Fourier BEM

Generalization of Boundary Element Methods by Fourier Transform

Fabian M.E. Duddeck (Autor)

Buch | Softcover

II, 182 Seiten

2011
Springer Berlin (Verlag)
978-3-642-07727-2 (ISBN)

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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. However they still demand an explicit expression of a fundamental solution, which is only known in simple cases. In this respect, 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. 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.

Introduction.- Traditional BEM.- Distributional BEM.- Fourier BEM.- Heat Conduction.- Elasticity.- Plates.- Waves.- Thermoelasticity.- Non-linearity.- Wavelets.- Conclusions.-Glossary.-Special Distributions.-Integration of BEM matrices.

"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

Erscheint lt. Verlag	9.10.2011
Reihe/Serie	Lecture Notes in Applied and Computational Mechanics
Zusatzinfo	II, 182 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	293 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Technik ► Maschinenbau
Schlagworte	boundary element methods • Engineering mechanics • Finite Element Method • Fourier transform • fundamental solutions • general elasticity • Linearity • Numerical Integration • Singular integral • transient dynamics • Wavelet
ISBN-10	3-642-07727-7 / 3642077277
ISBN-13	978-3-642-07727-2 / 9783642077272
Zustand	Neuware