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Mesh Refinement In Finite Element Analysis By Minimization Of The Stiffness Matrix Trace
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Author :National Aeronautics and Space Administration (NASA) Publisher :Createspace Independent Publishing Platform ISBN 13 :9781723205262 Total Pages :110 pages Book Rating :4.2/5 (52 download)
Book Synopsis Mesh Refinement in Finite Element Analysis by Minimization of the Stiffness Matrix Trace by : National Aeronautics and Space Administration (NASA)
Download or read book Mesh Refinement in Finite Element Analysis by Minimization of the Stiffness Matrix Trace written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-18 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most finite element packages provide means to generate meshes automatically. However, the user is usually confronted with the problem of not knowing whether the mesh generated is appropriate for the problem at hand. Since the accuracy of the finite element results is mesh dependent, mesh selection forms a very important step in the analysis. Indeed, in accurate analyses, meshes need to be refined or rezoned until the solution converges to a value so that the error is below a predetermined tolerance. A-posteriori methods use error indicators, developed by using the theory of interpolation and approximation theory, for mesh refinements. Some use other criterions, such as strain energy density variation and stress contours for example, to obtain near optimal meshes. Although these methods are adaptive, they are expensive. Alternatively, a priori methods, until now available, use geometrical parameters, for example, element aspect ratio. Therefore, they are not adaptive by nature. An adaptive a-priori method is developed. The criterion is that the minimization of the trace of the stiffness matrix with respect to the nodal coordinates, leads to a minimization of the potential energy, and as a consequence provide a good starting mesh. In a few examples the method is shown to provide the optimal mesh. The method is also shown to be relatively simple and amenable to development of computer algorithms. When the procedure is used in conjunction with a-posteriori methods of grid refinement, it is shown that fewer refinement iterations and fewer degrees of freedom are required for convergence as opposed to when the procedure is not used. The mesh obtained is shown to have uniform distribution of stiffness among the nodes and elements which, as a consequence, leads to uniform error distribution. Thus the mesh obtained meets the optimality criterion of uniform error distribution. Kittur, Madan G. and Huston, Ronald L. Unspecified Center ALGORITHMS; COMPUTATIONAL GRIDS; FINITE ELE...
Book Synopsis Finite-element Grid Improvement by Minimization of Stiffness Matrix Trace by :
Download or read book Finite-element Grid Improvement by Minimization of Stiffness Matrix Trace written by and published by . This book was released on 1987 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new and simple method of finite element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and by Masur. Identical results are obtained. Keywords: Finite element analysis; Mesh; Grid optimization; and Transmissions.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1990 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Monthly Catalog of United States Government Publications by :
Download or read book Monthly Catalog of United States Government Publications written by and published by . This book was released on with total page 1200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Monthly Catalogue, United States Public Documents by :
Download or read book Monthly Catalogue, United States Public Documents written by and published by . This book was released on 1991 with total page 1644 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Developments in Computational Engineering Mechanics by : B. H. V. Topping
Download or read book Developments in Computational Engineering Mechanics written by B. H. V. Topping and published by Hyperion Books. This book was released on 1993 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Included in this volume are a selection of papers on developments in computational engineering mechanics. The papers were presented at the Fifth International Conference on Civil and Structural Engineering Computing held 17-19 August 1993, Edinburgh.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1997 with total page 1060 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Deformation and Fracture in Materials by : Anoop Kumar Mukhopadhyay
Download or read book Deformation and Fracture in Materials written by Anoop Kumar Mukhopadhyay and published by CRC Press. This book was released on 2024-08-27 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides information on the basics of deformation and fracture in materials and on current, state-of-the-art experimental and numerical/theoretical methods, including data-driven approaches in the deformation and fracture study of materials. The blend of experimental test methods and numerical techniques to study deformation and fracture in materials is discussed. In addition, the application of data-driven approaches in predicting material performance in different types of loading and loading environments is illustrated. Features: Includes clear insights on deformation and fracture in materials, with clear explanations of mechanics and defects relating to them Provides effective treatments of modern numerical simulation methods Explores applications of data-driven approaches such as artificial intelligence, machine learning, and computer vision Reviews simple and basic experimental techniques to understand the concepts of deformation and fracture in materials Details modeling and simulation strategies of mechanics of materials at different scales This book is aimed at researchers and graduate students in fracture mechanics, finite element methods, and materials science.
Book Synopsis Monthly Catalog of United States Government Publications by :
Download or read book Monthly Catalog of United States Government Publications written by and published by . This book was released on 1991 with total page 826 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Government Reports Announcements & Index by :
Download or read book Government Reports Announcements & Index written by and published by . This book was released on 1990 with total page 1108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multibody Dynamics by : Ronald L. Huston
Download or read book Multibody Dynamics written by Ronald L. Huston and published by Butterworth-Heinemann. This book was released on 1990 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the fundamentals of multibody dynamics from the principles of elementary mechanics. It is written in a tutorial style with numerous examples and an emphasis upon computational methods. This book should be accessible to anyone with a basic knowledge of elementary mechanics and analysis. Multibody Dynamics examines the behavior of systems of bodies subjected to forces or constraints. The bodies may be securely or loosely connected, and flexible or rigid. Such generality allows the use of multibody systems to model an increasing number of physical systems ranging from robots, biosystems (human body models), satellite booms, large structures, chains and cables. Until recently, analyses of such systems were virtually intractable. With the availability of high-speed digital computers, however, and with corresponding advances in analysis methods, multibody dynamics analyses are not only feasible, they are also practical, and applicable, to these important physical systems.
Book Synopsis Bibliography of Lewis Research Center Technical Publications Announced in 1990 by :
Download or read book Bibliography of Lewis Research Center Technical Publications Announced in 1990 written by and published by . This book was released on 1991 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Gearing Mechanics by : Ronald L. Huston
Download or read book Computational Gearing Mechanics written by Ronald L. Huston and published by . This book was released on 1993 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Finite Element Method: Theory, Implementation, and Applications by : Mats G. Larson
Download or read book The Finite Element Method: Theory, Implementation, and Applications written by Mats G. Larson and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.
Book Synopsis TEXTBOOK OF FINITE ELEMENT ANALYSIS by : P. SESHU
Download or read book TEXTBOOK OF FINITE ELEMENT ANALYSIS written by P. SESHU and published by PHI Learning Pvt. Ltd.. This book was released on 2003-01-01 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for a one-semester course in Finite Element Method, this compact and well-organized text presents FEM as a tool to find approximate solutions to differential equations. This provides the student a better perspective on the technique and its wide range of applications. This approach reflects the current trend as the present-day applications range from structures to biomechanics to electromagnetics, unlike in conventional texts that view FEM primarily as an extension of matrix methods of structural analysis. After an introduction and a review of mathematical preliminaries, the book gives a detailed discussion on FEM as a technique for solving differential equations and variational formulation of FEM. This is followed by a lucid presentation of one-dimensional and two-dimensional finite elements and finite element formulation for dynamics. The book concludes with some case studies that focus on industrial problems and Appendices that include mini-project topics based on near-real-life problems. Postgraduate/Senior undergraduate students of civil, mechanical and aeronautical engineering will find this text extremely useful; it will also appeal to the practising engineers and the teaching community.
Book Synopsis Finite Element Bibliography by : Gerard De Vries
Download or read book Finite Element Bibliography written by Gerard De Vries and published by Springer. This book was released on 1976-12 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thjs bibliography had its inception in 1967, when the compilers first attempted a comprehensive cov erage of the finite element literature using both manual and computer-based retrieval. Initially, the data base was stored on a card index, but this was subsequently transferred to punched cards and magnetic tape. Computer processing was adopted at an early stage to derive the three index formats from the data base. Over the subsequent years, several versions of the bibliography were produced, with two of these being made available in a report form to other researchers. From the widespread interest in these documents, it became evident that there was a need for a commercially-available comprehensive bibliography in this area. A major effort was undertaken to revise, update, and extend the data base, resulting in this present volume. The bibliography covers the period 1956-1975 primarily, although some earlier publications of histori cal interest are included. The citations are not restricted to the English language and documents are listed in many languages and from diverse places of origin. All publication formats were accepted, so that references will be found to books, monographs, journal papers and articles, theses, dissertations, reports, surveys, and the like.
Book Synopsis The Scaled Boundary Finite Element Method by : John P. Wolf
Download or read book The Scaled Boundary Finite Element Method written by John P. Wolf and published by John Wiley & Sons. This book was released on 2003-03-14 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel computational procedure called the scaled boundary finite-element method is described which combines the advantages of the finite-element and boundary-element methods : Of the finite-element method that no fundamental solution is required and thus expanding the scope of application, for instance to anisotropic material without an increase in complexity and that singular integrals are avoided and that symmetry of the results is automatically satisfied. Of the boundary-element method that the spatial dimension is reduced by one as only the boundary is discretized with surface finite elements, reducing the data preparation and computational efforts, that the boundary conditions at infinity are satisfied exactly and that no approximation other than that of the surface finite elements on the boundary is introduced. In addition, the scaled boundary finite-element method presents appealing features of its own : an analytical solution inside the domain is achieved, permitting for instance accurate stress intensity factors to be determined directly and no spatial discretization of certain free and fixed boundaries and interfaces between different materials is required. In addition, the scaled boundary finite-element method combines the advantages of the analytical and numerical approaches. In the directions parallel to the boundary, where the behaviour is, in general, smooth, the weighted-residual approximation of finite elements applies, leading to convergence in the finite-element sense. In the third (radial) direction, the procedure is analytical, permitting e.g. stress-intensity factors to be determined directly based on their definition or the boundary conditions at infinity to be satisfied exactly. In a nutshell, the scaled boundary finite-element method is a semi-analytical fundamental-solution-less boundary-element method based on finite elements. The best of both worlds is achieved in two ways: with respect to the analytical and numerical methods and with respect to the finite-element and boundary-element methods within the numerical procedures. The book serves two goals: Part I is an elementary text, without any prerequisites, a primer, but which using a simple model problem still covers all aspects of the method and Part II presents a detailed derivation of the general case of statics, elastodynamics and diffusion.
