A nonlocal Peridynamic Differential Operator (PDDO) is presented for static analysis of laminated composite plates based on the First-order Shear Deformation Theory (FSDT). The equilibrium equations and boundary conditions of the FSDT were derived from the principle of virtual work. The local spatial derivatives in these equations were replaced with their nonlocal PD forms. The continuous transverse shear stresses were achieved by integrating the stress equilibrium equations through the thickness of the plate. This approach was validated against an existing analytical solution by considering a simply supported laminated composite plate under uniformly distributed sinusoidal load for different aspect ratios. The performance of this formulation was investigated by comparing through-the-thickness stress variations against the analytical solutions.

Composite materials are widely used in aerospace, military, and nuclear engineering fields due to their desirable properties such as lightness and high strength. The mismatch of the stiffness at the interfaces between distinct materials results in a stress concentration; thus, crack nucleation and inter-layer separations can be observed. The concept of functionally graded materials (FGMs) aims to achieve a structure whose material properties continuously vary in one or more coordinate directions. This continuous variation is obtained for the material properties of the FG structure.This situation provides a way to minimize the stress concentrations which may occur at the interfaces between the two different materials. FGMs are one of the most important structures in defense and aerospace industries owing to their superior properties. In order to design FG structures safely, it is very crucial to understand and investigate possible damages under different loads to increase the reliability of these structures. Since structural testing and analysis techniques may be costly, there is a necessity to use improved and accurate computational tools to predict the deformation and stress fields of the FG structures. Numerical modeling of the fracture and damage in FGMs remains a formidable challenge in computational mechanics due to the non-symmetric material variations in the FGMs. In PeriDynamic (PD) theory, the equations of classical continuum mechanics (CCM) are reformulated by replacing the derivatives with volumetric integral expressions. Hence, the equilibrium equations of PD theory are still valid even if the material includes a discontinuity, unlike CCM. In this study, the influence of the material variations in the FG plates on the crack nucleation and propagation is investigated by means of PD theory. As a result of the analysis, it is observed that the material distributions have an evident effect on the fracture behaviour of the plate, and the plate strength can be increased by tailoring the material properties in the FG plates.