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**The finite element analysis of shells – fundamentals.
2nd ed.**
*(English)*
Zbl 1211.74002

Computational Fluid and Solid Mechanics. Berlin: Springer (ISBN 978-3-642-16407-1/hbk; 978-3-642-16408-8/ebook). xv, 410 p. (2011).

[For a review of the first edition see (2003; Zbl 1103.74003).]

The main idea of this book may be described by R. W. Hamming’s maxim: “The purpose of computing is insight, not numbers”. The technical objective is to present fundamental formulations, theorems and results concerning the modern finite element procedures for shell structures. The fundamentals of shell theories, mathematical analysis and finite element methods are presented with a view towards the synergy between physical and mathematical understanding. It is assumed that the reader has a basic knowledge of analytical mechanics and mechanics of solids, as well as of mathematics at the basic university level.

This book is divided into 9 chapters: 1. Introduction; 2. Geometrical preliminaries; 3. Elements of functional and numerical analysis; 4. Shell mathematical models; 5. Asymptotic behaviour of shells models; 6. Displacement-based shell finite elements; 7. Influence of the thickness in the finite element approximation; 8. Towards the formulation of effective general shell elements; 9. On the nonlinear analysis of shells.

The major part of the book focuses on the linear analysis of shell structures, for which the authors give a thorough discussion of mathematical models and discretization procedures. In the last section of the book they discuss how the described methods can be directly applied to the nonlinear analysis.

On balance, this well-written book is a reader-friendly and well-organized monograph in the field of finite element analysis of shell structures. It can be highly recommended for experts in mechanics of solids, for engineers, and for graduate, postgraduate and doctoral students.

The main idea of this book may be described by R. W. Hamming’s maxim: “The purpose of computing is insight, not numbers”. The technical objective is to present fundamental formulations, theorems and results concerning the modern finite element procedures for shell structures. The fundamentals of shell theories, mathematical analysis and finite element methods are presented with a view towards the synergy between physical and mathematical understanding. It is assumed that the reader has a basic knowledge of analytical mechanics and mechanics of solids, as well as of mathematics at the basic university level.

This book is divided into 9 chapters: 1. Introduction; 2. Geometrical preliminaries; 3. Elements of functional and numerical analysis; 4. Shell mathematical models; 5. Asymptotic behaviour of shells models; 6. Displacement-based shell finite elements; 7. Influence of the thickness in the finite element approximation; 8. Towards the formulation of effective general shell elements; 9. On the nonlinear analysis of shells.

The major part of the book focuses on the linear analysis of shell structures, for which the authors give a thorough discussion of mathematical models and discretization procedures. In the last section of the book they discuss how the described methods can be directly applied to the nonlinear analysis.

On balance, this well-written book is a reader-friendly and well-organized monograph in the field of finite element analysis of shell structures. It can be highly recommended for experts in mechanics of solids, for engineers, and for graduate, postgraduate and doctoral students.

Reviewer: Igor Andrianov (Köln)

### MSC:

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

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

74K25 | Shells |