Boundary Element Methods in Mechanics
D. E. Beskos
North-Holland Pub., 1987 - Acoustique - 598 pages
Boundary Element Methods (BEM) have been successfully used in a variety of areas in engineering science, such as potential theory, elastostatics, elastodynamics, elastoplasticity, fracture, fluid mechanics, heat conduction, acoustics, electromagnetism and soil- or fluid-structure interaction. The most important topics in BEM are described here by well-known researchers in the field. It is a handbook characterized by a combination of tutorial and state-of-the-art aspects. Chapter 1 is an introduction to the fundamentals of the BEM, its history, advantages and disadvantages and future developments. In the second chapter, the potential theory is used to illustrate the mathematical and numerical aspects of the method. Further illustration is provided in the third chapter which deals with two- and three-dimensional elastostatics. Chapters 4 and 5 treat two- and three-dimensional elastodynamics (including viscoelasticity) from a general and a specific point of view, respectively. Nonlinear solid mechanics (including material and geometric nonlinearities) is taken up in the sixth chapter, while two- and three-dimensional fracture analysis is treated in the seventh chapter. Chapter 8 is devoted to fluid mechanics, and in particular to potential, viscous and ground water flow and water-waves, while Chapter 9 concerns itself with acoustics. Chapter 10 discusses heat conduction and mathematically related phenomena of transient thermoelasticity and soil-consolidation. The last two chapters deal with two important interaction phenomena: dynamic soil-structure interaction and fluid-structure interaction.
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Introduction to Boundary Element Methods
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Acoustical Analysis analytical Applied Mechanics approach approximation Arbitrary axisymmetric Berlin Beskos body force boundary conditions Boundary Element Methods Boundary Integral Equation Butterfield C.A. Brebbia calculated coefficients computed constant defined deformation derivative Developments in Boundary differential direct discretization displacement dynamic elastic elastodynamics elastostatics evaluated expressions field point Finite Element Method fluid formulation foundation fracture mechanics free surface frequency domain fundamental solutions geometry Green's function half-space harmonic Helmholtz equation infinite Integral Equation Method International Journal interpolation Journal for Numerical kernel Laplace equation Laplace transform linear London matrix Methods in Engineering nodal nodes nonlinear Numerical Methods Numerical Solution obtained P.K. Banerjee plane strain Potential Flow potential problems potential theory region shape functions shown in Fig singular soil Solid Mechanics solved Springer-Verlag T.A. Cruse techniques tensor theorem three-dimensional traction transform transient two-dimensional unknown values variables vector velocity viscoelastic wave zero