Boundary element techniques. Theory and applications in engineering.

*(English)*Zbl 0556.73086
Berlin etc.: Springer-Verlag. XIV, 464 p. DM 188.00; $ 70.20 (1984).

This book provides a comprehensive coverage of both fundamental and advanced topics in the area of BEM (boundary element method). The text is useful for learning the basics of BEM, as well as a reference for research and application.

The first three chapters of the book deal with introductory material on approximations and potential problems. Weighted residual methods serve for unification of approximate methods. The next nine chapters deal with application of BEM to a variety of areas, with emphasis put on solid mechanics. Problems addressed here include diffusion, solid mechanics, and a short discussion on fluid mechanics. Specific applications to solid mechanics are elastostatics, plasticity, plate bending, and dynamics (wave propagation and vibration). An important discussion of coupling BEM and FEM (finite element method) follows. The last chapter provides a FORTRAN program for 2-D elastostatics, based on linear boundary elements. Three appendices provide formulas for numerical integration, a treatment of semi-infinite (half-space, half-plane) solutions, and expressions for 2-D inelastic problems.

In conclusion, this is an excellent textbook for the student and teacher, and an invaluable reference for researchers and engineers. It almost completely covers the entire area of BEM, with mathematical rigor, and with a wide range of applications. The computer program illustrates how the theory can be implemented, and serves as a basis for developing (BEM) solutions for other problems.

The first three chapters of the book deal with introductory material on approximations and potential problems. Weighted residual methods serve for unification of approximate methods. The next nine chapters deal with application of BEM to a variety of areas, with emphasis put on solid mechanics. Problems addressed here include diffusion, solid mechanics, and a short discussion on fluid mechanics. Specific applications to solid mechanics are elastostatics, plasticity, plate bending, and dynamics (wave propagation and vibration). An important discussion of coupling BEM and FEM (finite element method) follows. The last chapter provides a FORTRAN program for 2-D elastostatics, based on linear boundary elements. Three appendices provide formulas for numerical integration, a treatment of semi-infinite (half-space, half-plane) solutions, and expressions for 2-D inelastic problems.

In conclusion, this is an excellent textbook for the student and teacher, and an invaluable reference for researchers and engineers. It almost completely covers the entire area of BEM, with mathematical rigor, and with a wide range of applications. The computer program illustrates how the theory can be implemented, and serves as a basis for developing (BEM) solutions for other problems.

Reviewer: Sh.Ginsburg

##### MSC:

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |

74-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids |

74S99 | Numerical and other methods in solid mechanics |

76M99 | Basic methods in fluid mechanics |

74-04 | Software, source code, etc. for problems pertaining to mechanics of deformable solids |