Meshless Methods and Their Numerical Properties
Meshless Methods and Their Numerical Properties

Author: Hua Li

Publisher: CRC Press

Published: 2013-02-22

Total Pages: 451

ISBN-13: 1466517468

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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.

Meshless Methods and Their Numerical Properties
Meshless Methods and Their Numerical Properties

Author: Hua Li

Publisher: CRC Press

Published: 2013-02-22

Total Pages: 429

ISBN-13: 1466517476

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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

An Introduction to Meshfree Methods and Their Programming
An Introduction to Meshfree Methods and Their Programming

Author: G.R. Liu

Publisher: Springer Science & Business Media

Published: 2005-12-05

Total Pages: 497

ISBN-13: 1402034687

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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.

Numerical Methods for Energy Applications
Numerical Methods for Energy Applications

Author: Naser Mahdavi Tabatabaei

Publisher: Springer Nature

Published: 2021-03-22

Total Pages: 1033

ISBN-13: 303062191X

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This book provides a thorough guide to the use of numerical methods in energy systems and applications. It presents methods for analysing engineering applications for energy systems, discussing finite difference, finite element, and other advanced numerical methods. Solutions to technical problems relating the application of these methods to energy systems are also thoroughly explored. Readers will discover diverse perspectives of the contributing authors and extensive discussions of issues including: • a wide variety of numerical methods concepts and related energy systems applications;• systems equations and optimization, partial differential equations, and finite difference method;• methods for solving nonlinear equations, special methods, and their mathematical implementation in multi-energy sources;• numerical investigations of electrochemical fields and devices; and• issues related to numerical approaches and optimal integration of energy consumption. This is a highly informative and carefully presented book, providing scientific and academic insight for readers with an interest in numerical methods and energy systems.

Numerical Methods and Implementation in Geotechnical Engineering – Part 1
Numerical Methods and Implementation in Geotechnical Engineering – Part 1

Author: Y.M. Cheng

Publisher: Bentham Science Publishers

Published: 2020-04-01

Total Pages: 594

ISBN-13: 9811437378

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Numerical Methods and Implementation in Geotechnical Engineering explains several numerical methods that are used in geotechnical engineering. The first part of this reference set includes methods such as the finite element method, distinct element method, discontinuous deformation analysis, numerical manifold method, smoothed particle hydrodynamics method, material point method, plasticity method, limit equilibrium and limit analysis, plasticity, slope stability and foundation engineering, optimization analysis and reliability analysis. The authors have also presented different computer programs associated with the materials in this book which will be useful to students learning how to apply the models explained in the text into practical situations when designing structures in locations with specific soil and rock settings. This reference book set is a suitable textbook primer for civil engineering students as it provides a basic introduction to different numerical methods (classical and modern) in comprehensive readable volumes.

Environmental Contaminants
Environmental Contaminants

Author: Tarun Gupta

Publisher: Springer

Published: 2017-11-28

Total Pages: 441

ISBN-13: 9811073325

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This book addresses the measurement of environmental contaminants in water, air, and soil. It also presents modifications of and improvements to existing control technologies for remediation of environmental contaminants. It covers improved designs of wastewater systems and innovations in designing newer membranes for water treatment. In addition, it includes two separate sections on the modelling and control of different existing and emerging pollutants. It covers major topics such as: pharmaceutical wastes, paper and pulp waste, poly aromatic hydrocarbons, mining dust, bioaerosols, endosulphan, biomass combustion, and landfill design aspects. It also features chapters on environmental exposure and modelling of aerosol deposition within human lungs. The content of this book will be of interest to researchers, professionals, and policymakers whose work involves environmental contaminants and related solutions.

Hygro-Thermo-Magneto-Electro-Elastic Theory of Anisotropic Doubly-Curved Shells
Hygro-Thermo-Magneto-Electro-Elastic Theory of Anisotropic Doubly-Curved Shells

Author: Francesco Tornabene

Publisher: Società Editrice Esculapio

Published: 2023-10-13

Total Pages: 1073

ISBN-13:

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This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for studying the Hygro-Thermo-Magneto-Electro- Elastic Theory of Anisotropic Doubly-Curved Shells. In particular, a general coupled multifield theory regarding anisotropic shell structures is provided. The three-dimensional multifield problem is reduced in a two-dimensional one following the principles of the Equivalent Single Layer (ESL) approach and the Equivalent Layer-Wise (ELW) approach, setting a proper configuration model. According to the adopted configuration assumptions, several Higher-order Shear Deformation Theories (HSDTs) are obtained. Furthermore, 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 physical 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 used to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are considered, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. The Theory of Composite Thin Shells is derived in a simple and intuitive manner from the theory of thick and moderately thick shells (First-order Shear Deformation Theory or Reissner- Mindlin Theory). In particular, the Kirchhoff-Love Theory and the Membrane Theory for composite shells are shown. Furthermore, the Theory of Composite Arches and Beams is also exposed. In particular, the equations of the Timoshenko Theory and the Euler-Bernoulli Theory are directly deducted from the equations of singly-curved shells of translation and of plates.

Mesh Free Methods
Mesh Free Methods

Author: G.R. Liu

Publisher: CRC Press

Published: 2002-07-29

Total Pages: 715

ISBN-13: 1420040588

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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,

Meshfree Methods
Meshfree Methods

Author: G.R. Liu

Publisher: CRC Press

Published: 2009-10-06

Total Pages: 772

ISBN-13: 1420082108

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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

Reduced Modelling of Planar Fuel Cells
Reduced Modelling of Planar Fuel Cells

Author: Zhongjie He

Publisher: Springer

Published: 2016-12-25

Total Pages: 306

ISBN-13: 331942646X

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This book focuses on novel reduced cell and stack models for proton exchange membrane fuel cells (PEMFCs) and planar solid oxide fuel cells (P-SOFCs) that serve to reduce the computational cost by two orders of magnitude or more with desired numerical accuracy, while capturing both the average properties and the variability of the dependent variables in the 3D counterparts. The information provided can also be applied to other kinds of plate-type fuel cells whose flow fields consist of parallel plain channels separated by solid ribs. These fast and efficient models allow statistical sensitivity analysis for a sample size in the order of 1000 without prohibitive computational cost to be performed to investigate not only the individual, but also the simultaneous effects of a group of varying geometrical, material, and operational parameters. This provides important information for cell/stack design, and to illustrate this, Monte Carlo simulation of the reduced P-SOFC model is conducted at both the single-cell and stack levels.