Via the nonlocal stress–strain gradient continuum mechanics, the microscale-dependent linear and nonlinear large deflections of transversely loaded composite sector microplates with different thickness variation schemes are investigated. Microplates are assumed to be prepared from functionally graded materials (FGMs) the characteristics of which are changed along the thickness direction. A quasi-3D plate theory with a sinusoidal transverse shear function in conjunction with a trigonometric normal function was employed for the establishment of size-dependent modelling of FGM microplates with different thickness variation schemes. Then, to solve the nonlocal stress–strain gradient flexural problem, the non-uniform rational B-spline type of isogeometric solution methodology was applied for an accurate integration of geometric discerptions. It was found that the gap between load–deflection curves drawn for linear, concave and convex thickness variation patterns became greater by changing FGM composite microplate boundary conditions from clamped to simply supported. In addition, it was found that by considering only the nonlocal size effect, the plate deflection obtained by the nonlocal strain gradient quasi-3D plate model was greater than that extracted by the classical continuum elasticity because of the softening character of nonlocal size effect, while the strain gradient microstructural size dependency acted in opposite way and represented a stiffening character.

通过非局部应力-应变梯度连续力学，研究了不同厚度变化方案的横向加载复合扇形微板的微尺度相关线性和非线性大挠度。假定微板是由功能梯度材料（FGM）制备的，这些材料的特性沿厚度方向变化。利用具有正弦曲线横向剪力函数和三角法向函数的准3D板理论，建立了具有不同厚度变化方案的FGM微板的尺寸相关模型。然后，为了解决非局部应力-应变梯度弯曲问题，将非均匀有理B样条类型的等几何求解方法应用于几何离散的精确积分。结果发现，通过改变FGM复合微板的边界条件从夹紧到简单支撑，为线性，凹形和凸形厚度变化图绘制的载荷-挠度曲线之间的间隙变得更大。另外，发现仅考虑非局部尺寸效应，由于非局部尺寸效应的软化特性，非局部应变梯度准3D板模型获得的板挠度大于经典连续统弹性所提取的板挠度。应变梯度的微观结构尺寸依赖性以相反的方式起作用，并表现出一种刚性特征。