Download or read book Partitioned Polytopal Finite element Methods for Nonlinear Solid Mechanics written by Brian Doran Giffin and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a novel polytopal finite-element framework that addresses the collective issues of discretization sensitivity and mesh generation for computational solid mechanics problems. The use of arbitrary polygonal and polyhedral shapes in place of canonical isoparametric elements seeks to remediate issues pertaining to meshing and mesh quality (particularly for irregularly shaped elements), while maintaining many of the desirable features of a traditional finite element method. A general class of partitioned element methods (PEM) is proposed and analyzed, constituting a family of approaches for constructing piecewise polynomial approximations to harmonic shape functions on arbitrary polytopes. Such methods require a geometric partition of each element, and under certain conditions will directly yield integration consistency. Two partitioned element methods are explored in detail, including a novel approach herein referred to as the discontinuous Galerkin partitioned-element method (DG-PEM). An implementational framework for the DG-PEM is presented, along with a discussion of its associated numerical challenges. The numerical precision of the PEM is explored via classical patch tests and single element tests for a representative sampling of polygonal element shapes. Solution sensitivity with respect to element shape is examined for a handful of problems, including a mesh convergence study in the nearly incompressible regime. Finally, the efficacy of the DG-PEM is assessed for a number of benchmark problems involving large deformations and nonlinear material behavior.
Download or read book BEM based Finite Element Approaches on Polytopal Meshes written by Steffen Weißer and published by Springer. This book was released on 2019-07-18 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to one of the first methods developed for the numerical treatment of boundary value problems on polygonal and polyhedral meshes, which it subsequently analyzes and applies in various scenarios. The BEM-based finite element approaches employs implicitly defined trial functions, which are treated locally by means of boundary integral equations. A detailed construction of high-order approximation spaces is discussed and applied to uniform, adaptive and anisotropic polytopal meshes. The main benefits of these general discretizations are the flexible handling they offer for meshes, and their natural incorporation of hanging nodes. This can especially be seen in adaptive finite element strategies and when anisotropic meshes are used. Moreover, this approach allows for problem-adapted approximation spaces as presented for convection-dominated diffusion equations. All theoretical results and considerations discussed in the book are verified and illustrated by several numerical examples and experiments. Given its scope, the book will be of interest to mathematicians in the field of boundary value problems, engineers with a (mathematical) background in finite element methods, and advanced graduate students.
Download or read book Adaptive Finite Element Methods for Direct and Inverse Problems in Nonlinear Solid Mechanics written by Kai-Uwe Widany and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Elements of Nonlinear Continua written by J. T. Oden and published by Courier Corporation. This book was released on 2013-04-15 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view. The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical solution of the equations governing the discrete model. Though the theory and methods are sufficiently general to be applied to any nonlinear problem, emphasis has been placed on problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity. Problems in rarefied gas dynamics and nonlinear partial differential equations are also examined. Other topics include topological properties of finite element models, applications to linear and nonlinear boundary value problems, and discrete models of nonlinear thermomechanical behavior of dissipative media. This comprehensive text is valuable not only to students of structural analysis and continuum mechanics but also to professionals researching the numerical analysis of continua
Download or read book Smoothed Finite Element Methods for Nonlinear Solid Mechanics Problems 2D and 3D Case Studies written by Manfred Staat and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multiscale Finite Element Methods written by Yalchin Efendiev and published by Springer Science & Business Media. This book was released on 2009-01-10 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this monograph is to describe the main concepts and recent - vances in multiscale ?nite element methods. This monograph is intended for thebroaderaudienceincludingengineers,appliedscientists,andforthosewho are interested in multiscale simulations. The book is intended for graduate students in applied mathematics and those interested in multiscale compu- tions. It combines a practical introduction, numerical results, and analysis of multiscale ?nite element methods. Due to the page limitation, the material has been condensed. Each chapter of the book starts with an introduction and description of the proposed methods and motivating examples. Some new techniques are introduced using formal arguments that are justi?ed later in the last chapter. Numerical examples demonstrating the signi?cance of the proposed methods are presented in each chapter following the description of the methods. In the last chapter, we analyze a few representative cases with the objective of demonstrating the main error sources and the convergence of the proposed methods. A brief outline of the book is as follows. The ?rst chapter gives a general introductiontomultiscalemethodsandanoutlineofeachchapter.Thesecond chapter discusses the main idea of the multiscale ?nite element method and its extensions. This chapter also gives an overview of multiscale ?nite element methods and other related methods. The third chapter discusses the ext- sion of multiscale ?nite element methods to nonlinear problems. The fourth chapter focuses on multiscale methods that use limited global information.
Download or read book Finite Element Methods for Nonlinear Problems written by Pal G. Bergan and published by Springer. This book was released on 1986 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of papers presented at the Europe-US Symposium on Finite Element Methods for Nonlinear Problems. The symposium was held at the Norwegian Institute of Technology, Trondheim, Norway during August 12 to 16, 1985. The finite element method has during recent years gained a position as the most important discipline in computational mechanics. The basis for this method was laid out about two decades ago, and linear finite element techniques are today well established and well understood. Much work is still being done in order to make these linear methods more efficient and reliable. However, a sub stantial part of the current research efforts in the finite element field is focused on developing the nonlinear capabilities of the method. This task is highly challenging and demanding, both from a theoretical and practical point of view. It was in this spirit that the Europe-US Symposium on Finite Element Methods for Nonlinear Problems was organized. The meeting may be seen as the continuation of the US-Germany Symposium on Finite Element Methods held in 1976 at MIT, Cambridge, USA and the Europe- US Workshop on Nonlinear Finite Element Analysis in Structural Mechanics held in 1980 at the Ruhr-Universitat, Bochum, West-Germany.
Download or read book Polyhedral Finite element Approximants in 3D Solid Mechanics written by Mili Selimotić and published by . This book was released on 2008 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element Methods written by Duc Thai Nguyen and published by Springer Nature. This book was released on with total page 813 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Incremental Finite Element Modelling in Non linear Solid Mechanics written by Michał Kleiber and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Incremental Finite Element Modelling in Non Linear Solid Mechanics written by Michal Kleiber and published by . This book was released on 1989-02-01 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hp Finite Element Methods for Singular Perturbations written by Jens M. Melenk and published by Springer Science & Business Media. This book was released on 2002-10-10 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.
Download or read book Hybrid Finite Element Methods for Non linear and Non smooth Problems in Solid Mechanics written by Linus Maximilian Wunderlich and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non standard Finite Element Method in Nonlinear Inelastic Solid Mechanics written by Satyanadham Atluri and published by . This book was released on 1986 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non linear Finite Element Analysis of Solids and Structures written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element Method written by O. C. Zienkiewicz and published by . This book was released on 2000-08-01 with total page 1440 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the years since the fourth edition of this seminal work was published, active research has developed the Finite Element Method into the pre-eminent tool for the modelling of physical systems. Written by the pre-eminent professors in their fields, this new edition of the Finite Element Method maintains the comprehensive style of the earlier editions and authoritatively incorporates the latest developments of this dynamic field. Expanded to three volumes the book now covers the basis of the method and its application to advanced solid mechanics and also advanced fluid dynamics. Aimed at undergraduate and postgraduate students, and essential as a reference tool for professional engineers, it provides a complete introduction to the method. Volume 1 of The Finite Element Method provides a complete introduction to the method, and is essential reading for undergraduates, postgraduates and professional engineers. Volume 2 concentrates on non-linear solid and structural mechanics and is ideal for postgraduate students and professional engineers working in this discipline. Volume 3 covers the whole range of fluid dynamics and is ideal reading for postgraduate level students and professional engineers working in this discipline. New material on fields that have rapidly altered since the previous edition. A 'must have' reference in this field.
Download or read book Nonlinear Finite Elements for Continua and Structures written by Ted Belytschko and published by . This book was released on 2007 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt:
