# Finite–Element Modelling of Unbounded Media

• ID: 2182630
• Book
• 350 Pages
• John Wiley and Sons Ltd
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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.
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SIMILARITY–BASED FORMULATION FOR UNIT–IMPULSE RESPONSE AND DYNAMIC STIFFNESS.

Displacement, Velocity and Acceleration Unit–Impulse Response with Dynamic Stiffness and Rational Approximation.

Forecasting Method.

Consistent Infinitesimal Finite–Element Cell Method Applied to Bounded Medium.

DAMPING–SOLVENT EXTRACTION FOR DYNAMIC STIFFNESS AND INTERACTION FORCE.

Fundamentals of Damping–Solvent Extraction Method.

DOUBLY–ASYMPTOTIC MULTI–DIRECTIONAL TRANSMITTING BOUNDARY.

Concept and Numerical Implementation of Doubly–Asymptotic Multi–Directional Transmitting Boundary.

Accuracy and Modelling Procedure of Doubly–Asymptotic Multi–Directional Transmitting Boundary.

Appendices.

References.

Index.
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