The Scaled Boundary Finite Element Method

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:
∗ spatial discretisation reduced by one
∗ boundary condition at infinity satisfied exactly
with those of the finite element method:
∗ no fundamental solution required
∗ no singular integrals
∗ the processing of anisotropic material without any additional computational effort
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.
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.
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.
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.

Spis treści:
Foreword.
Preface.
Fundamentals of Numerical Analysis.
Novel Computational Procedure.
PAR T I: MODEL PROBLEM: LINE ELEMENT FOR SCALAR WAVE EQUATION.
Concepts of Scaled Boundary Transformation of Geometry and Similarity.
Wedge and Truncated Semi–Infinite Wedge of Shear Plate.
Scaled Boundary Transformation–Based Derivation.
Mechanically–Based Derivation.
Modelisation with Single Line Finite Element.
Statics.
Mass of Wedge.
 High–Frequency Asymptotic Expansion for Dynamic Stiffness of Truncated Semi–Infinite Wedge.
Numerical Solution of Dynamic Stiffness, Unit–Impulse Response and Displacement of Truncated Semi–Infinite Wedge.
Analytical Solution in Frequency Domain.
Implementation.
Conclusions.
Appendix A: Solid Modelling.
Appendix B: Harmonic Motion and Fourier Transformation.
Appendix C: Dynamic Unbounded Medium–Structure Interaction.
Appendix D: Historical Note.
PART II: TWO– AND THREE–DIMENSIONAL ELASTODYNAMICS, STATICS AND DIFFUSION.
Fundamental Equations.
Statics.
Mass Matrix of Bounded Medium.
High–Frequency Asymptotic Expansion for Dynamic Stiffness of Unbounded Medium.
Numerical Solution of Dynamic Stiffness, Unit–Impulse Response and Displacement of Unbounded Medium.
Analytical Solution in Frequency Domain.
Extensions.
Substructuring.
Examples for Bounded Media.
Examples for Unbounded Media.
Error Estimation and Adaptivity.
Concluding Remarks.
References.
Index.

Okładka tylna:
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:
∗ spatial discretisation reduced by one
∗ boundary condition at infinity satisfied exactly
with those of the finite element method:
∗ no fundamental solution required
∗ no singular integrals
∗ the processing of anisotropic material wit hout any additional computational effort
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.
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.
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.
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.