The proposed study scrutinizes the small scale-dependent geometrical nonlinear flexural response of arbitrary-shaped microplates having variable thickness made of functional graded (FG) composites. Accordingly, the modified couple stress continuum elasticity incorporating the von Karman large deflection supposition is established within a quasi-three dimensional (quasi-3D) plate framework in which the transverse shear deformation and normal deflection are assumed to be distributed in and trigonometric schemes. The thickness variation of microplates are assumed in linear, convex and concave patterns. Next, to resolve the couple stress-based nonlinear bending problem, the isogeometric technique incorporating non-uniform B-spline functions is taken into consideration to implement the both discretized-based estimation and accurate geometric description. The gradient of rotation associated with the couple stress type of size dependency causes a stiffening phenomenon in the both linear and nonlinear flexural responses. Also, through considering a change in the thickness variation pattern firstly from the convex kind to the linear one, thereafter from the linear kind to concave one, the role of couple stress size dependency becomes a bit more pronounced. In addition, it is deduced that the gap between nonlinear flexural curves associated with the convex, linear and concave patterns of thickness variation gets larger by changing the boundary conditions of the FG composite arbitrary-shaped microplates from clamped ones to simply supported ones.

拟议的研究仔细研究了由功能梯度 (FG) 复合材料制成的具有可变厚度的任意形状微板的小尺度相关几何非线性弯曲响应。因此，在准三维 (quasi-3D) 板框架内建立了包含 von Karman 大挠度假设的修正偶应力连续弹性，其中假设横向剪切变形和法向挠度分布在三角函数中。微孔板的厚度变化假设为线性、凸面和凹面图案。接下来，为了解决基于耦合应力的非线性弯曲问题，考虑了结合非均匀 B 样条函数的等几何技术来实现基于离散化的估计和精确的几何描述。与尺寸相关的耦合应力类型相关的旋转梯度会导致线性和非线性弯曲响应中的硬化现象。此外，通过考虑厚度变化模式的变化，首先从凸型到线性，然后从线性到凹型，耦合应力大小依赖性的作用变得更加明显。此外，推导出与凸面相关的非线性弯曲曲线之间的间隙，