Fourier Bem: Generalization of Boundary Element Methods by Fourier Transform

ISBN-13: 9783540431381 / Angielski / Twarda / 2002 / 182 str.

Fabian M. E. Duddeck

Opis

This text links applied mathematics to real world engineering problems by proposing an alternative BEM (boundary element method) formulation based on the Fourier transform, which can be applied to almost all cases relevant in engineering mechanics.

Recenzje

"In this reviewer's opinion, the contents of this book, which gathers in a systematic concise fashion several original results due to its author, represents a major contribution to the developments of BEMs and to the literature on them... an elegant and potentially fruitful combination of mathematics and computational mechanics."

Appl Mech Rev

Spis treści

1 Introduction.- 2. Traditional BEM.- 3 Distributional BEM.- 4 Fourier BEM.- 5 Heat Conduction.- 6 Elasticity.- 7 Plates.- 8 Waves.- 9 Thermoelasticity.- 10 Non-linearity.- 11 Wavelets.- 12 Conclusions.- A Glossary.- A.1 Distribution theory.- A.2 Boundary Element Method.- B Special Distributions.- C Integration of BEM matrices.- C.1 Analytical integrations.- C.1.1 Singular integrals by Fourier transform.- C.1.2 Additional regular Fourier pairs.- C.1.3 Additional singular Fourier pairs.- C.2 Numerical integrations.

Blurb

Like FEM, the boundary element method (BEM) provides a general numerical tool for the solution of complex engineering problems. In the last decades, the range of its applications has remarkably been enlarged. Therefore dynamic and nonlinear problems can be tackled. Nevertheless, they still demand an explicit expression of a fundamental solution, which is only known in simple cases. Therefore, the present book proposes an alternative BEM-formulation based on the Fourier transform, which can be applied to almost all cases relevant in engineering mechanics. The basic principle is presented for the heat equation. Applications are taken from solid mechanics (e.g. poroelasticity, thermoelasticity). Transient and stationary examples are given as well as linear and nonlinear. Completed with a mathematical and mechanical glossary, the book will serve as a comprehensive text book linking applied mathematics to real world engineering problems.