Methods Of Fundamental Solutions In Solid Mechanics
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Methods Of Fundamental Solutions In Solid Mechanics
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Author : Hui Wang
language : en
Publisher: Elsevier
Release Date : 2019-06-06
Methods Of Fundamental Solutions In Solid Mechanics written by Hui Wang and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-06 with Technology & Engineering categories.
Methods of Fundamental Solutions in Solid Mechanics presents the fundamentals of continuum mechanics, the foundational concepts of the MFS, and methodologies and applications to various engineering problems. Eight chapters give an overview of meshless methods, the mechanics of solids and structures, the basics of fundamental solutions and radical basis functions, meshless analysis for thin beam bending, thin plate bending, two-dimensional elastic, plane piezoelectric problems, and heat transfer in heterogeneous media. The book presents a working knowledge of the MFS that is aimed at solving real-world engineering problems through an understanding of the physical and mathematical characteristics of the MFS and its applications. - Explains foundational concepts for the method of fundamental solutions (MFS) for the advanced numerical analysis of solid mechanics and heat transfer - Extends the application of the MFS for use with complex problems - Considers the majority of engineering problems, including beam bending, plate bending, elasticity, piezoelectricity and heat transfer - Gives detailed solution procedures for engineering problems - Offers a practical guide, complete with engineering examples, for the application of the MFS to real-world physical and engineering challenges
Computational Methods In Solid Mechanics
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Author : A. Curnier
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-05-31
Computational Methods In Solid Mechanics written by A. Curnier 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 1994-05-31 with Mathematics categories.
This volume presents an introduction to the three numerical methods most commonly used in the mechanical analysis of deformable solids, viz. the finite element method (FEM), the linear iteration method (LIM), and the finite difference method (FDM). The book has been written from the point of view of simplicity and unity; its originality lies in the comparable emphasis given to the spatial, temporal and nonlinear dimensions of problem solving. This leads to a neat global algorithm. Audience: Graduate students and researchers whose work involves the theory and application of computational solid mechanics.
Advanced Mechanics Of Solids
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Author : Lester W. Schmerr
language : en
Publisher: Cambridge University Press
Release Date : 2021-02-18
Advanced Mechanics Of Solids written by Lester W. Schmerr and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-18 with Science categories.
Build on elementary mechanics of materials texts with this treatment of the analysis of stresses and strains in elastic bodies.
Trefftz And Fundamental Solution Based Finite Element Methods
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Author : Qing-Hua Qin
language : en
Publisher: Bentham Science Publishers
Release Date : 2021-09-07
Trefftz And Fundamental Solution Based Finite Element Methods written by Qing-Hua Qin and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-07 with Mathematics categories.
This reference explains hybrid-Trefftz finite element method (FEM). Readers are introduced to the basic concepts and general element formulations of the method. This is followed by topics on non-homogeneous parabolic problems, thermal analysis of composites, and heat conduction in nonlinear functionally graded materials. A brief summary of the fundamental solution based-FEM is also presented followed by a discussion on axisymmetric potential problems and the rotordynamic response of tapered composites. The book is rounded by chapters that cover the n-sided polygonal hybrid finite elements and analysis of piezoelectric materials. Key Features - Systematic presentation of 9 topics - Covers FEMs in two sections: 1) hybrid-Trefftz method and 2) fundamental FEM solutions - Bibliographic references - Includes solutions to problems in the numerical analysis of different material types - Includes solutions to some problems encountered in civil engineering (seepage, heat transfer, etc). This reference is suitable for scholars involved in advanced courses in mathematics and engineering (civil engineering/materials engineering). Professionals involved in developing analytical tools for materials and construction testing can also benefit from the methods presented in the book.
Modern Mathematics And Mechanics
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Author : Victor A. Sadovnichiy
language : en
Publisher: Springer
Release Date : 2018-11-29
Modern Mathematics And Mechanics written by Victor A. Sadovnichiy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-29 with Technology & Engineering categories.
In this book international expert authors provide solutions for modern fundamental problems including the complexity of computing of critical points for set-valued mappings, the behaviour of solutions of ordinary differential equations, partial differential equations and difference equations, or the development of an abstract theory of global attractors for multi-valued impulsive dynamical systems. These abstract mathematical approaches are applied to problem-solving in solid mechanics, hydro- and aerodynamics, optimization, decision making theory and control theory. This volume is therefore relevant to mathematicians as well as engineers working at the interface of these fields.
A Method Of Fundamental Solutions In Poroelasticity To Model The Stress Field In Geothermal Reservoirs
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Author : Matthias Albert Augustin
language : en
Publisher: Birkhäuser
Release Date : 2015-07-15
A Method Of Fundamental Solutions In Poroelasticity To Model The Stress Field In Geothermal Reservoirs written by Matthias Albert Augustin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with Mathematics categories.
This monograph focuses on the numerical methods needed in the context of developing a reliable simulation tool to promote the use of renewable energy. One very promising source of energy is the heat stored in the Earth’s crust, which is harnessed by so-called geothermal facilities. Scientists from fields like geology, geo-engineering, geophysics and especially geomathematics are called upon to help make geothermics a reliable and safe energy production method. One of the challenges they face involves modeling the mechanical stresses at work in a reservoir. The aim of this thesis is to develop a numerical solution scheme by means of which the fluid pressure and rock stresses in a geothermal reservoir can be determined prior to well drilling and during production. For this purpose, the method should (i) include poroelastic effects, (ii) provide a means of including thermoelastic effects, (iii) be inexpensive in terms of memory and computational power, and (iv) be flexible with regard to the locations of data points. After introducing the basic equations and their relations to more familiar ones (the heat equation, Stokes equations, Cauchy-Navier equation), the “method of fundamental solutions” and its potential value concerning our task are discussed. Based on the properties of the fundamental solutions, theoretical results are established and numerical examples of stress field simulations are presented to assess the method’s performance. The first-ever 3D graphics calculated for these topics, which neither requiring meshing of the domain nor involving a time-stepping scheme, make this a pioneering volume.
Dynamic Fracture Of Piezoelectric Materials
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Author : Petia Dineva
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-30
Dynamic Fracture Of Piezoelectric Materials written by Petia Dineva 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 2014-01-30 with Technology & Engineering categories.
Dynamic Fracture of Piezoelectric Materials focuses on the Boundary Integral Equation Method as an efficient computational tool. The presentation of the theoretical basis of piezoelectricity is followed by sections on fundamental solutions and the numerical realization of the boundary value problems. Two major parts of the book are devoted to the solution of problems in homogeneous and inhomogeneous solids. The book includes contributions on coupled electro-mechanical models, computational methods, its validation and the simulation results, which reveal different effects useful for engineering design and practice. The book is self-contained and well-illustrated, and it serves as a graduate-level textbook or as extra reading material for students and researchers.
Radial Basis Function Methods For Large Scale Wave Propagation
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Author : Jun-Pu Li
language : en
Publisher: Bentham Science Publishers
Release Date : 2021-12-24
Radial Basis Function Methods For Large Scale Wave Propagation written by Jun-Pu Li and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-24 with Science categories.
This book details the development of techniques and ideas from the radial basis function. It begins with a mathematical description of the basic concept of radial function method with chapters progressively delving into the derivation and construction of radial basis functions for large-scale wave propagation problems including singularity problems, high-frequency wave problems and large-scale computation problems. This reference, written by experts in numerical analysis, demonstrates how the functions arise naturally in mathematical analyses of structures responding to external loads. Readers are also equipped with mathematical knowledge about the radial basis function for understanding key algorithms required for practical solutions. Key features: - Introduces basic concepts of radial basis function methods - Provides detailed derivations of several radial basis functions - Explains complex problems using simple language - Contains a wide range of numerical examples to demonstrate applications of relevant functions - Combines the radial basis function with other known numerical methods (boundary element methods and differential equations). - Includes references and appropriate chapter appendices - Includes MATLAB codes for origin intensity factors and nearly singular factors for radial basis calculations The book is designed to make information about radial basis function methods more accessible to research scientists, professional engineers and postgraduate students, with a specific focus on large-scale wave propagation problems.
Boundary Elements And Other Mesh Reduction Methods Xxxiii
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Author : C. A. Brebbia
language : en
Publisher: WIT Press
Release Date : 2011
Boundary Elements And Other Mesh Reduction Methods Xxxiii written by C. A. Brebbia and has been published by WIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The Wessex Institute of Technology has been convening conferences on the Boundary Element Method since 1978. The now-annual conference series is recognised internationally as the premiere forum for sharing the latest advances on the boundary element method and other meshless techniques and their applications, which continue to evolve and grow in importance. The papers presented at the latest conference will cover topics such as Advanced meshless and mesh reduction methods; Heat and mass transfer; Electrical engineering and electromagnetics; Fluid flow; Advanced formulations; Computational techniques; Advanced structural applications; Dynamics and vibrations; Damage mechanics and fracture; Material characterisation; Financial engineering applications; Stochastic modelling; and Emerging applications..
Approximate Solution Methods In Engineering Mechanics
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Author : Arthur P. Boresi
language : en
Publisher: John Wiley & Sons
Release Date : 2003
Approximate Solution Methods In Engineering Mechanics written by Arthur P. Boresi and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
The only complete collection of prevalent approximation methods Unlike any other resource, Approximate Solution Methods in Engineering Mechanics, Second Edition offers in-depth coverage of the most common approximate numerical methods used in the solution of physical problems, including those used in popular computer modeling packages. Descriptions of each approximation method are presented with the latest relevant research and developments, providing thorough, working knowledge of the methods and their principles. Approximation methods covered include: * Boundary element method (BEM) * Weighted residuals method * Finite difference method (FDM) * Finite element method (FEM) * Finite strip/layer/prism methods * Meshless method Approximate Solution Methods in Engineering Mechanics, Second Edition is a valuable reference guide for mechanical, aerospace, and civil engineers, as well as students in these disciplines.