Meshfree formulation based on the element free Galerkin method (EFGM) in conjunction with moving kriging (MK) shape function is employed to investigate buckling and parametric instability behaviour of shear deformable isotropic and laminated composite trapezoidal plates subjected to different types of non-uniform periodic edge compressive loads. Hamilton’s principle is used to derive the governing equations, which are transformed into the discretized form using the EFG method. The actual pre-buckling stresses are determined from static analysis to evaluate the accurate buckling loads of isotropic and laminated composite trapezoidal plates under non-uniform edge compression. The ordinary differential equations of Mathieu–Hill type are solved using Bolotin’s method to determine regions of dynamic instability. The accuracy of the present formulation is examined first by comparing results with those available in the literature. Thereafter, the influence of geometric parameters, lamination scheme, boundary conditions, static pre-load, and various types of non-uniform edge compression on the critical buckling loads and dynamic instability behaviour of both isotropic and laminated composite trapezoidal plate is investigated. The new results on dynamic stability behaviour of trapezoidal plates under non-uniform edge loads are presented for the first time, which may serve as benchmark results for future research. Furthermore, the time history response and corresponding phase plots are also presented for a better understanding of the dynamic behaviour of the trapezoidal plates.

基于无网格Galerkin方法（EFGM）结合运动克里格（MK）形状函数的无网格公式用于研究受剪变形的各向同性和层合复合梯形板在不同类型的非均匀周期边沿作用下的屈曲和参数不稳定性行为压缩载荷。使用汉密尔顿原理导出控制方程，使用EFG方法将其转换为离散形式。通过静态分析确定实际的预屈曲应力，以评估各向同性和层压复合梯形板在非均匀边缘压缩下的准确屈曲载荷。使用Bolotin的方法求解Mathieu–Hill型常微分方程，以确定动态不稳定区域。首先通过将结果与文献中可获得的结果进行比较来检查本制剂的准确性。此后，研究了几何参数，层压方案，边界条件，静态预紧力以及各种类型的非均匀边缘压缩对各向同性和层压复合梯形板的临界屈曲载荷和动态不稳定性行为的影响。首次提出了梯形板在非均匀边缘载荷下的动态稳定性行为的新结果，可作为今后研究的基准结果。此外，还提供了时程响应和相应的相位图，以更好地了解梯形板的动态行为。此后，研究了几何参数，层压方案，边界条件，静态预紧力以及各种类型的非均匀边缘压缩对各向同性和层压复合梯形板的临界屈曲载荷和动态不稳定性行为的影响。首次提出了梯形板在非均匀边缘载荷下的动态稳定性行为的新结果，可作为今后研究的基准结果。此外，还提供了时程响应和相应的相位图，以更好地了解梯形板的动态行为。此后，研究了几何参数，层压方案，边界条件，静态预紧力以及各种类型的非均匀边缘压缩对各向同性和层压复合梯形板的临界屈曲载荷和动态不稳定性行为的影响。首次提出了梯形板在非均匀边缘载荷下的动态稳定性行为的新结果，可作为今后研究的基准结果。此外，还提供了时程响应和相应的相位图，以更好地了解梯形板的动态行为。研究了各向同性和层状复合梯形板的临界屈曲载荷和动态失稳行为的各种类型的非均匀边缘压缩。首次提出了梯形板在非均匀边缘载荷下的动态稳定性行为的新结果，可作为今后研究的基准结果。此外，还提供了时程响应和相应的相位图，以更好地了解梯形板的动态行为。研究了各向同性和层状复合梯形板的临界屈曲载荷和动态失稳行为的各种类型的非均匀边缘压缩。首次提出了梯形板在非均匀边缘载荷下的动态稳定性行为的新结果，可作为今后研究的基准结果。此外，还提供了时程响应和相应的相位图，以更好地了解梯形板的动态行为。