## 4 Results and Discussion
### Buckling Load Intensity for Various Poisson's Ratio Layup  
The buckling load intensity with bending lamination parameters for various Poisson's ratio layups were investigated. The geometry of the chosen plate is \(100\) mm \(\times\)\(100\) mm and the thickness is \(2\) mm.  
Firstly, the minimum NPR of \(-0.360\) with \([V_{1}^{A},V_{2}^{A},V_{3}^{A},V_{4}^{A}]=[-0.35,0.25,-0.6,0.25]\) was selected for the buckling load investigation. According to the feasible region of Equation (9), different combinations of bending lamination parameters can be obtained with \([V_{1}^{A},V_{2}^{A},V_{3}^{A},V_{4}^{A}]=[-0.35,0.25,-0.6,0.25]\). Note that the buckling load Equation (24) assumes that the bending-twisting coupling terms \(D_{16}\) and \(D_{26}\) are negligible compared with the remaining terms \(D_{11}\), \(D_{12}\), \(D_{22}\), and \(D_{66}\). Therefore, it is better to calculate the buckling load for the laminate configuration with \(V_{3}^{D}=V_{4}^{D}=0\). However, the lamination parameter combination of \([V_{1}^{A},V_{2}^{A},V_{3}^{A},V_{4}^{A},V_{2}^{B},V_{4}^{A}]=[-0.35,0.25,-0.6, 0.25,0,0]\)does not satisfy the feasible region of lamination parameters. Thus, a combination of \(V_{3}^{D}=0.05,V_{4}^{D}=0\) to ensure the orthotropic condition to the highest extent is used to illustrate the \(V_{1}^{D},V_{2}^{D}\) plane for the buckling load contours.  
From the buckling load contours of Figure 5, two different buckling models may exist in the whole region of \(V_{1}^{D},V_{2}^{D}\). Four sets as follows are chosen to examine the effect of lamination parameters on the buckling modes:  
The buckling modes of point A and point C are consistent; there are two half wavelengths in the \(x\) direction (\(m=2\)) and one in the \(y\) direction (\(n=1\)), while there is one half wavelength in \(x\) direction (\(m=1\)) and one in \(y\) direction (\(n=1\)) for point B. Point D is the dividing point of the two buckling modes. When \(m=2\), \(n=1\) or \(m=1\), \(n=1\), the buckling load is the same. The buckling mode is not only related to the stiffness, but also to the aspect ratio of the plate. The buckling load contour lines for 200 mm \(\times\) 100 mm and 300 mm \(\times\) 100 mm plates are given in Figures 6 and 7, respectively.  
Secondly, the lamination parameters of \([V_{1}^{A},V_{2}^{A},V_{3}^{A},V_{4}^{A}]=[0.4,-0.05,-0.6,-0.1]\) with a PR of 0, and \([V_{1}^{A},V_{2}^{A},V_{3}^{A},V_{4}^{A}]=[0,0,0,0]\) with a PR of 0.296, are both studied for buckling load with various bending lamination parameters combinations. It can be seen from the contours that the buckling load is almost only related to \(V_{2}^{D}\). The buckling load decreases with an increase in \(V_{2}^{D}\). From Figures 5 and 8, the possible maximum buckling load decreases with an increase in Poisson's ratio.  
The influence of Poisson's ratio and the in-plane translational restraint coefficient on the buckling load of quasi isotropic laminates (\([V_{1}^{A},V_{2}^{A},V_{3}^{A},V_{4}^{A}]=[0,0,0,0]\)) was studied. \(\alpha\) is the in-plane translational restraint coefficient, which represents the degree of translational limitation. Figure 9 reveals the variation of the buckling loads of the rectangular plate with the Poisson's ratio for different in-plane translational restraint coefficients. The buckling load remains unchanged when the restraint coefficient \(\alpha\) equals zero and, when the Poisson's ratio is zero, the buckling load is the same for various restraint coefficients. If the in-plane translational restraint exists (\(\alpha>0\)), the buckling load gradually decreases as the Poisson's ratio increases. These results imply that the buckling load is a decreasing function of the laminate's Poisson's ratio, and hence the buckling performance of a rectangular plate under uniaxial compression can be enhanced by replacing the traditional layup that has a positive Poisson's ratio with an auxetic design.