Meshless Methods And Their Numerical Properties

Author : Hua Li,Shantanu S. Mulay
Publisher : CRC Press
Page : 451 pages
File Size : 40,7 Mb
Release : 2013-02-22
Category : Mathematics
ISBN : 9781466517462

Get Book

Meshless Methods and Their Numerical Properties by Hua Li,Shantanu S. Mulay Pdf

Meshless, or meshfree methods, which overcome many of the limitations of the finite element method, have achieved significant progress in numerical computations of a wide range of engineering problems. A comprehensive introduction to meshless methods, Meshless Methods and Their Numerical Properties gives complete mathematical formulations for the most important and classical methods, as well as several methods recently developed by the authors. This book also offers a rigorous mathematical treatment of their numerical properties—including consistency, convergence, stability, and adaptivity—to help you choose the method that is best suited for your needs. Get Guidance for Developing and Testing Meshless Methods Developing a broad framework to study the numerical computational characteristics of meshless methods, the book presents consistency, convergence, stability, and adaptive analyses to offer guidance for developing and testing a particular meshless method. The authors demonstrate the numerical properties by solving several differential equations, which offer a clearer understanding of the concepts. They also explain the difference between the finite element and meshless methods. Explore Engineering Applications of Meshless Methods The book examines how meshless methods can be used to solve complex engineering problems with lower computational cost, higher accuracy, easier construction of higher-order shape functions, and easier handling of large deformation and nonlinear problems. The numerical examples include engineering problems such as the CAD design of MEMS devices, nonlinear fluid-structure analysis of near-bed submarine pipelines, and two-dimensional multiphysics simulation of pH-sensitive hydrogels. Appendices supply useful template functions, flowcharts, and data structures to assist you in implementing meshless methods. Choose the Best Method for a Particular Problem Providing insight into the special features and intricacies of meshless methods, this is a valuable reference for anyone developing new high-performance numerical methods or working on the modelling and simulation of practical engineering problems. It guides you in comparing and verifying meshless methods so that you can more confidently select the best method to solve a particular problem.

Author : Hua Li,Shantanu S. Mulay
Publisher : CRC Press
Page : 429 pages
File Size : 42,6 Mb
Release : 2013-02-22
Category : Mathematics
ISBN : 9781466517479

Get Book

Meshless Methods and Their Numerical Properties by Hua Li,Shantanu S. Mulay Pdf

Meshless, or meshfree methods, which overcome many of the limitations of the finite element method, have achieved significant progress in numerical computations of a wide range of engineering problems. A comprehensive introduction to meshless methods, Meshless Methods and Their Numerical Properties gives complete mathematical formulations for the m

Author : Youping Chen,James Lee,Azim Eskandarian
Publisher : Springer Science & Business Media
Page : 211 pages
File Size : 52,8 Mb
Release : 2006-04-28
Category : Science
ISBN : 9780387307367

Get Book

Meshless Methods in Solid Mechanics by Youping Chen,James Lee,Azim Eskandarian Pdf

This book covers the fundamentals of continuum mechanics, the integral formulation methods of continuum problems, the basic concepts of finite element methods, and the methodologies, formulations, procedures, and applications of various meshless methods. It also provides general and detailed procedures of meshless analysis on elastostatics, elastodynamics, non-local continuum mechanics and plasticity with a large number of numerical examples. Some basic and important mathematical methods are included in the Appendixes. For readers who want to gain knowledge through hands-on experience, the meshless programs for elastostatics and elastodynamics are provided on an included disc.

Author : G.R. Liu,Y.T. Gu
Publisher : Springer Science & Business Media
Page : 497 pages
File Size : 49,6 Mb
Release : 2005-12-05
Category : Technology & Engineering
ISBN : 9781402034688

Get Book

An Introduction to Meshfree Methods and Their Programming by G.R. Liu,Y.T. Gu Pdf

The finite difference method (FDM) hasbeen used tosolve differential equation systems for centuries. The FDM works well for problems of simple geometry and was widely used before the invention of the much more efficient, robust finite element method (FEM). FEM is now widely used in handling problems with complex geometry. Currently, we are using and developing even more powerful numerical techniques aiming to obtain more accurate approximate solutions in a more convenient manner for even more complex systems. The meshfree or meshless method is one such phenomenal development in the past decade, and is the subject of this book. There are many MFree methods proposed so far for different applications. Currently, three monographs on MFree methods have been published. Mesh Free Methods, Moving Beyond the Finite Element Method d by GR Liu (2002) provides a systematic discussion on basic theories, fundamentals for MFree methods, especially on MFree weak-form methods. It provides a comprehensive record of well-known MFree methods and the wide coverage of applications of MFree methods to problems of solids mechanics (solids, beams, plates, shells, etc.) as well as fluid mechanics. The Meshless Local Petrov-Galerkin (MLPG) Method d by Atluri and Shen (2002) provides detailed discussions of the meshfree local Petrov-Galerkin (MLPG) method and itsvariations. Formulations and applications of MLPG are well addressed in their book.

Author : Francesco Tornabene,Michele Bacciocchi
Publisher : Società Editrice Esculapio
Page : 1199 pages
File Size : 40,6 Mb
Release : 2019-11-01
Category : Technology & Engineering
ISBN : 9788835328995

Get Book

Anisotropic Doubly-Curved Shells by Francesco Tornabene,Michele Bacciocchi Pdf

This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for the mechanical analysis of doubly-curved shell structures made of anisotropic and composite materials. In particular, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. The approach presented in this volume is completely general and represents a valid tool to investigate the structural behavior of many arbitrarily shaped structures. An isogeometric mapping procedure is also illustrated to this aim. Special attention is given also to advanced and innovative constituents, such as Carbon Nanotubes (CNTs), Variable Angle Tow (VAT) composites and Functionally Graded Materials (FGMs). In addition, several numerical applications are developed to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are presented, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. Finally, two numerical techniques, named Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM), are developed to deal with multi-element domains characterized by arbitrary shapes and discontinuities.

Author : V.M.A. Leitao,C.J.S. Alves,C. Armando Duarte
Publisher : Springer Science & Business Media
Page : 315 pages
File Size : 49,6 Mb
Release : 2007-05-26
Category : Technology & Engineering
ISBN : 9781402060953

Get Book

Advances in Meshfree Techniques by V.M.A. Leitao,C.J.S. Alves,C. Armando Duarte Pdf

The book collects extended original contributions presented at the first ECCOMAS Conference on Meshless Methods held in 2005 in Lisbon. The list of contributors is a mix of highly distinguished authors as well as promising young researchers. This means that the reader gets a varied and contemporary view on different mesh reduction methods and its range of applications. The material presented is appropriate for researchers, engineers, physicists, applied mathematicians and graduate students interested in this active research area.

Author : G.R. Liu
Publisher : CRC Press
Page : 772 pages
File Size : 46,6 Mb
Release : 2009-10-06
Category : Mathematics
ISBN : 9781420082104

Get Book

Meshfree Methods by G.R. Liu Pdf

Understand How to Use and Develop Meshfree TechniquesAn Update of a Groundbreaking WorkReflecting the significant advances made in the field since the publication of its predecessor, Meshfree Methods: Moving Beyond the Finite Element Method, Second Edition systematically covers the most widely used meshfree methods. With 70% new material, this edit

Author : Jan Sladek,Vladimir Sladek
Publisher : Unknown
Page : 363 pages
File Size : 40,5 Mb
Release : 2006
Category : Engineering mathematics
ISBN : 0971788022

Get Book

Advances in meshless methods by Jan Sladek,Vladimir Sladek Pdf

Meshless methods belong to one of the most progressivelydeveloped part of computational mechanics. These methods are increasingly applied to many fields of engineering and sciences. Therefore, the number of new results in this field is growing significantly during the past few years. It is a natural need to organize a conference in this subject to discuss about further developments of meshless methods. The first ICCES meshless symposium held in High Tatras, Slovakia brought together both mathematicians and engineers interested in developing new progressive computational methods. The best selected lectures from the symposium are collected in this book in their extended form.

Author : Jorge Belinha
Publisher : Springer
Page : 328 pages
File Size : 41,5 Mb
Release : 2014-05-14
Category : Technology & Engineering
ISBN : 9783319064000

Get Book

Meshless Methods in Biomechanics by Jorge Belinha Pdf

This book presents the complete formulation of a new advanced discretization meshless technique: the Natural Neighbour Radial Point Interpolation Method (NNRPIM). In addition, two of the most popular meshless methods, the EFGM and the RPIM, are fully presented. Being a truly meshless method, the major advantages of the NNRPIM over the FEM and other meshless methods, are the remeshing flexibility and the higher accuracy of the obtained variable field. Using the natural neighbour concept, the NNRPIM permits to determine organically the influence-domain, resembling the cellulae natural behaviour. This innovation permits the analysis of convex boundaries and extremely irregular meshes, which is an advantage in the biomechanical analysis, with no extra computational effort associated. This volume shows how to extend the NNRPIM to the bone tissue remodelling analysis, expecting to contribute with new numerical tools and strategies in order to permit a more efficient numerical biomechanical analysis.

Author : G.R. Liu
Publisher : CRC Press
Page : 715 pages
File Size : 48,7 Mb
Release : 2002-07-29
Category : Mathematics
ISBN : 9781420040586

Get Book

Mesh Free Methods by G.R. Liu Pdf

As we attempt to solve engineering problems of ever increasing complexity, so must we develop and learn new methods for doing so. The Finite Difference Method used for centuries eventually gave way to Finite Element Methods (FEM), which better met the demands for flexibility, effectiveness, and accuracy in problems involving complex geometry. Now,

Author : Romesh C. Batra
Publisher : Springer
Page : 500 pages
File Size : 53,7 Mb
Release : 2016-06-26
Category : Mathematics
ISBN : 1441956824

Get Book

Finite Element and Meshless Methods in Computational Mechanics by Romesh C. Batra Pdf

The finite element and meshless methods are numerical simulation algorithms used to mathematically model physical phenomena. The finite element method relies on the creation of an underlying simplex structure in the region that is being modeled. By specifying these finite elements, a rough model can be developed that can be used to generate approximate solutions while requiring minimal processor time. The meshless method eliminates these finite elements and instead generates a dynamic model from a particle perspective using a complex matrix of integral equations to define the properties of the region being modeled. Without the limitations of the simplex structure, the model can account for large deformations, advanced materials, complex geometries, nonlinear behavior, and discontinuities. However, this utility results in a significant increase in the computational time that is require to generate a solution. Application of these techniques extends to all areas of computational physics, engineering, and mechanics. Although several textbooks exist on the topic of the finite element method and there are some that focus specifically on the meshless method, this is the first textbook to describe both modeling techniques in detail and evaluate their relative advantages.

Author : C. S. Chen,Andreas Karageorghis,Yiorgos S. Smyrlis
Publisher : Unknown
Page : 338 pages
File Size : 49,9 Mb
Release : 2008
Category : Meshfree methods (Numerical analysis)
ISBN : 1890888044

Get Book

The Method of Fundamental Solutions by C. S. Chen,Andreas Karageorghis,Yiorgos S. Smyrlis Pdf

Author : G.R. Liu
Publisher : CRC Press
Page : 692 pages
File Size : 53,8 Mb
Release : 2003
Category : Computers
ISBN : 0849312388

Get Book

Mesh Free Methods by G.R. Liu Pdf

As we attempt to solve engineering problems of ever increasing complexity, so must we develop and learn new methods for doing so. The Finite Difference Method used for centuries eventually gave way to Finite Element Methods (FEM), which better met the demands for flexibility, effectiveness, and accuracy in problems involving complex geometry. Now, however, the limitations of FEM are becoming increasingly evident, and a new and more powerful class of techniques is emerging. For the first time in book form, Mesh Free Methods: Moving Beyond the Finite Element Method provides full, step-by-step details of techniques that can handle very effectively a variety of mechanics problems. The author systematically explores and establishes the theories, principles, and procedures that lead to mesh free methods. He shows that meshless methods not only accommodate complex problems in the mechanics of solids, structures, and fluids, but they do so with a significant reduction in pre-processing time. While they are not yet fully mature, mesh free methods promise to revolutionize engineering analysis. Filled with the new and unpublished results of the author's award-winning research team, this book is your key to unlocking the potential of these techniques, implementing them to solve real-world problems, and contributing to further advancements.

Author : Jorge Belinha,R.M. Natal Jorge,J.C. Reis Campos,Mário A.P. Vaz,João Manuel R.S. Tavares
Publisher : CRC Press
Page : 294 pages
File Size : 43,8 Mb
Release : 2019-02-13
Category : Medical
ISBN : 9780429555848

Get Book

Biodental Engineering V by Jorge Belinha,R.M. Natal Jorge,J.C. Reis Campos,Mário A.P. Vaz,João Manuel R.S. Tavares Pdf

Dentistry is a branch of medicine with its own particularities and very different fields of action, and is generally regarded as an interdisciplinary field. The use of new technologies is currently the main driving force for the series of international conferences on Biodental Engineering (BIODENTAL). BIODENTAL ENGINEERING V contains the full papers presented at the 5th International Conference on Biodental Engineering (BIODENTAL 2018, Porto, Portugal, 22-23 June 2018). The conference had two workshops, one of them dealing with computational imaging combined with finite element method, the other dealing with bone tissue remodelling models. Additionally, the conference had three special sessions and sixty contributed presentations. The topics discussed in BIODENTAL ENGINEERING V include: Aesthetics Bioengineering Biomaterials Biomechanical disorders Biomedical devices Computational bio- imaging and visualization Computational methods Dental medicine Experimental mechanics Signal processing and analysis Implantology Minimally invasive devices and techniques Orthodontics Prosthesis and orthosis Simulation Software development Telemedicine Tissue engineering Virtual reality The purpose of the series of BIODENTAL Conferences on Biodental Engineering, initiated in 2009, is to perpetuate knowledge on bioengineering applied to dentistry, by promoting a comprehensive forum for discussion on recent advances in related fields in order to identify potential collaboration between researchers and end-users from different sciences.

Author : Ken P. Chong,Arthur P. Boresi,Sunil Saigal,James D. Lee
Publisher : CRC Press
Page : 318 pages
File Size : 55,5 Mb
Release : 2017-11-27
Category : Technology & Engineering
ISBN : 9781351380997

Get Book

Numerical Methods in Mechanics of Materials by Ken P. Chong,Arthur P. Boresi,Sunil Saigal,James D. Lee Pdf

In the dynamic digital age, the widespread use of computers has transformed engineering and science. A realistic and successful solution of an engineering problem usually begins with an accurate physical model of the problem and a proper understanding of the assumptions employed. With computers and appropriate software we can model and analyze complex physical systems and problems. However, efficient and accurate use of numerical results obtained from computer programs requires considerable background and advanced working knowledge to avoid blunders and the blind acceptance of computer results. This book provides the background and knowledge necessary to avoid these pitfalls, especially the most commonly used numerical methods employed in the solution of physical problems. It offers an in-depth presentation of the numerical methods for scales from nano to macro in nine self-contained chapters with extensive problems and up-to-date references, covering: Trends and new developments in simulation and computation Weighted residuals methods Finite difference methods Finite element methods Finite strip/layer/prism methods Boundary element methods Meshless methods Molecular dynamics Multiphysics problems Multiscale methods