## 3 Results and Discussion
### Parametric Study  
In this section, a parametric study is presented to study the variations in the displacement for composite plates with varying configurations of single and multiple interface deformations in presence of geometric non-linearity. CFRP square composite plates with size of 100 \(\times\) 100 mm and thickness 2.25 mm have been chosen for this purpose. The material properties of the laminate are as follows: \(E_{1}=144.8\) GPa; \(E_{2}=9.65\) GPa; \(G_{12}=4.14\) GPa; \(v_{12}=0.3\); \(G_{13}=4.14\) GPa; \(G_{23}=3.45\) GPa; \(\rho=1600\) Kg/m\({}^{3}\). The parameters considered for the study are boundary conditions, lamina orientation, delamination location, delamination size and delamination interface. All the combinations based on these parameters are presented in Table 3. Three different lamina orientations namely, cross ply, symmetric angle ply and antisymmetric angle ply have been chosen. These are the most widely used lamina sequences. In composite material applications, cross-ply sequences (e.g., 0\({}^{\circ}\)/90\({}^{\circ}\)) are commonly used for their balanced properties along different axes, providing resistance to loads in both the longitudinal and transverse directions. Angle-ply laminates, particularly symmetric and anti-symmetric types, are chosen for their ability to increase shear stiffness and minimize warping under complex loading conditions, meeting the demands frequently seen in aerospace, automotive, and marine applications. A typical diagram of the plate, showing the delamination locations and sizes, is presented in Figure 3.  
First, the static analysis for all types of composite laminates (Table 3) was conducted under undamaged condition. The uniformly distributed load was gradually increased from 0 to 3500 kN/m\({}^{2}\) to calculate the maximum displacement of the plates and corresponding load vs. maximum displacement curves have been plotted for SSSS, CSCS, CCCC, CEFF in Figure 4a-d, respectively. All results were compared to the linear analysis outcomes. As expected, the inclusion of geometric nonlinearity increases the stiffness of the structures, resulting in lower maximum displacements for a particular load value compared to its linear counterpart. At lower load levels, the difference between linear and nonlinear results  
Figure 3: Schematic representation of delamination location and size.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Boundary** & **Lamina Orientation** & \
\begin{tabular}{l} **Delamination** \\ **Location** \\ \end{tabular} & **Delamination Size** &
\begin{tabular}{l} **Delamination** \\ **Interface** \\ \end{tabular} \\ \hline SSSS & \((0/90/0)_{3S}\) & Centre & \(0.1a\times 0.1a\) & Single (middle) \\ CSCS & \((0/45/90)_{3S}\) & Edge & \(0.2a\times 0.2a\) & Multiple \\ CCCC & \((0/-45/90)_{3A}\) & Corner & \(0.5a\times 0.5a\) & – \\ CEFF & – & – & – & – \\ \hline \hline \end{tabular}
\end{table}
Table 3: Details of all the varying parameters for the composite plate.  
was minimal; however, significant differences emerged with increasing load intensity. When assessing the impact of nonlinearity across different boundary conditions, the plate with SSSS boundary conditions exhibited the most pronounced effect (35-42%), followed by CFFF (13-29%), CSCS (7-15%) and CCCC (3-5%), respectively, at the maximum load of 3500 kN/m\({}^{2}\). Among different laminate orientations, the symmetric cross-ply laminate was the most affected by nonlinearity, followed by symmetric and anti-symmetric angle-ply laminates under SSSS and CSCS boundary conditions. On the other hand, for CFFF and CCCC boundary conditions, the anti-symmetric angle-ply laminate was most affected by nonlinearity, followed by the symmetric angle-ply and symmetric cross-ply laminates. Therefore, it is clear that incorporating geometric nonlinearity in the FE model has a significant impact depending on the boundary conditions and lamina orientation.