## Mechanics of laminated composite plates. Theory and analysis.(English)Zbl 0899.73002

Boca Raton, FL: CRC Press. 782 p. (1997).
This book is concerned with the mechanics of laminated composite plates and consists of 13 chapters. The first chapter is devoted to the mathematical background material, such as vectors, matrices and tensors. The second chapter presents kinematics, balance laws of continuum mechanics, and constitutive equations of anisotropic elasticity, thermoelasticity and electroelasticity. In chapter 3, the principle of virtual work and variational methods are elaborated with emphasis on the concept of virtual work, variational operators and extrema of functionals. Chapter 4 is devoted to the investigation of composite materials, namely, to constitutive relations of a lamina, and to the characterization of material constants in terms of material coefficients. The author also gives the transformations of stresses, strains and material coefficient tensors.
In chapter 5, the classical and first-order theories of laminated composite plates are cultivated, and the stiffness of a plate is expressed in terms of geometrical and material characteristics of the lamina. Additionally, the author discusses some special arrangements of laminates. Chapter 6 is concerned with one-dimensional analysis of cylindrical bending of laminated plates using the classical laminated plate theory (CLPT) and the first-order shear deformation theory (FSDT). The analysis of orthotropic plates by use of the CLPT is specially presented in chapter 7. In this chapter the reader is informed about the bending of simply supported rectangular plates, the bending of plates with two opposite edges, the buckling of simply supported plates under compressive loadings, the buckling of rectangular plates under in-plane shear load, and about buckling and vibrations of plates with two parallel edges. Analytical solutions of rectangular laminates by using CLPT are given in chapter 8. In particular, the author gives here the Navier solutions of antisymmetric cross-ply and angle-ply laminates, Lévy solutions, the analysis of midplane symmetric laminates, and the transient analysis. Analytical solutions of rectangular laminates by use of the FSDT are explained in chapter 9 on examples of simply supported antisymmetric cross-ply and angle-ply laminates, simply supported antisymmetric cross-ply and angle-ply laminates with two opposite edges, and the transient solutions.
Chapter 10 is devoted to the finite element analysis of composite laminates. In the same context, the author investigates laminated beams and plate strips by CLPT, Timoshenko beam/plate theory, and constructs finite element models of laminated plates by use of CLPT and FSDT. More refined theories of laminated composite plates are presented in chapter 11. In particular, the author discusses here higher-order laminate stiffness characteristics, Navier solutions, Lévy solutions of cross-ply laminates, and the displacement finite element model. The layerwise theories and variable kinematic models are described in chapter 12. Particularly, the general theory of such structures, finite element formulations and variable kinematic formulations are explored. Finally, chapter 13 deals with the nonlinear analysis of composite laminates. In this chapter, the author discusses nonlinear stiffness coefficients, solution methods for nonlinear algebraic equations, and the related computational aspects.
The book is very well organized and can undoubtedly find readers working in the area of laminated composite plates.

### MSC:

 74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids 74K20 Plates 74E30 Composite and mixture properties