Iterative equation solvers for structural mechanics problems

presented at the winter annual meeting of the American Society of Mechanical Engineers, Atlanta, Georgia, December 1-6, 1991 by American Society of Mechanical Engineers. Winter Meeting

Publisher: American Society of Mechanical Engineers in New York, N.Y

Written in English
Published: Pages: 77 Downloads: 922
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Subjects:

  • Structural analysis (Engineering) -- Congresses.,
  • Iterative methods (Mathematics) -- Congresses.
  • Edition Notes

    Includes bibliographical references and index.

    Statementedited by I.D. Parsons, B. Nour-Omid ; sponsored by the Finite Element Technology Committee of the Computers in Engineering Division, ASME.
    SeriesCED ;, vol. 4, CED (Series) ;, vol. 4.
    ContributionsParsons, I. D., Nour-Omid, B., American Society of Mechanical Engineers. Finite Element Technology Committee.
    Classifications
    LC ClassificationsTA640.2 .A44 1991
    The Physical Object
    Pagination77 p. :
    Number of Pages77
    ID Numbers
    Open LibraryOL1568462M
    LC Control Number91058419

speedup, even for problems with only 10 - 20 design parameters. The coupling of AD with iterative solvers is a problem of current research (see e.g. GRIEWANK [Gri00] and references therein). As the use of iterative methods (e.g. multilevel methods) is impor-tant for solving fine discretizations of the state equation efficiently. For the. @article{osti_, title = {Use of the iterative solution method for coupled finite element and boundary element modeling; Yucca Mountain Site Characterization Project}, author = {Koteras, J R}, abstractNote = {Tunnels buried deep within the earth constitute an important class geomechanics problems. Two numerical techniques used for the analysis of geomechanics problems, the finite element. Edit: the following is a very good reference on Nonlinear Programming methods and software that might be useful. I know you are solving system of equations, but you can always an optimization solver to solve a feasibility problem (constant objective, thus solving only the constraints given by your nonlinear system) or, as you have degrees of freedom, impose some objective (like norm minimization). Iterative techniques for the solution of the algebraic equations associated with the direct boundary element analysis (BEA) method are discussed. Continuum structural response analysis problems are considered, employing single‐ and multi‐zone boundary element models with and without zone condensation. The impact on convergence rate and computer resource requirements associated with .

Solve the first equation for x 2 This equation represents a straight line with an intercept of 7/2 and a slope of (-3/2). Now, solve the second equation for x 2 This is also a straight line, but with an intercept of 1 and a slope of (-4). These lines are plotted in the following Figure. The solution is File Size: 1MB. Iterative Linear Solvers. PARALUTION, parallel sparse iterative methods for multi-core CPU, GPU (CUDA and OpenCL) and Intel Xeon Phi. Ginkgo sparse iterative methods for GPU-accelerated systems. MLBiCGStab Code for MATLAB. Regularization Tools, Matlab package for analysis and solution of discrete ill-posed problems, (by Per Christian Hansen). MOORe Tools, object oriented toolbox in . problems independently. This book is a part of a four-book series designed to supplement the engineering mechanics courses. This series instructs and applies the principles required to solve practical engineering problems in the follow-ing branches of mechanics: statics, kinematics, dynamics, and advanced kinetics. Each book contains between 6 File Size: KB.   An extensively expanded and revised edition of the leading major reference work in computational engineering. The completely updated and extended second edition of Encyclopedia of Computational Mechanics, Second Edition has, once again, been prepared under the guidance of three of the world's foremost experts in the field. It follows the same structure as the first edition, yet has Author: Erwin Stein.

Iterative algorithms solve linear equations while only performing multiplictions by A, and perform-ing a few vector operations. Unlike the direct methods which are based on elimination, the iterative algorithms do not get exact solutions. Rather, they get closer and closer to the solution the longer they work. In this paper, we propose an iterative method for solving a beam problem which is described by a nonlinear fourth-order equation with nonlinear boundary conditions. The method reduces this nonlinear fourth-order problem to a sequence of linear second-order problems with linear boundary conditions. The convergence of the method is proved, and some numerical examples demonstrate the efficiency Cited by: 3. Customers require coupling of various solvers and systems in the solution of coupled, multi-physics problems • Customers don’t want to learn how to do couplings. differently using various physics solvers. System Coupling: General Motivation. Fluid Dynamics Structural Mechanics. ElectromagneticsFile Size: 2MB.   I would like to incorporate a simple algbraic equation ax^3+bx^2+c=0 into my structural mechanics module (coupled with heat transfer). x is then used in a creep model. In this equation, a is a function of temperature, b is a function of temperature and stress and c is a function of temperature.

Iterative equation solvers for structural mechanics problems by American Society of Mechanical Engineers. Winter Meeting Download PDF EPUB FB2

Get this from a library. Iterative equation solvers for structural mechanics problems: presented at the winter annual meeting of the American Society of Mechanical Engineers, Atlanta, Georgia, December[I D Parsons; B Nour-Omid; American Society of Mechanical Engineers.

Winter Annual Meeting; American Society of Mechanical Engineers. I am still interested to proceed this discussion about efficient iterative solvers for CFD problems. Is there something more efficient than the combination of ILU + Krylov subspace methods for nasty CFD problems on unstructured grids.

but more for structural problems. The multi-level aggregation method is one example of this work. The use. Iterative solvers within sequences of large linear systems in non‐linear structural mechanics. direct sparse solvers are applied due to the fact that iterative solvers might have problems. Direct solvers are commonly used in implicit finite element codes for structural mechanics problems.

This study explores an alternative approach to solving the resulting linear systems by using. I would like to hear users views on the observed differences when using direct solvers vs iterative linear solvers for highly non-linear problems in either structural or fluid dynamic problems.

The more non-linear the better!!. I am fully aware of the well known academic differences of speed, memory, robustness and accuracy etc. The classification of solvers into direct and iterative mainly depends on the method of getting {u} in the linear equation. The selection of the solver depends on the process mechanics and problem size and is nowadays automatically chosen by most of the commercially available FE tools.

Abstract. Direct solvers are commonly used in implicit finite element codes for structural mechanics problems. This study explores an alternative approach to solving the resulting linear systems by using the Conjugate Gradient by: 1.

Iterative solvers have only rarely been used, see e.g. [9] and [8], and were rather limited to small size beam problems and did not show considerable efficiency. For very large well conditioned structures, however, iterative solvers are known as a very Iterative equation solvers for structural mechanics problems book tool, in particular as parallelization of these iterative algorithms is very : K.

Schweizerhof, Th. Rottner, G. Alefeld, I. Lenhardt. beneficial. In view of helpful textbooks on iterative solver s, we refer to [22], [43] and to [36, in German]. The main purpose of this paper Iterative equation solvers for structural mechanics problems book to show that with an appropriate combination of acceleration techniques iterative solvers may outperform direct solvers in structural mechanics problems surprisingly easily.

In particular, the. Elliptic Problem Solvers, II covers the proceedings of the Elliptic Problem Solvers Conference, held at the Naval Postgraduate School in Monterey, California from January 10 to 12, The book focuses on various aspects of the numerical solution of elliptic boundary value problems.

This book can be an invaluable supplement to standard textbooks for students studying mechanics. The book is divided into 26 chapters, each dealing with a separate topic.

The subject matter is developed beginning with statics and extending through friction, kinematics, impulse and momentum, systems of particles, rigid body kinetics, and vibrations/5(11). Problems in structural mechanics can be very large scale and also extremely ill-conditioned due to both a small mesh-size parameter and extreme values of the problem parameters.

Their numerical solution require iterative solvers with efficient by: An extensively expanded and revised edition of the leading major reference work in computational engineering.

The completely updated and extended second edition of Encyclopedia of Computational Mechanics, Second Edition has, once again, been prepared under the guidance of three of the world's foremost experts in the field. It follows the same structure as the first edition, yet has been.

Excellent book for science and engineering majors. Its all here, all you ever need to master a subject. The REA Problem solvers are the very best. I have several on different subjects, they are all excellent. Read more.

One person found this helpful. Helpful. Comment Report abuse/5(3). Iterative Methods for Linear and Nonlinear Equations C. Kelley North Carolina State University Society for Industrial and Applied Mathematics Philadelphia An extensively expanded and revised edition of the leading major reference work in computational engineering The completely updated and extended second edition of Encyclopedia of Computational Mechanics, Second Edition has, once again, been prepared under the guidance of three of the worlds foremost experts in the field.

It follows the same structure as the first edition, yet has been expanded. For cases where memory limitations require the utilization of iterative equation solvers, we suggest efficient procedures based on alternative termination criteria for such solvers. These approaches are tested on two- and three-dimensional topology optimization problems including minimum compliance design and compliant mechanism by: 8.

The subject of this book is the efficient solution of partial differential equations (PDEs) that arise when modelling incompressible fluid flow.

The material is organized into four groups of two chapters each, covering the Poisson equation (chapters 1 & 2); the convection-diffucion equation (chapters 3 & 4); the Stokes equations (chapters 5 & 6. Linear solvers for large algebraic systems from structural mechanics Symposium of Advances in Contact Mechanics: a tribute to Prof J.

Kalker Problems with algorithm Scale 15 Number of Iterative solvers Deflation 31 Z. Elliptic Problem Solvers, II covers the proceedings of the Elliptic Problem Solvers Conference, held at the Naval Postgraduate School in Monterey, California from January 10 to 12, The book focuses on various aspects of the numerical solution of elliptic boundary value Edition: 1.

A preconditioned iterative method for indefinite linear systems corresponding to certain saddlepoint problems is suggested. The block structure of the systems is utilized in order to design effective preconditioners, while the governing iterative solver is a standard minimum residual method.

The method is applied to systems derived from discretizations of the Stokes problem and mixed Cited by: The JUT AMlIACM Symposium on Discretization Methods in Structural Mechanics was nd th held in Vienna, Austria, from 2 to 6 June The site of the Symposium was the "Theatersaal" of the Austrian Academy of Sciences.

The Symposium was attended by 71. Analysis Methods & Solvers Contact Analysis ANSYS Structural Mechanics Non-iterative –i.e.

will not fail to converge Does not miss modes Applications Beam, shell or thin geometries Automotive, aerospace High frequency response analysis, etc. Natural Preconditioning and Iterative Methods for Saddle Point Systems. so saddle point systems arising from the discretization of partial differential equation problems, such as those describing electromagnetic problems or incompressible flow, lead to equations with this structure, as do, for example, interior point methods and the Cited by: Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics.

Second Edition. Howard Elman, David Silvester, and Andy Wathen Numerical Mathematics and Scientific Computation. Shows relations between discretization methods and solution methods for partial differential equations; Free software accompanying the book.

Structural Mechanics Module very versatile. For instance, you can use a function to describe loads and constraints. The documentation set for The Structural Mechanics Module consists of three books.

The one in your hands, the Structural Mechanics Module User’s Guide, introducesFile Size: 8MB. The next version is rather better suited for FEM applications, and is based on the constraint () in the form Kty = O, completed by the scaling functional l(y).

The extended system reads and has been used in structural mechanics by a number of authors (Seydel, Moore, Spence, Werner et al.). Create a special structural analysis container for a solid (3-D), plane stress, or plane strain model. Define 2-D or 3-D geometry and mesh it. Assign structural properties of the material, such as Young's modulus, Poisson's ratio, and mass pde: Create model.

Finite element methods have become ever more important to engineers as tools for design and optimization, now even for solving non-linear technological problems.

However, several aspects must be considered for finite-element simulations which are specific for non-linear problems: These problems require the knowledge and the understanding of theoretical foundations and their finite-element 5/5(2).

Buy Finite Elements and Fast Iterative Solvers: With Applications In Incompressible Fluid Dynamics (Numerical Mathematics And Scientific Computation) 2 by Elman, Howard, Silvester, David, Wathen, Andy (ISBN: ) from Amazon's Book Store. Get this from a library!

IUTAM Symposium on Discretization Methods in Structural Mechanics: Proceedings of the IUTAM Symposium held in Vienna, Austria, June [H A Mang; F G Rammerstorfer] -- This book contains papers presented at the IUTAM/IACM Symposium `Discretization Methods in Structural Mechanics II' held in Vienna, Austria, in June Mathematics in Structural Engineering Dr Colin Caprani About Me • Degree in Structural Engineering • Full time consultancy until • PhD in UCD from to • Lecturing in DIT and UCD • Consultant in buildings & bridges Guess my Leaving result!

C1 File Size: 2MB. I am trying to understand how my structural mechanics model is computing its solution.

The model solves and gives me a reasonable solution. However, I don't understand how it is arriving at its answer. I am looking at the Subdomain Settings - Equation System .