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Methods of Fundamental Solutions in Solid Mechanics

Methods of Fundamental Solutions in Solid Mechanics
A Book

by 王辉,秦庆华

  • Publisher : Unknown Publisher
  • Release : 2021
  • Pages : 293
  • ISBN : 9787040558197
  • Language : En, Es, Fr & De
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Methods of Fundamental Solutions in Solid Mechanics

Methods of Fundamental Solutions in Solid Mechanics
A Book

by Hui Wang,Qing-Hua Qin

  • Publisher : Elsevier
  • Release : 2019-06-06
  • Pages : 312
  • ISBN : 0128182849
  • Language : En, Es, Fr & De
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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

Engineering Solid Mechanics

Engineering Solid Mechanics
Fundamentals and Applications

by Abdel-Rahman A. Ragab,Salah Eldin Ahm Bayoumi

  • Publisher : CRC Press
  • Release : 1998-12-22
  • Pages : 944
  • ISBN : 9780849316074
  • Language : En, Es, Fr & De
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Engineering Solid Mechanics bridges the gap between elementary approaches to strength of materials and more advanced, specialized versions on the subject. The book provides a basic understanding of the fundamentals of elasticity and plasticity, applies these fundamentals to solve analytically a spectrum of engineering problems, and introduces advanced topics of mechanics of materials - including fracture mechanics, creep, superplasticity, fiber reinforced composites, powder compacts, and porous solids. Text includes: stress and strain, equilibrium, and compatibility elastic stress-strain relations the elastic problem and the stress function approach to solving plane elastic problems applications of the stress function solution in Cartesian and polar coordinates Problems of elastic rods, plates, and shells through formulating a strain compatibility function as well as applying energy methods Elastic and elastic-plastic fracture mechanics Plastic and creep deformation Inelastic deformation and its applications This book presents the material in an instructive manner, suitable for individual self-study. It emphasizes analytical treatment of the subject, which is essential for handling modern numerical methods as well as assessing and creating software packages. The authors provide generous explanations, systematic derivations, and detailed discussions, supplemented by a vast variety of problems and solved examples. Primarily written for professionals and students in mechanical engineering, Engineering Solid Mechanics also serves persons in other fields of engineering, such as aerospace, civil, and material engineering.

Trefftz and Fundamental Solution-Based Finite Element Methods

Trefftz and Fundamental Solution-Based Finite Element Methods
A Book

by Qing-Hua Qin

  • Publisher : Bentham Science Publishers
  • Release : 2021-09-07
  • Pages : 355
  • ISBN : 9814998559
  • Language : En, Es, Fr & De
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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.

Computational Methods in Solid Mechanics

Computational Methods in Solid Mechanics
A Book

by A. Curnier

  • Publisher : Springer Science & Business Media
  • Release : 2012-12-06
  • Pages : 404
  • ISBN : 940111112X
  • Language : En, Es, Fr & De
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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. Chapter 1 addresses the problem of a one-dimensional bar, with emphasis being given to the virtual work principle. Chapters 2--4 present the three numerical methods. Although the discussion relates to a one-dimensional model, the formalism used is extendable to two-dimensional situations. Chapter 5 is devoted to a detailed discussion of the compact combination of the three methods, and contains several sections concerning their computer implementation. Finally, Chapter 6 gives a generalization to two and three dimensions of both the mechanical and numerical aspects. For graduate students and researchers whose work involves the theory and application of computational solid mechanics.

Radial Basis Function Methods For Large-Scale Wave Propagation

Radial Basis Function Methods For Large-Scale Wave Propagation
A Book

by Jun-Pu Li

  • Publisher : Bentham Science Publishers
  • Release : 2021-12-24
  • Pages : 185
  • ISBN : 1681088991
  • Language : En, Es, Fr & De
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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.

Meshless Methods in Solid Mechanics

Meshless Methods in Solid Mechanics
A Book

by Youping Chen,James Lee,Azim Eskandarian

  • Publisher : Springer
  • Release : 2010-02-12
  • Pages : 200
  • ISBN : 9781441921482
  • Language : En, Es, Fr & De
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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.

Boundary Elements and Other Mesh Reduction Methods XXXIII

Boundary Elements and Other Mesh Reduction Methods XXXIII
A Book

by C. A. Brebbia,Viktor Popov,V. Popov

  • Publisher : WIT Press
  • Release : 2011-01-01
  • Pages : 345
  • ISBN : 1845645421
  • Language : En, Es, Fr & De
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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..

Computational Structural Mechanics & Fluid Dynamics

Computational Structural Mechanics & Fluid Dynamics
Advances and Trends

by A.K. Noor,D.L. Dwoyer

  • Publisher : Elsevier
  • Release : 2013-10-22
  • Pages : 467
  • ISBN : 1483287041
  • Language : En, Es, Fr & De
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Computational structural mechanics (CSM) and computational fluid dynamics (CFD) have emerged in the last two decades as new disciplines combining structural mechanics and fluid dynamics with approximation theory, numerical analysis and computer science. Their use has transformed much of theoretical mechanics and abstract science into practical and essential tools for a multitude of technological developments which affect many facets of our life. This collection of over 40 papers provides an authoritative documentation of major advances in both CSM and CFD, helping to identify future directions of development in these rapidly changing fields. Key areas covered are fluid structure interaction and aeroelasticity, CFD technology and reacting flows, micromechanics, stability and eigenproblems, probabilistic methods and chaotic dynamics, perturbation and spectral methods, element technology (finite volume, finite elements and boundary elements), adaptive methods, parallel processing machines and applications, and visualization, mesh generation and artificial intelligence interfaces.

Fundamental Solutions for Differential Operators and Applications

Fundamental Solutions for Differential Operators and Applications
A Book

by Prem Kythe

  • Publisher : Springer Science & Business Media
  • Release : 2012-12-06
  • Pages : 414
  • ISBN : 1461241065
  • Language : En, Es, Fr & De
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A self-contained and systematic development of an aspect of analysis which deals with the theory of fundamental solutions for differential operators, and their applications to boundary value problems of mathematical physics, applied mathematics, and engineering, with the related computational aspects.

IUTAM Symposium on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics

IUTAM Symposium on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics
Proceedings of the IUTAM-ISIMM Symposium held in Nottingham, U.K., 30 August – 3 September 1994

by David F. Parker,Arthur H. England

  • Publisher : Springer Science & Business Media
  • Release : 2013-11-11
  • Pages : 520
  • ISBN : 940158494X
  • Language : En, Es, Fr & De
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Proceedings of the IUTAM-ISIMM Symposium, held in Nottingham, U.K., 30 August--3 September 1994

Boundary Elements and Other Mesh Reduction Methods XXXIV

Boundary Elements and Other Mesh Reduction Methods XXXIV

by C.A. Brebbia,D. Poljak

  • Publisher : WIT Press
  • Release : 2012-06-25
  • Pages : 364
  • ISBN : 1845646223
  • Language : En, Es, Fr & De
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This book contains papers presented at the Thirty Fourth International Conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM), recognised as the international forum for the latest advances of these methods and their applications in science and engineering. The success of the meeting, since the first conference took place in Southampton, UK, in 1978, is an indication of the strength of the research being carried out by many different groups around the world. This continuous growth is a result of the evolution of the techniques from methods based on classical integral equations to techniques now covering a wide variety of mathematical approaches, the main objective of which is to reduce or eliminate the mesh. The mesh, a concept inherited from more primitive methods, such as finite differences and finite elements, is alien to the solution of the problem and dictated only by the limitations of first generation analysis techniques. Topics covered include: Advanced meshless and mesh reduction methods, Electrical engineering and electromagnetics, Fluid flow, Heat and mass transfer, Advanced structural applications, Dynamics and vibrations, Damage mechanics and fracture, Material characterisation, Advanced formulations, Computational techniques, Stochastic modelling, Emerging applications.

Boundary Element Programming in Mechanics

Boundary Element Programming in Mechanics
A Book

by Xiao-Wei Gao,Trevor G. Davies

  • Publisher : Cambridge University Press
  • Release : 2002-03-11
  • Pages : 254
  • ISBN : 9780521773591
  • Language : En, Es, Fr & De
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Nonlinear stress analysis (a branch of solid mechanics) is an essential feature in the design of such diverse structures as aircraft, bridges, machines, and dams. Computational techniques have become vital tools in dealing with the complex, time-consuming problems associated with nonlinear stress analysis. Although finite element techniques are widely used, boundary element methods (BEM) offer a powerful alternative, especially in tackling problems of three-dimensional plasticity. This book describes the application of BEM in solid mechanics, beginning with basic theory and then explaining the numerical implementation of BEM in nonlinear stress analysis. The book includes a state-of-the-art CD-ROM containing BEM source code for use by the reader. This book will be especially useful to stress analysts in industry, research workers in the field of computational plasticity, and postgraduate students taking courses in engineering mechanics.

Dynamic Fracture of Piezoelectric Materials

Dynamic Fracture of Piezoelectric Materials
Solution of Time-Harmonic Problems via BIEM

by Petia Dineva,Dietmar Gross,Ralf Müller,Tsviatko Rangelov

  • Publisher : Springer Science & Business Media
  • Release : 2014-01-30
  • Pages : 249
  • ISBN : 331903961X
  • Language : En, Es, Fr & De
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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.

Wave Propagation in Viscoelastic and Poroelastic Continua

Wave Propagation in Viscoelastic and Poroelastic Continua
A Boundary Element Approach

by Martin Schanz

  • Publisher : Springer Science & Business Media
  • Release : 2012-11-27
  • Pages : 170
  • ISBN : 3540445757
  • Language : En, Es, Fr & De
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Wave propagation is an important topic in engineering sciences, especially, in the field of solid mechanics. A description of wave propagation phenomena is given by Graff [98]: The effect of a sharply applied, localized disturbance in a medium soon transmits or 'spreads' to other parts of the medium. These effects are familiar to everyone, e.g., transmission of sound in air, the spreading of ripples on a pond of water, or the transmission of radio waves. From all wave types in nature, here, attention is focused only on waves in solids. Thus, solely mechanical disturbances in contrast to electro-magnetic or acoustic disturbances are considered. of waves - the compression wave similar to the In solids, there are two types pressure wave in fluids and, additionally, the shear wave. Due to continual reflec tions at boundaries and propagation of waves in bounded solids after some time a steady state is reached. Depending on the influence of the inertia terms, this state is governed by a static or dynamic equilibrium in frequency domain. However, if the rate of onset of the load is high compared to the time needed to reach this steady state, wave propagation phenomena have to be considered.

Slope Analysis Using Boundary Elements

Slope Analysis Using Boundary Elements
A Book

by Yansheng Jiang

  • Publisher : Springer Science & Business Media
  • Release : 2013-03-09
  • Pages : 176
  • ISBN : 3642839185
  • Language : En, Es, Fr & De
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The aim of this book is to provide a new angle on the analysis of slope stability with the Boundary Element Method. The main advantages of BEM are the reduction of the dimensionality of the problem to be solved and accurate selective calculation of internal stresses. This makes it possible, as shown in the book, to develop the algorithms of slip surface analysis of slope more accurate, more rigorous and more easy to be used than in the conventional limit equilibrium methods. The full elastoplastic analysis of slope is also investigated. Besides, the interested reader can find a detailed study of Melan's fundamental solution such as its displacements, its corresponding Galerkin tensor and the treatment of body forces in the half-plan. The basic theory of BEM is outlined in the book so that undergraduate and graduate students of civil engineering, mining engineering and engineering geology can read it without difficulty.

A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs

A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs
A Book

by Matthias Albert Augustin

  • Publisher : Birkhäuser
  • Release : 2015-07-15
  • Pages : 235
  • ISBN : 3319170791
  • Language : En, Es, Fr & De
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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.

Computational Fluid and Solid Mechanics 2003

Computational Fluid and Solid Mechanics 2003
A Book

by K.J Bathe

  • Publisher : Elsevier
  • Release : 2003-06-02
  • Pages : 2524
  • ISBN : 9780080529479
  • Language : En, Es, Fr & De
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Bringing together the world's leading researchers and practitioners of computational mechanics, these new volumes meet and build on the eight key challenges for research and development in computational mechanics. Researchers have recently identified eight critical research tasks facing the field of computational mechanics. These tasks have come about because it appears possible to reach a new level of mathematical modelling and numerical solution that will lead to a much deeper understanding of nature and to great improvements in engineering design. The eight tasks are: The automatic solution of mathematical models Effective numerical schemes for fluid flows The development of an effective mesh-free numerical solution method The development of numerical procedures for multiphysics problems The development of numerical procedures for multiscale problems The modelling of uncertainties The analysis of complete life cycles of systems Education - teaching sound engineering and scientific judgement Readers of Computational Fluid and Solid Mechanics 2003 will be able to apply the combined experience of many of the world's leading researchers to their own research needs. Those in academic environments will gain a better insight into the needs and constraints of the industries they are involved with; those in industry will gain a competitive advantage by gaining insight into the cutting edge research being carried out by colleagues in academia. Features Bridges the gap between academic researchers and practitioners in industry Outlines the eight main challenges facing Research and Design in Computational mechanics and offers new insights into the shifting the research agenda Provides a vision of how strong, basic and exciting education at university can be harmonized with life-long learning to obtain maximum value from the new powerful tools of analysis

Stress Analysis by Boundary Element Methods

Stress Analysis by Boundary Element Methods
A Book

by Ján Balaš,Ján Sládek,Vladimír Sládek

  • Publisher : Elsevier Science Limited
  • Release : 1989
  • Pages : 686
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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The boundary element method is an extremely versatile and powerful tool of computational mechanics which has already become a popular alternative to the well established finite element method. This book presents a comprehensive and up-to-date treatise on the boundary element method (BEM) in its applications to various fields of continuum mechanics such as: elastostatics, elastodynamics, thermoelasticity, micropolar elasticity, elastoplasticity, viscoelasticity, theory of plates and stress analysis by hybrid methods. The fundamental solution of governing differential equations, integral representations of the displacement and temperature fields, regularized integral representations of the stress field and heat flux, boundary integral equations and boundary integro-differential equations are derived. Besides the mathematical foundations of the boundary integral method, the book deals with practical applications of this method. Most of the applications concentrate mainly on the computational problems of fracture mechanics. The method has been found to be very efficient in stress-intensity factor computations.

Boundary Element Advances in Solid Mechanics

Boundary Element Advances in Solid Mechanics
A Book

by Dimitri Beskos,Giulio Maier

  • Publisher : Springer
  • Release : 2014-05-04
  • Pages : 307
  • ISBN : 3709127904
  • Language : En, Es, Fr & De
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This volume presents and discusses recent advances in boundary element methods and their solid mechanics applications. It illustrates these methods in their latest forms, developed during the last five to ten years, and demonstrates their advantages in solving a wide range of solid mechanics problems.