Finite-Element Modelling of Unbounded Media

Dynamic unbounded medium-structure interactions occur in manyfields of engineering and physical science, such as wavepropagation in soil-structure and fluid-structure interactions,acoustics and electromagnetism and as diffusion in heat conductionand consolidation. This book presents three novel concepts, basedon the finite-element methodology, to model the unboundedmedium:
* The consistent infinitesimal finite-element cell method, aboundary finite-element procedure, requires the discretization ofthe structure-medium interface only and is exact in thefinite-element sense. It is applied to unbounded media governed bythe hyperbolic, parabolic and elliptic differentialequations.
* The damping-solvent extraction method permits the analysis of abounded medium only.
* The doubly-asymptotic multi-directional transmitting boundary isexact for the low- and high-frequency limits at preselected wavepropagation directions.
All concepts are explained using simple examples that the readercan follow step by step. A computer program of the consistentinfinitesimal finite-element cell method available on disk analysestwo- and three-dimensional unbounded and bounded media for thescalar and vector wave equations and the diffusion equation in thefrequency and time domains. Partial table of contents:

SIMILARITY-BASED FORMULATION FOR UNIT-IMPULSE RESPONSE AND DYNAMICSTIFFNESS.

Displacement, Velocity and Acceleration Unit-Impulse Response withDynamic Stiffness and Rational Approximation.

Forecasting Method.

Consistent Infinitesimal Finite-Element Cell Method Applied toBounded Medium.

DAMPING-SOLVENT EXTRACTION FOR DYNAMIC STIFFNESS AND INTERACTIONFORCE.

Fundamentals of Damping-Solvent Extraction Method.

DOUBLY-ASYMPTOTIC MULTI-DIRECTIONAL TRANSMITTING BOUNDARY.

Concept and Numerical Implementation of Doubly-AsymptoticMulti-Directional Transmitting Boundary.

Accuracy and Modelling Procedure of Doubly-AsymptoticMulti-Directional Transmitting Boundary.

Appendices.

References.

Index.

John P. Wolf is the author of Finite-Element Modelling of Unbounded Media, published by Wiley. Chongmin Song is the author of Finite-Element Modelling of Unbounded Media, published by Wiley. Dynamic unbounded medium-structure interactions occur in many fields of engineering and physical science, such as wave propagation in soil-structure and fluid-structure interactions, acoustics and electromagnetism and as diffusion in heat conduction and consolidation. This book presents three novel concepts, based on the finite-element methodology, to model the unbounded medium:

1. The consistent infinitesimal finite-element cell method, a boundary finite-element procedure, requires the discretization of the structure-medium interface only and is exact in the finite-element sense. It is applied to unbounded media governed by the hyperbolic, parabolic and elliptic differential equations.
2. The damping-solvent extraction method permits the analysis of a bounded medium only.
3. The doubly-asymptotic multi-directional transmitting boundary is exact for the low- and high-frequency limits at preselected wave propagation directions.

All concepts are explained using simple examples that the reader can follow step by step. A computer program of the consistent infinitesimal finite-element cell method available on disk analyses two- and three-dimensional unbounded and bounded media for the scalar and vector wave equations and the diffusion equation in the frequency and time domains.