The Scaled Boundary Finite Element MethodISBN: 9780471486824
378 pages
March 2003

In a nutshell, the scaled boundary finiteelement method is a semianalytical fundamentalsolutionless boundaryelement 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 finiteelement and boundaryelement methods within the numerical procedures.
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.
Preface.
Fundamentals of Numerical Analysis.
Novel Computational Procedure.
PART I: MODEL PROBLEM: LINE ELEMENT FOR SCALAR WAVE EQUATION.
Concepts of Scaled Boundary Transformation of Geometry and Similarity.
Wedge and Truncated SemiInfinite Wedge of Shear Plate.
Scaled Boundary TransformationBased Derivation.
MechanicallyBased Derivation.
Modelisation with Single Line Finite Element.
Statics.
Mass of Wedge.
HighFrequency Asymptotic Expansion for Dynamic Stiffness of Truncated SemiInfinite Wedge.
Numerical Solution of Dynamic Stiffness, UnitImpulse Response and Displacement of Truncated SemiInfinite Wedge.
Analytical Solution in Frequency Domain.
Implementation.
Conclusions.
Appendix A: Solid Modelling.
Appendix B: Harmonic Motion and Fourier Transformation.
Appendix C: Dynamic Unbounded MediumStructure Interaction.
Appendix D: Historical Note.
PART II: TWO AND THREEDIMENSIONAL ELASTODYNAMICS, STATICS AND DIFFUSION.
Fundamental Equations.
Statics.
Mass Matrix of Bounded Medium.
HighFrequency Asymptotic Expansion for Dynamic Stiffness of Unbounded Medium.
Numerical Solution of Dynamic Stiffness, UnitImpulse 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.