We present a nonlinear Kirchhoff–Love micro-shell element based on isogeometric analysis (IGA) and couple stress theory. Higher-order NURBS functions are exploited for analyzing the strain gradient effect which automatically fulfill the higher-order continuity requirements. We express the strain gradient elastic formulation in natural curvilinear coordinates, which leads to an efficient numerical tool to examine geometric nonlinearities of thin micro-shell structures. The presented IGA formulation is verified through comparisons to analytical solution, experimental data as well as other popular benchmark problems of nonlinear geometric shells. We believe that the presented formulation is particularly suitable for analyzing two-dimensional materials at larger length scales, which are commonly studied at nanoscale.

我们基于等几何分析（IGA）和耦合应力理论提出了一种非线性的Kirchhoff-Love微壳单元。利用高阶NURBS函数来分析应变梯度效应，该效应会自动满足高阶连续性要求。我们用自然曲线坐标表示应变梯度弹性公式，这导致了一种有效的数值工具来检查薄微壳结构的几何非线性。通过与解析解决方案，实验数据以及非线性几何壳的其他常见基准问题进行比较，验证了所提出的IGA公式。我们认为，提出的配方特别适合于分析较大长度尺度的二维材料，而二维尺度材料通常是在纳米尺度上研究的。