##
**Mechanics of laminated composite plates. Theory and analysis.
2nd ed.**
*(English)*
Zbl 1075.74001

Boca Raton, FL: CRC Press (ISBN 0-8493-1592-1/hbk). xxiii, 831 p. (2004).

This is the rearranged and extended second edition of a well-known and highly esteemed textbook on the analysis of composite structures [for the review of the 1. ed. see (1997; Zbl 0899.73002)]. It includes examples, problem exercises and references for additional reading after each chapter. Avoiding symbolic notation leads to lengthy formulas in some cases. A single lamina with homogeneous anisotropic properties is assumed as the smallest entity from which the laminated structural elements are built. Only limited attention is paid to actual material properties or the difficulties to measure them. The main emphasis is on laminated composite plate and shell models with a focus on classical and first-order shear deformation theory. Exact analytical solutions for one-dimensional problems of laminated beams and cylindrical bending of plate strips are developed. Bending, buckling, vibration and vibration suppression by means of actuating layers are analysed. One chapter is devoted to rectangular plates made of orthotropic laminates; it may represent reasonable approximations to more general laminates. Theory and analysis of laminated shells are presented, including analytical solutions for simply supported cross-ply shells.

Finite element models for different plate theories are developed with observance of locking phenomena and procedures to avoid them. Using these elements, the geometric nonlinear behaviour of laminated plates and shells is studied. Newton-Raphson and Riks method are proposed as solution procedures. A short sub-chapter also treats plates of functionally graded material. Further, some application of maximum stress and Tsai-Wu failure criteria to two plane graphite-epoxy panels loaded in axial compression into the postbuckling range are given; the recent development in failure criteria is not covered. A full chapter is devoted to Reddy’s third-order theory. The results obtained therewith clearly differentiate between constitutively- and equilibrium-derived transverse shear stresses. Finally, layer-wise theories are treated, which, developed into a finite element formulation, are applied to calculate free edge stresses. The variable kinematics formulation proposes different models for local and global regions. A corresponding finite element superimposes two or more different types of assumed displacement fields in the same element domain.

Finite element models for different plate theories are developed with observance of locking phenomena and procedures to avoid them. Using these elements, the geometric nonlinear behaviour of laminated plates and shells is studied. Newton-Raphson and Riks method are proposed as solution procedures. A short sub-chapter also treats plates of functionally graded material. Further, some application of maximum stress and Tsai-Wu failure criteria to two plane graphite-epoxy panels loaded in axial compression into the postbuckling range are given; the recent development in failure criteria is not covered. A full chapter is devoted to Reddy’s third-order theory. The results obtained therewith clearly differentiate between constitutively- and equilibrium-derived transverse shear stresses. Finally, layer-wise theories are treated, which, developed into a finite element formulation, are applied to calculate free edge stresses. The variable kinematics formulation proposes different models for local and global regions. A corresponding finite element superimposes two or more different types of assumed displacement fields in the same element domain.

Reviewer: Klaus Rohwer (Braunschweig)

### MSC:

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

74K20 | Plates |

74K25 | Shells |

74E30 | Composite and mixture properties |

76S05 | Flows in porous media; filtration; seepage |