3R22. Boundary Element Analysis of Cracks in Shear Deformable Plates and Shells. Topics in Engineering, Vol 43. - T Dirgantara (Aerospace Eng Dept, Inst Teknologi Bandung, Indonesia). WIT Press, Southampton, UK. Distributed in USA by Comput Mech Publ, Billerica, MA. 2002. 250 pp. ISBN 1-85312-950-X. $169.00.
Reviewed by L Mishnaevsky Jr (MPA, Univ of Stuttgart, Pfaffenwaldring 32, Stuttgart, D-70569, Germany).
The purpose of this monograph is to present recent developments of the boundary element method for the analysis of bending problems and fracture of shear deformable plates and shells. The author is successful in his aim to provide a detailed and consecutive introduction into the concepts and methods of the new boundary element formulation for the modeling the deformation and fracture in shear deformable plates and shells.
The book consists of eight chapters. The discussion of the importance of the strength of shells and plates problem for the aircraft industry and the short history of the numerical analysis of fracture of plates and shells are given in the Introduction.
Chapter 2, Basic concepts, contains definitions, concepts, and equations of the elastic theory of shear deformable shallow shells and flat shear deformable plates, as well as a short review of the linear elastic fracture mechanics.
In Chapter 3, Boundary Element Method, boundary integral equations (BIE) are derived for the analysis of shallow shear deformable shells. The formulation is developed by coupling the BE formulation of the shear deformable plate bending and the two-dimensional (2D) plane stress elasticity equations. The domain integrals that appear in the formulation are treated in two different ways: first, using the constant cell discretization and second, by transforming the domain integrals into the boundary integrals using the dual reciprocity technique. BIE for the analysis of the shear deformable plates and 2D plane stress problems are presented as well. Several numerical examples for shallow shell problems with different geometries and loading conditions are given.
Chapter 4, Hypersingular integral equations, presents the hypersingular (stress based) formulation for the analysis of the shear deformable shell bending. The traction (hypersingular) boundary integral equations are derived, which contain both domain and boundary integrals. The domain integrals are transformed to boundary integrals using the dual reciprocity technique. Computational aspects of the singular integrals are discussed in this chapter as well.
In Chapter 5, Dual Boundary Element Method, the dual boundary element formulation for the analysis of shear deformable shallow shells and plates subjected to bending and tension is presented. The dual boundary element method (DBEM), based on displacement and traction integral equations, is introduced. Some new solutions for the discretization of the problem and the analysis of the stress intensity factors (SIFs) and the displacement distribution near the crack tip are suggested, as special crack tip shape functions and the crack surface displacements extrapolation (CSDE) for determination of SIFs. Some examples are solved to demonstrate the accuracy of the method of determination of the stress intensity factors for shear deformable plates subjected to bending and tension.
In Chapter 6, Crack growth simulation, the crack propagation in shear deformable shallow shells and plates subjected to bending and tension is modeled using the dual boundary element method. The crack extension is simulated by introducing a new boundary element in each crack growth increment. The single and multiple crack growth problems are studied, and the fatigue life is determined using the developed method.
In Chapter 7, Multi-domain BEM formulation for assembled plate-structures, the deformation of assembled plate-structures subjected to arbitrary loadings is analyzed. The structures are divided into several regions, and the conditions of the compatibility of translations and rotations are enforced along the interface. Finally, conclusions and directions of future works are discussed in Chapter 8. Details of the mathematical approaches used in the book are given in the appendices.
The layout of the book is pleasant, the figures are original, and a list of notations is available. The list of references includes many pioneering scientific papers on the strength of plates and shells and the boundary element method in engineering, as well as most recent research publications. All the concepts, ideas and solutions are presented and explained clearly and exactly, taking into account the state of the art of the corresponding areas of the theories of BEM, and shells and plates. When a new idea or a concept is introduced, the history of the development of this and related concepts and the place of the concept in the overall picture are described. Possibilities of the practical application of the new concepts are illustrated by many numerical examples at the end of the chapters.
Boundary Element Analysis of Cracks in Shear Deformable Plates and Shells is highly recommended to libraries and specialists working in the areas of the strength and reliability of the shell and plate structures and fracture mechanics, as well as to engineering and science students.