Finite element method. Vol. 2: Solid mechanics. 5th ed.

*(English)*Zbl 0991.74003
Oxford: Butterworth-Heinemann. 480 p. (2000).

The second volume deals with problems of solid mechanics that are of practical importance and continue to be of research interest. As in the first volume [see the foregoing entry], the discussion of each problem begins with theoretical explanations of the model and with the corresponding boundary value problem. So the book is self-contained in a certain sense. Moreover, it is independent of the first volume in the sense that the reader having some, not too much, knowledge of FEM can read it and use it for practical purposes.

The second volume examines two classes of nonlinear solid mechanics problems: (1) problems of elasticity, viscoelacticity, plasticity, and viscoplasticity, and (2) the theory of plates and shells. The nonlinear problems are considered in two cases: small deformations (chapters 1-3), and large deformations (chapters 10-12). Chapters 4-9 deal with the plate-shell theory. The authors demonstrate how to construct and implement a workable version of FEM for each particular problem. The book discusses not only numerical implementation, but also mechanical results obtained on the basis of proposed methods. In this way such important problems as stability and instability are discussed on a good level. The FEM for plates and shells remains of research interest even for linear problems, since here it is unclear which version of FEM is preferable or which criterion for best approximation should be used. The volume discusses various types of elements implemented in this theory, and compares them.

The book is strongly recommended to postgraduate students in mechanical and structural engineering, as well as to engineers and researchers in nonlinear solid mechanics and in the shell theory.

The second volume examines two classes of nonlinear solid mechanics problems: (1) problems of elasticity, viscoelacticity, plasticity, and viscoplasticity, and (2) the theory of plates and shells. The nonlinear problems are considered in two cases: small deformations (chapters 1-3), and large deformations (chapters 10-12). Chapters 4-9 deal with the plate-shell theory. The authors demonstrate how to construct and implement a workable version of FEM for each particular problem. The book discusses not only numerical implementation, but also mechanical results obtained on the basis of proposed methods. In this way such important problems as stability and instability are discussed on a good level. The FEM for plates and shells remains of research interest even for linear problems, since here it is unclear which version of FEM is preferable or which criterion for best approximation should be used. The volume discusses various types of elements implemented in this theory, and compares them.

The book is strongly recommended to postgraduate students in mechanical and structural engineering, as well as to engineers and researchers in nonlinear solid mechanics and in the shell theory.

Reviewer: L.P.Lebedev (Rostov-na-Donu)

##### MSC:

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

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

74S05 | Finite element methods applied to problems in solid mechanics |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

74K20 | Plates |

74K25 | Shells |