Abstract This work extends isogeometric thin shell formulations to incorporate constitutive laws generated by stochastic multiscale analyses. The integration of the constitutive law is performed through the thickness of the shell, in order to account for material heterogeneity. At each thickness integration point, a corresponding representative volume element is assigned, defining the microstructural topology of a composite material comprised of a matrix with arbitrary volumetric inclusions. With the aid of stochastic processes, the impact of material and inclusion variability on the structural response is demonstrated in benchmark and real-scale numerical examples. Spatial material variability is considered in both surface and through thickness coordinates of the shell. As a result, the elimination of geometric error, together with the realistic material descriptions, renders this formulation an ideal candidate for the simulation of shell structures made of composite materials.

中文翻译：

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等几何复合基尔霍夫-洛夫壳的随机多尺度公式

摘要 这项工作扩展了等几何薄壳公式，以纳入由随机多尺度分析生成的本构法则。本构定律的积分是通过壳的厚度进行的，以考虑材料的异质性。在每个厚度积分点，分配一个相应的代表性体积元素，定义复合材料的微观结构拓扑，该复合材料由具有任意体积夹杂物的矩阵组成。在随机过程的帮助下，材料和夹杂物可变性对结构响应的影响在基准和实际比例的数值例子中得到了证明。在壳的表面坐标和整个厚度坐标中都考虑了空间材料可变性。因此，消除几何误差，