The Scaled Boundary Finite Element Method

John P. Wolf

376 pages, parution le 23/01/2003

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Résumé

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.

Contents

Fundamentals of numerical analysis
Novel computational procedure

I- Mdel 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
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

Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	John P. Wolf
Parution	23/01/2003
Nb. de pages	376
Format	17 x 25
Couverture	Relié
Poids	777g
Intérieur	Noir et Blanc
EAN13	9780471486824
ISBN13	978-0-471-48682-4