Deformation and stress of aerospace composites

This chapter is dedicated to the analysis of stress and displacement in composite plates under quasi-static conditions. The analysis presented in this chapter is done with the classical lamination theory that assumes a state of plane-stress in the composite plies as discussed in the previous chapters. The kinematic and boundary-condition hypothesis of the Love-Kirchhoff plate theory are assumed. The main difference between the composite plate theory and the conventional Love-Kirchhoff plate theory is in the inherent coupling between the axial (in-plane) and flexural (out-of-plane) motions and deformations. In the isotropic plate, the axial and flexural motions and deformations are not coupled, and hence the axial analysis (aka, membrane analysis) and flexural analysis (aka plate bending analysis) could be performed independently. In composite plates, the axial and flexural deformations are strongly coupled. If only one type of loading is applied, say, in-plane loading, then both axial and flexural deformations may appear due to the coupling effect. Similarly, out-of-plane loading may also generate not only flexural but also axial strains and deformation. This coupling situation is apparent in the differential equations that govern the composite plate behavior. However, the axial-flexural coupling disappears in the restrictive case of orthotropic composites. First, the series-expansion solution for the analysis of simply supported isotropic plates under flexural loads is reviewed. The displacement and stress solutions are derived and convergence studies are performed. Next, the same procedure is applied to the analysis of orthotropic composite plates in which coupling between axial and flexural deformations does not exist. Thermal and piezo effects are included. A large number of worked-out examples, problems and exercises, as well as references and bibliography are presented.