In the present article, the couple stress models in the non-polynomial framework are developed and employed to examine the structural response characteristics of composite micro-plates. The length scale effects in the micro-laminates are considered using the couple stress theory. The trigonometric, inverse-trigonometric, hyperbolic, inverse-hyperbolic and exponential shear shape functions are considered to model transverse shear deformation effects in micro-plates. The Hamilton principle is employed to formulate the governing equations assuming linear structural kinematics. The governing equations are solved for simply supported micro-plates using the Navier solution for the prediction of analytical results. The structural responses of the composite micro-plates are examined for bending, free vibration, and buckling responses. The nondimensionalized deflection, stresses, frequencies, and axial buckling loads are evaluated using the present methodology. The higher buckling modes and free vibration modes are also obtained. The response characteristics due to five plate theories are compared and the applicability of the considered transverse shear deformation theories to model and analyze composite micro-plates is assessed. The effects of various parameters on the structural responses of micro-laminates are examined.

在本文中，开发了非多项式框架中的耦合应力模型，并将其用于检查复合微板的结构响应特性。使用耦合应力理论来考虑微层压板中的长度尺度效应。三角函数，反三角函数，双曲线函数，反双曲线函数和指数剪切形状函数被认为可以模拟微板中的横向剪切变形效应。汉密尔顿原理用于假设线性结构运动学来制定控制方程。使用Navier解决方案对简单支撑的微板求解控制方程，以预测分析结果。检查复合微板的结构响应的弯曲，自由振动和屈曲响应。使用本方法可以评估无量纲的挠度，应力，频率和轴向屈曲载荷。还可以获得较高的屈曲模式和自由振动模式。比较了五种板理论的响应特性，并评估了所考虑的横向剪切变形理论对复合微板进行建模和分析的适用性。检查了各种参数对微层压板结构响应的影响。比较了五种板理论的响应特性，并评估了所考虑的横向剪切变形理论对复合微板进行建模和分析的适用性。检查了各种参数对微层压板结构响应的影响。比较了五种板理论的响应特性，并评估了所考虑的横向剪切变形理论对复合微板进行建模和分析的适用性。检查了各种参数对微层压板结构响应的影响。