{"product_id":"the-scaled-boundary-finite-element-method-isbn-9780471486824","title":"The Scaled Boundary Finite Element Method","description":"A novel computational procedure called the scaled boundary finite-element method is described which combines the advantages of the finite-element and boundary-element methods : Of the finite-element method that no fundamental solution is required and thus expanding the scope of application, for instance to anisotropic material without an increase in complexity and that singular integrals are avoided and that symmetry of the results is automatically satisfied. Of the boundary-element method that the spatial dimension is reduced by one as only the boundary is discretized with surface finite elements, reducing the data preparation and computational efforts, that the boundary conditions at infinity are satisfied exactly and that no approximation other than that of the surface finite elements on the boundary is introduced. In addition, the scaled boundary finite-element method presents appealing features of its own : an analytical solution inside the domain is achieved, permitting for instance accurate stress intensity factors to be determined directly and no spatial discretization of certain free and fixed boundaries and interfaces between different materials is required. In addition, the scaled boundary finite-element method combines the advantages of the analytical and numerical approaches. In the directions parallel to the boundary, where the behaviour is, in general, smooth, the weighted-residual approximation of finite elements applies, leading to convergence in the finite-element sense. In the third (radial) direction, the procedure is analytical, permitting e.g. stress-intensity factors to be determined directly based on their definition or the boundary conditions at infinity to be satisfied exactly.\u003cbr\u003e In a nutshell, the scaled boundary finite-element method is a semi-analytical fundamental-solution-less boundary-element method based on finite elements. The best of both worlds is achieved in two ways: with respect to the analytical and numerical methods and with respect to the finite-element and boundary-element methods within the numerical procedures.\u003cbr\u003e The book serves two goals: Part I is an elementary text, without any prerequisites, a primer, but which using a simple model problem still covers all aspects of the method and Part II presents a detailed derivation of the general case of statics, elastodynamics and diffusion. FOREWORD.\u003cbr\u003e \u003cbr\u003e PREFACE.\u003cbr\u003e \u003cbr\u003e ACKNOWLEDGEMENTS.\u003cbr\u003e \u003cbr\u003e FUNDAMENTALS OF NUMERICAL ANALYSIS.\u003cbr\u003e \u003cbr\u003e NOVEL COMPUTATIONAL PROCEDURE.\u003cbr\u003e \u003cbr\u003e PART I. MODEL PROBLEM: LINE ELEMENT FOR SCALAR WAVE EQUATION.\u003cbr\u003e \u003cbr\u003e CONCEPTS OF SCALED BOUNDARY TRANSFORMATION OF GEOMETRY AND SIMILARITY.\u003cbr\u003e \u003cbr\u003e WEDGE AND TRUNCATED SEMI-INFINITE WEDGE OF SHEAR PLATE.\u003cbr\u003e \u003cbr\u003e SCALED-BOUNDARY-TRANSFORMATION-BASED DERIVATION.\u003cbr\u003e \u003cbr\u003e MECHANICALLY-BASED DERIVATION.\u003cbr\u003e \u003cbr\u003e MODELISATION WITH SINGLE LINE FINITE ELEMENT.\u003cbr\u003e \u003cbr\u003e STATICS.\u003cbr\u003e \u003cbr\u003e MASS OF WEDGE.\u003cbr\u003e \u003cbr\u003e HIGH-FREQUENCY ASYMPTOTIC EXPANSION FOR DYNAMIC STIFFNESS OF TRUNCATED SEMI-INFINITE WEDGE.\u003cbr\u003e \u003cbr\u003e NUMERICAL SOLUTION OF DYNAMIC STIFFNESS, UNIT-IMPULSE RESPONSE AND DISPLACEMENT OF TRUNCATED SEMI-INFINITE WEDGE.\u003cbr\u003e \u003cbr\u003e ANALYTICAL SOLUTION IN FREQUENCY DOMAIN.\u003cbr\u003e \u003cbr\u003e IMPLEMENTATION.\u003cbr\u003e \u003cbr\u003e CONCLUSIONS.\u003cbr\u003e \u003cbr\u003e APPENDIX A: SOLID MODELLING.\u003cbr\u003e \u003cbr\u003e APPENDIX B: HARMONIC MOTION AND FOURIER TRANSFORMATION.\u003cbr\u003e \u003cbr\u003e APPENDIX C: DYNAMIC UNBOUNDED MEDIUM-STRUCTURE INTERACTION.\u003cbr\u003e \u003cbr\u003e APPENDIX D: HISTORICAL NOTE. PART II. TWO- AND THREE- DIMENSIONAL ELASTODYNAMICS, STATICS AND DIFFUSION.\u003cbr\u003e \u003cbr\u003e FUNDAMENTAL EQUATIONS.\u003cbr\u003e \u003cbr\u003e STATICS.\u003cbr\u003e \u003cbr\u003e MASS MATRIX OF BOUNDED MEDIUM.\u003cbr\u003e \u003cbr\u003e HIGH-FREQUENCY ASYMPTOTIC EXPANSION FOR DYNAMIC STIFFNESS OF UNBOUNDED MEDIUM.\u003cbr\u003e \u003cbr\u003e NUMERICAL SOLUTION OF DYNAMIC STIFFNESS, UNIT-IMPULSE RESPONSE AND DISPLACEMENT OF UNBOUNDED MEDIUM.\u003cbr\u003e \u003cbr\u003e ANALYTICAL SOLUTION IN FREQUENCY DOMAIN.\u003cbr\u003e \u003cbr\u003e EXTENSIONS.\u003cbr\u003e \u003cbr\u003e SUBSTRUCTURING.\u003cbr\u003e \u003cbr\u003e EXAMPLES FOR BOUNDED MEDIA.\u003cbr\u003e \u003cbr\u003e EXAMPLES FOR UNBOUNDED MEDIA.\u003cbr\u003e \u003cbr\u003e ERROR ESTIMATION AND ADAPTIVITY.\u003cbr\u003e \u003cbr\u003e CONCLUDING REMARKS.\u003cbr\u003e \u003cbr\u003e REFERENCES.\u003cbr\u003e \u003cbr\u003e INDEX. \u003cp\u003e\"... very helpful for anyone who wants to apply this new method... summarises all essentials... self consistent....\" (\u003ci\u003eComputational Mechanics,\u003c\/i\u003e Vol 33, 2004)\u003c\/p\u003e \u003cp\u003e\"... exceptionally well-written book... needless to say all libraries should have this valuable book....\" (\u003ci\u003eJournal of Sound and Vibration,\u003c\/i\u003e Vol 270, 2004)\u003c\/p\u003e  \u003cp\u003eJohn P. Wolf is the author of The Scaled Boundary Finite Element Method, published by Wiley.  The Scaled Boundary Finite Element Method describes a fundamental solution-less boundary element method, based on finite elements. As such, it combines the advantages of the boundary element method:\u003cbr\u003e * spatial discretisation reduced by one\u003cbr\u003e \u003cbr\u003e * boundary condition at infinity satisfied exactly\u003cbr\u003e with those of the finite element method:\u003cbr\u003e * no fundamental solution required\u003cbr\u003e \u003cbr\u003e * no singular integrals\u003cbr\u003e \u003cbr\u003e * the processing of anisotropic material without any additional computational effort\u003cbr\u003e Other benefits include the fact that the analytical solution inside the domain permits stress singularities to be determined directly, and also that there is no spatial discretisation of certain boundaries such as crack faces and free surfaces and interfaces between different materials.\u003cbr\u003e \u003cbr\u003e The scaled boundary finite element method can be used to analyse any bounded and unbounded media governed by linear elliptic, parabolic and hyperbolic partial differential equations.\u003cbr\u003e \u003cbr\u003e The book serves two goals which can be pursued independently. Part I is a primer, with a model problem addressing the simplest wave propagation but still containing all essential features. Part II derives the fundamental equations for statics, elastodynamics and diffusion, and discusses the solution procedures from scratch in great detail.\u003cbr\u003e \u003cbr\u003e In summary this comprehensive text presents a novel procedure which will be of interest not only to engineers, researchers and students working in engineering mechanics, acoustics, heat-transfer, earthquake engineering, electromagnetism, and computational mathematics, but also consulting engineers dealing with nuclear structures, offshore platforms, hardened structures, critical facilities, dams, machine foundations and other structures subjected to earthquakes, wave loads, explosions and traffic.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47990334849253,"sku":"NP9780471486824","price":184.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780471486824.jpg?v=1761787404","url":"https:\/\/k12savings.com\/products\/the-scaled-boundary-finite-element-method-isbn-9780471486824","provider":"K12savings","version":"1.0","type":"link"}