The Scaled Boundary Finite Element Method (Hardcover)

Foreword.

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 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.