Meshless Methods and Their Numerical Properties - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Meshless Methods and Their Numerical Properties write by Hua Li. This book was released on 2013-02-22. Meshless Methods and Their Numerical Properties available in PDF, EPUB and Kindle. 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.
An Introduction to Meshfree Methods and Their Programming
An Introduction to Meshfree Methods and Their Programming - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Meshfree Methods and Their Programming write by G.R. Liu. This book was released on 2005-12-05. An Introduction to Meshfree Methods and Their Programming available in PDF, EPUB and Kindle. 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.
Advances in Meshfree Techniques
Advances in Meshfree Techniques - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in Meshfree Techniques write by V.M.A. Leitao. This book was released on 2007-05-26. Advances in Meshfree Techniques available in PDF, EPUB and Kindle. 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.
Anisotropic Doubly-Curved Shells
Anisotropic Doubly-Curved Shells - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Anisotropic Doubly-Curved Shells write by Francesco Tornabene. This book was released on 2019-11-01. Anisotropic Doubly-Curved Shells available in PDF, EPUB and Kindle. 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.
Finite Element and Meshless Methods in Computational Mechanics
Finite Element and Meshless Methods in Computational Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Element and Meshless Methods in Computational Mechanics write by Romesh C. Batra. This book was released on 2016-06-26. Finite Element and Meshless Methods in Computational Mechanics available in PDF, EPUB and Kindle. 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.
