In this study, a bubble complex finite strip method (BCFSM) with the higher-order zigzag theory is formulated for mechanical buckling and free vibration analysis of laminated composite plates, including cross-ply and angle-ply laminates. Few studies have been done to obtain the analytical solutions for clamped and free boundary conditions in the longitudinal and transverse edges. Therefore, this study, for the first time, investigates the effects of various boundary conditions on the stability and vibration results of laminated composite plates subjected to axial or pure shear forces with the use of higher-order zigzag theory and BCFSM. Following this, both the interlaminar continuity conditions of transverse shear stresses and the shear-free surface conditions are satisfied by applying a cubic displacement and a zigzag linear varying displacement with the same number of unknowns as the first-order shear deformation theories. Moreover, the effects of width-to-thickness ratio, fiber orientation, number of modes, different dimensional ratios of the plate, and finally, the number of layers are investigated through numerical examples. The bubble shape functions are exploited in the transverse direction to improve the convergence of the method. Finally, the shearing and axial interaction diagrams of composite laminated plates are presented for various types of boundary conditions.

中文翻译：

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气泡复合有限条法在正交各向异性层压复合板的稳定性和振动分析中

在这项研究中，基于高阶锯齿形理论的气泡复合有限条带法 (BCFSM) 被制定用于层压复合板的机械屈曲和自由振动分析，包括交叉层和角层层压板。很少有研究获得纵向和横向边缘的夹紧和自由边界条件的解析解。因此，本研究首次运用高阶之字形理论和BCFSM研究了各种边界条件对层合复合板在轴向或纯剪力作用下稳定性和振动结果的影响。按照此，通过应用与一阶剪切变形理论相同数量的未知数的三次位移和锯齿形线性变化位移，可以满足横向剪切应力的层间连续性条件和无剪切表面条件。此外，通过数值实例研究了宽厚比、纤维取向、模式数、板的不同尺寸比以及层数的影响。在横向上利用气泡形状函数来提高方法的收敛性。最后，给出了复合材料层合板在各种边界条件下的剪切和轴向相互作用图。通过数值算例研究了板的宽厚比、纤维取向、模数、不同尺寸比以及层数的影响。在横向上利用气泡形状函数来提高方法的收敛性。最后，给出了复合材料层合板在各种边界条件下的剪切和轴向相互作用图。通过数值算例研究了板的宽厚比、纤维取向、模数、不同尺寸比以及层数的影响。在横向上利用气泡形状函数来提高方法的收敛性。最后，给出了复合材料层合板在各种边界条件下的剪切和轴向相互作用图。