The Meshless Local Petrov Galerkin Mlpg Method

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The Meshless Local Petrov Galerkin Mlpg Method

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Author : Satya N. Atluri
language : en
Publisher: Crest
Release Date : 2002

The Meshless Local Petrov Galerkin Mlpg Method written by Satya N. Atluri and has been published by Crest this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

An Introduction To Meshfree Methods And Their Programming

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Author : G.R. Liu
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-05

An Introduction To Meshfree Methods And Their Programming written by G.R. Liu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-05 with Technology & Engineering categories.

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.

Meshless Methods In Solid Mechanics

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Author : Youping Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-28

Meshless Methods In Solid Mechanics written by Youping Chen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-28 with Science categories.

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.

Mesh Free Methods

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Author : G.R. Liu
language : en
Publisher: CRC Press
Release Date : 2002-07-29

Mesh Free Methods written by G.R. Liu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-29 with Mathematics categories.

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,

Three Dimensional Meshless Local Petrov Galerkin Mlpg Method

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Author : Qiuzhan Li
language : en
Publisher:
Release Date : 2005

Three Dimensional Meshless Local Petrov Galerkin Mlpg Method written by Qiuzhan Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Boundary element methods categories.

Meshfree Particle Methods

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Author : Shaofan Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-07

Meshfree Particle Methods written by Shaofan Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-07 with Mathematics categories.

Meshfree Particle Methods is a comprehensive and systematic exposition of particle methods, meshfree Galerkin and partitition of unity methods, molecular dynamics methods, and multiscale methods. Most theories, computational formulations, and simulation results presented are recent developments in meshfree methods. They were either just published recently or even have not been published yet, many of them resulting from the authors ́ own research. The presentation of the technical content is heuristic and explanatory with a balance between mathematical rigor and engineering practice. It can be used as a graduate textbook or a comprehensive source for researchers, providing the state of the art on Meshfree Particle Methods.

Meshfree Methods

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Author : G.R. Liu
language : en
Publisher: CRC Press
Release Date : 2009-10-06

Meshfree Methods written by G.R. Liu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-06 with Mathematics categories.

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

Methods Of Computer Modeling In Engineering The Sciences A Unified Treatment Of Finite Volume Finite Element Field Boundary Element Meshless Boundary Methods

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Author : Satya N. Atluri
language : en
Publisher: Crest
Release Date : 2005

Methods Of Computer Modeling In Engineering The Sciences A Unified Treatment Of Finite Volume Finite Element Field Boundary Element Meshless Boundary Methods written by Satya N. Atluri and has been published by Crest this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computers categories.

Generalized Differential And Integral Quadrature

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Author : Francesco Tornabene
language : en
Publisher: Società Editrice Esculapio
Release Date : 2023-10-17

Generalized Differential And Integral Quadrature written by Francesco Tornabene and has been published by Società Editrice Esculapio this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-17 with Technology & Engineering categories.

The main aim of this book is to analyze the mathematical fundamentals and the main features of the Generalized Differential Quadrature (GDQ) and Generalized Integral Quadrature (GIQ) techniques. Furthermore, another interesting aim of the present book is to shown that from the two numerical techniques mentioned above it is possible to derive two different approaches such as the Strong and Weak Finite Element Methods (SFEM and WFEM), that will be used to solve various structural problems and arbitrarily shaped structures. A general approach to the Differential Quadrature is proposed. The weighting coefficients for different basis functions and grid distributions are determined. Furthermore, the expressions of the principal approximating polynomials and grid distributions, available in the literature, are shown. Besides the classic orthogonal polynomials, a new class of basis functions, which depend on the radial distance between the discretization points, is presented. They are known as Radial Basis Functions (or RBFs). The general expressions for the derivative evaluation can be utilized in the local form to reduce the computational cost. From this concept the Local Generalized Differential Quadrature (LGDQ) method is derived. The Generalized Integral Quadrature (GIQ) technique can be used employing several basis functions, without any restriction on the point distributions for the given definition domain. To better underline these concepts some classical numerical integration schemes are reported, such as the trapezoidal rule or the Simpson method. An alternative approach based on Taylor series is also illustrated to approximate integrals. This technique is named as Generalized Taylor-based Integral Quadrature (GTIQ) method. The major structural theories for the analysis of the mechanical behavior of various structures are presented in depth in the book. In particular, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. Generally speaking, two formulations of the same system of governing equations can be developed, which are respectively the strong and weak (or variational) formulations. Once the governing equations that rule a generic structural problem are obtained, together with the corresponding boundary conditions, a differential system is written. In particular, the Strong Formulation (SF) of the governing equations is obtained. The differentiability requirement, instead, is reduced through a weighted integral statement if the corresponding Weak Formulation (WF) of the governing equations is developed. Thus, an equivalent integral formulation is derived, starting directly from the previous one. In particular, the formulation in hand is obtained by introducing a Lagrangian approximation of the degrees of freedom of the problem. The need of studying arbitrarily shaped domains or characterized by mechanical and geometrical discontinuities leads to the development of new numerical approaches that divide the structure in finite elements. Then, the strong form or the weak form of the fundamental equations are solved inside each element. The fundamental aspects of this technique, which the author defined respectively Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM), are presented in the book.