Fourier BEM

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.

Concise and clear derivation of the traditional Galerkin-BEM approach Large range of applications from solid mechanics New generalization of BEM Better theoretical insight Includes supplementary material: sn.pub/extras

Texte du rabat
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.

Contenu
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.