Methods of Fundamental Solutions in Solid Mechanics Book

Methods of Fundamental Solutions in Solid Mechanics


  • Author : Hui Wang
  • Publisher : Elsevier
  • Release Date : 2019-06-06
  • Genre: Technology & Engineering
  • Pages : 312
  • ISBN 10 : 9780128182840

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Methods of Fundamental Solutions in Solid Mechanics Excerpt :

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

Trefftz and Fundamental Solution Based Finite Element Methods Book

Trefftz and Fundamental Solution Based Finite Element Methods


  • Author : Qing-Hua Qin
  • Publisher : Bentham Science Publishers
  • Release Date : 2021-09-07
  • Genre: Mathematics
  • Pages : 357
  • ISBN 10 : 9789814998550

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Trefftz and Fundamental Solution Based Finite Element Methods Excerpt :

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.

Radial Basis Function Methods For Large Scale Wave Propagation Book

Radial Basis Function Methods For Large Scale Wave Propagation


  • Author : Jun-Pu Li
  • Publisher : Bentham Science Publishers
  • Release Date : 2021-12-24
  • Genre: Science
  • Pages : 185
  • ISBN 10 : 9781681088990

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Radial Basis Function Methods For Large Scale Wave Propagation Excerpt :

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.

Computational Methods in Solid Mechanics Book

Computational Methods in Solid Mechanics


  • Author : A. Curnier
  • Publisher : Springer Science & Business Media
  • Release Date : 1994-05-31
  • Genre: Mathematics
  • Pages : 424
  • ISBN 10 : 0792327616

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Computational Methods in Solid Mechanics Excerpt :

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.

Computational Fluid and Solid Mechanics 2003 Book
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Computational Fluid and Solid Mechanics 2003


  • Author : K.J Bathe
  • Publisher : Elsevier
  • Release Date : 2003-06-02
  • Genre: Science
  • Pages : 2524
  • ISBN 10 : 008052947X

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Computational Fluid and Solid Mechanics 2003 Excerpt :

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

Boundary Elements and Other Mesh Reduction Methods XXXIII Book

Boundary Elements and Other Mesh Reduction Methods XXXIII


  • Author : C. A. Brebbia
  • Publisher : WIT Press
  • Release Date : 2011-01-01
  • Genre: Mathematics
  • Pages : 345
  • ISBN 10 : 9781845645427

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Boundary Elements and Other Mesh Reduction Methods XXXIII Excerpt :

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..

Fundamental Solutions for Differential Operators and Applications Book

Fundamental Solutions for Differential Operators and Applications


  • Author : Prem Kythe
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Mathematics
  • Pages : 414
  • ISBN 10 : 9781461241065

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Fundamental Solutions for Differential Operators and Applications Excerpt :

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.

Boundary Elements and Other Mesh Reduction Methods XXXIV Book

Boundary Elements and Other Mesh Reduction Methods XXXIV


  • Author : C.A. Brebbia
  • Publisher : WIT Press
  • Release Date : 2012-06-25
  • Genre: Mathematics
  • Pages : 365
  • ISBN 10 : 9781845646226

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Boundary Elements and Other Mesh Reduction Methods XXXIV Excerpt :

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.

Computational Structural Mechanics   Fluid Dynamics Book

Computational Structural Mechanics Fluid Dynamics


  • Author : A.K. Noor
  • Publisher : Elsevier
  • Release Date : 2013-10-22
  • Genre: Technology & Engineering
  • Pages : 467
  • ISBN 10 : 9781483287041

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Computational Structural Mechanics Fluid Dynamics Excerpt :

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.

Boundary Element Methods in Applied Mechanics Book

Boundary Element Methods in Applied Mechanics


  • Author : Masataka Tanaka
  • Publisher : Elsevier
  • Release Date : 2013-10-22
  • Genre: Technology & Engineering
  • Pages : 571
  • ISBN 10 : 9781483286969

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Boundary Element Methods in Applied Mechanics Excerpt :

This Proceedings features a broad range of computational mechanics papers on both solid and fluid mechanics as well as electromagnetics, acoustics, heat transfer and other interdisciplinary problems. Topics covered include theoretical developments, numerical analysis, intelligent and adaptive solution strategies and practical applications.

Boundary Element Advances in Solid Mechanics Book

Boundary Element Advances in Solid Mechanics


  • Author : Dimitri Beskos
  • Publisher : Springer
  • Release Date : 2014-05-04
  • Genre: Technology & Engineering
  • Pages : 307
  • ISBN 10 : 9783709127902

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Boundary Element Advances in Solid Mechanics Excerpt :

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.

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

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


  • Author : Matthias Albert Augustin
  • Publisher : Birkhäuser
  • Release Date : 2015-07-15
  • Genre: Mathematics
  • Pages : 235
  • ISBN 10 : 9783319170794

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

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.

Boundary Collocation Techniques and their Application in Engineering Book

Boundary Collocation Techniques and their Application in Engineering


  • Author : J.A. Kołodziej
  • Publisher : WIT Press
  • Release Date : 2009-10-01
  • Genre: Mathematics
  • Pages : 336
  • ISBN 10 : 9781845643942

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Boundary Collocation Techniques and their Application in Engineering Excerpt :

Methods of mathematical modelling applied in contemporary computational mechanics can be divided into purely numerical and analytical-numerical procedures. In this book, the first part is a general presentation of the boundary collocation approach and its numerous variants and in the second part the method is applied to many engineering problems.