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Computational Mechanics (computational + mechanic)
Selected AbstractsMultiscale Methods in Computational MechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8-9 2010Ted Belytschko No abstract is available for this article. [source] ODDLS: A new unstructured mesh finite element method for the analysis of free surface flow problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2008Julio Garcia-Espinosa Abstract This paper introduces a new stabilized finite element method based on the finite calculus (Comput. Methods Appl. Mech. Eng. 1998; 151:233,267) and arbitrary Lagrangian,Eulerian techniques (Comput. Methods Appl. Mech. Eng. 1998; 155:235,249) for the solution to free surface problems. The main innovation of this method is the application of an overlapping domain decomposition concept in the statement of the problem. The aim is to increase the accuracy in the capture of the free surface as well as in the resolution of the governing equations in the interface between the two fluids. Free surface capturing is based on the solution to a level set equation. The Navier,Stokes equations are solved using an iterative monolithic predictor,corrector algorithm (Encyclopedia of Computational Mechanics. Wiley: New York, 2004), where the correction step is based on imposing the divergence-free condition in the velocity field by means of the solution to a scalar equation for the pressure. Examples of application of the ODDLS formulation (for overlapping domain decomposition level set) to the analysis of different free surface flow problems are presented. Copyright © 2008 John Wiley & Sons, Ltd. [source] Special Issue on The Fifth World Congress on Computational MechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004Josef Eberhardsteiner Guest Editor No abstract is available for this article. [source] 5th U.S. National Congress on Computational MechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1-2 2001Kaspar Willam Guest Editor No abstract is available for this article. [source] Computational mechanics of the steel,concrete interface,INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2002M. R. Ben Romdhane Abstract Concrete cracking in reinforced concrete structures is governed by two mechanisms: the activation of bond forces at the steel,concrete interface and the bridge effects of the reinforcement crossing a macro-crack. The computational modelling of these two mechanisms, acting at different scales, is the main objective of this paper. The starting point is the analysis of the micro-mechanisms, leading to an appropriate choice of (measurable) state variables describing the energy state in the surface systems: on the one side the relative displacement between the steel and the concrete, modelling the bond activation; on the other hand, the crack opening governing the bridge effects. These displacement jumps are implemented in the constitutive model using thermodynamics of surfaces of discontinuity. On the computational side, the constitutive model is implemented in a discrete crack approach. A truss element with slip degrees of freedom is developed. This degree of freedom represents the relative displacement due to bond activation. In turn, the bridge effect is numerically taken into account by modifying the post-cracking behaviour of the contact elements representing discrete concrete cracks crossed by a rebar. First simulation results obtained with this model show a good agreement in crack pattern and steel stress distribution with micro-mechanical results and experimental results. Copyright © 2001 John Wiley & Sons, Ltd. [source] Preface to computational mechanics of concrete and concrete structuresINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7-8 2004Nenad Bi No abstract is available for this article. [source] A unified method for eigendecomposition of graph productsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2005A. Kaveh Abstract In this paper, a unified method is developed for calculating the eigenvalues of the weighted adjacency and Laplacian matrices of three different graph products. These products have many applications in computational mechanics, such as ordering, graph partitioning, and subdomaining of finite element models. Copyright © 2005 John Wiley & Sons, Ltd. [source] A study on the lumped preconditioner and memory requirements of FETI and related primal domain decomposition methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2008Yannis Fragakis Abstract In recent years, domain decomposition methods (DDMs) have emerged as advanced solvers in several areas of computational mechanics. In particular, during the last decade, in the area of solid and structural mechanics, they reached a considerable level of advancement and were shown to be more efficient than popular solvers, like advanced sparse direct solvers. The present contribution follows the lines of a series of recent publications on the relationship between primal and dual formulations of DDMs. In some of these papers, the effort to unify primal and dual methods led to a family of DDMs that was shown to be more efficient than the previous methods. The present paper extends this work, presenting a new family of related DDMs, thus enriching the theory of the relations between primal and dual methods, with the primal methods, which correspond to the dual DDM that uses the lumped preconditioner. The paper also compares the numerical performance of the new methods with that of the previous ones and focuses particularly on memory requirement issues related to the use of the lumped preconditioner, suggesting a particularly memory-efficient formulation. Copyright © 2007 John Wiley & Sons, Ltd. [source] Smart element method I. The Zienkiewicz,Zhu feedbackINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2005Shaofan Li Abstract A new error control finite element formulation is developed and implemented based on the variational multiscale method, the inclusion theory in homogenization, and the Zienkiewicz,Zhu error estimator. By synthesizing variational multiscale method in computational mechanics, the equivalent eigenstrain principle in micromechanics, and the Zienkiewicz,Zhu error estimator in the finite element method (FEM), the new finite element formulation can automatically detect and subsequently homogenize its own discretization errors in a self-adaptive and a self-adjusting manner. It is the first finite element formulation that combines an optimal feedback mechanism and a precisely defined homogenization procedure to reduce its own discretization errors and hence to control numerical pollutions. The paper focuses on the following two issues: (1) how to combine a multiscale method with the existing finite element error estimate criterion through a feedback mechanism, and (2) convergence study. It has been shown that by combining the proposed variational multiscale homogenization method with the Zienkiewicz,Zhu error estimator a clear improvement can be made on the coarse scale computation. It is also shown that when the finite element mesh is refined, the solution obtained by the variational eigenstrain multiscale method will converge to the exact solution. Copyright © 2004 John Wiley & Sons, Ltd. [source] DSC-Ritz method for high-mode frequency analysis of thick shallow shellsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2005C. W. Lim Abstract This paper addresses a challenging problem in computational mechanics,the analysis of thick shallow shells vibrating at high modes. Existing methods encounter significant difficulties for such a problem due to numerical instability. A new numerical approach, DSC-Ritz method, is developed by taking the advantages of both the discrete singular convolution (DSC) wavelet kernels of the Dirichlet type and the Ritz method for the numerical solution of thick shells with all possible combinations of commonly occurred boundary conditions. As wavelets are localized in both frequency and co-ordinate domains, they give rise to numerical schemes with optimal accurate, stability and flexibility. Numerical examples are considered for Mindlin plates and shells with various edge supports. Benchmark solutions are obtained and analyzed in detail. Experimental results validate the convergence, stability, accuracy and reliability of the proposed approach. In particular, with a reasonable number of grid points, the new DSC-Ritz method is capable of producing highly accurate numerical results for high-mode vibration frequencies, which are hitherto unavailable to engineers. Moreover, the capability of predicting high modes endows us the privilege to reveal a discrepancy between natural higher-order vibration modes of a Mindlin plate and those calculated via an analytical relationship linking Kirchhoff and Mindlin plates. Copyright © 2004 John Wiley & Sons, Ltd. [source] The birth of the finite element method and of computational mechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004*Article first published online: 21 APR 200, O. C. Zienkiewicz Abstract This brief paper attempts to indicate the motivation which led to the development of the finite element method by engineers and shows how later this became integrated with various current mathematical procedures. In the opinion of the writer, the broad definition of finite elements today includes all the known procedures of approximation for solving partial differential equations and allows the users to include a variety of methods which are mathematically acceptable. Copyright 2004 © John Wiley & Sons, Ltd. [source] An augmented spatial digital tree algorithm for contact detection in computational mechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2002Y. T. Feng Abstract Based on the understanding of existing spatial digital tree-based contact detection approaches, and the alternating digital tree (ADT) algorithm in particular, a more efficient algorithm, termed the augmented spatial digital tree (ASDT) algorithm, is proposed in the present work. The ASDT algorithm adopts a different point representation scheme that uses only the lower corner vertex to represent a (hyper-)rectangle, with the upper corner vertex serving as the augmented information. Consequently, the ASDT algorithm can keep the working space the same as the original n -dimensional space and, in general, a much better balanced tree can be expected. This, together with the introduction of an additional bounding subregion for the rectangles associated with each tree node, makes it possible to significantly reduce the number of node visits in the region search, although each node visit may be slightly more expensive. Three examples arising in computational mechanics are presented to provide an assessment of the performance of the ASDT. The numerical results indicate that the ASDT is, at least, over 3.9 times faster than the ADT. Copyright © 2002 John Wiley & Sons, Ltd. [source] Error norm estimation and stopping criteria in preconditioned conjugate gradient iterationsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2001Owe Axelsson Abstract Some techniques suitable for the control of the solution error in the preconditioned conjugate gradient method are considered and compared. The estimation can be performed both in the course of the iterations and after their termination. The importance of such techniques follows from the non-existence of some reasonable a priori error estimate for very ill-conditioned linear systems when sufficient information about the right-hand side vector is lacking. Hence, some a posteriori estimates are required, which make it possible to verify the quality of the solution obtained for a prescribed right-hand side. The performance of the considered error control procedures is demonstrated using real-world large-scale linear systems arising in computational mechanics. Copyright © 2001 John Wiley & Sons, Ltd. [source] | ||||||||||