IRBFN, which is introduced to obtain variable approximation at irregular points in irregular domains. The proposed method is well suited to problems with mixed boundary conditions on both regular and irregular domains. The main results obtained are (a) the boundary conditions for the reformulated problem are of Dirichlet type only; (b) the integrated RBFN approximation avoids the well-known reduction of convergence rate associated with differential formulations; (c) the primary variable (e.g. displacement, temperature) and the dual variable (e.g. stress, temperature gradient) have similar convergence order; (d) the volumetric locking effects associated with incompressible materials in solid mechanics are alleviated. Numerical experiments show that the proposed method achieves very good accuracy and high convergence rates. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    A 3D mortar method for solid mechanics,

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004
    Michael A. Puso
    Abstract A version of the mortar method is developed for tying arbitrary dissimilar 3D meshes with a focus on issues related to large deformation solid mechanics. Issues regarding momentum conservation, large deformations, computational efficiency and bending are considered. In particular, a mortar method formulation that is invariant to rigid body rotations is introduced. A scheme is presented for the numerical integration of the mortar surface projection integrals applicable to arbitrary 3D curved dissimilar interfaces. Here, integration need only be performed at problem initialization such that coefficients can be stored and used throughout a quasi-static time stepping process even for large deformation problems. A degree of freedom reduction scheme exploiting the dual space interpolation method such that direct linear solution techniques can be applied without Lagrange multipliers is proposed. This provided a significant reduction in factorization times. Example problems which touch on the aforementioned solid mechanics related issues are presented. Published in 2003 by John Wiley & Sons, Ltd. [source]

    An arbitrary Lagrangian,Eulerian finite element method for finite strain plasticity

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2003
    Francisco Armero
    Abstract This paper presents a new arbitrary Lagrangian,Eulerian (ALE) finite element formulation for finite strain plasticity in non-linear solid mechanics. We consider the models of finite strain plasticity defined by the multiplicative decomposition of the deformation gradient in an elastic and a plastic part (F = FeFp), with the stresses given by a hyperelastic relation. In contrast with more classical ALE approaches based on plastic models of the hypoelastic type, the ALE formulation presented herein considers the direct interpolation of the motion of the material with respect to the reference mesh together with the motion of the spatial mesh with respect to this same reference mesh. This aspect is shown to be crucial for a simple treatment of the advection of the plastic internal variables and dynamic variables. In fact, this advection is carried out exactly through a particle tracking in the reference mesh, a calculation that can be accomplished very efficiently with the use of the connectivity graph of the fixed reference mesh. A staggered scheme defined by three steps (the smoothing, the advection and the Lagrangian steps) leads to an efficient method for the solution of the resulting equations. We present several representative numerical simulations that illustrate the performance of the newly proposed methods. Both quasi-static and dynamic conditions are considered in these model examples. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    A vertex-based finite volume method applied to non-linear material problems in computational solid mechanics

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2003
    G. A. Taylor
    Abstract A vertex-based finite volume (FV) method is presented for the computational solution of quasi-static solid mechanics problems involving material non-linearity and infinitesimal strains. The problems are analysed numerically with fully unstructured meshes that consist of a variety of two- and three-dimensional element types. A detailed comparison between the vertex-based FV and the standard Galerkin FE methods is provided with regard to discretization, solution accuracy and computational efficiency. For some problem classes a direct equivalence of the two methods is demonstrated, both theoretically and numerically. However, for other problems some interesting advantages and disadvantages of the FV formulation over the Galerkin FE method are highlighted. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Evaluation of three unstructured multigrid methods on 3D finite element problems in solid mechanics,

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2002
    Mark Adams
    Abstract Multigrid has been a popular solver method for finite element and finite difference problems with regular grids for over 20 years. The application of multigrid to unstructured grid problems, in which it is often difficult or impossible for the application to provide coarse grids, is not as well understood. In particular, methods that are designed to require only data that are easily available in most finite element applications (i.e. fine grid data), constructing the grid transfer operators and coarse grid operators internally, are of practical interest. We investigate three unstructured multigrid methods that show promise for challenging problems in 3D elasticity: (1) non-nested geometric multigrid, (2) smoothed aggregation, and (3) plain aggregation algebraic multigrid. This paper evaluates the effectiveness of these three methods on several unstructured grid problems in 3D elasticity with up to 76 million degrees of freedom. Published in 2002 by John Wiley & Sons, Ltd. [source]

    Computability in non-linear solid mechanics

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1-2 2001
    T. Belytschko
    Abstract The computability of non-linear problems in solid and structural mechanics problems is examined. Several factors which contribute to the level of difficulty of a simulation are discussed: the smoothness and stability of the response, the required resolution, the uncertainties in the load, boundary conditions and initial conditions and inadequacies and uncertainties in the constitutive equation. An abstract measure of the level of difficulty is proposed, and some examples of typical engineering simulations are classified by this measure. We have put particular emphasis on engineering calculations, where many of the factors that diminish computability play a prominent role. Copyright © 2001 John Wiley & Sons, Ltd. [source]