A novel Isogeometric topology optimization (ITO) method considering stress constraint and load uncertainties is proposed for the fiber reinforced composite structures. Firstly, with the density and fiber orientations at the control points of Non-Uniform Rational B-Splines (NURBS) defined as design variables while the magnitudes and direction angles of uncertain external loads described as interval variables, the ITO model for the fiber reinforced composite structures is constructed to minimize the structural compliance under the constraints on both material usage and global failure coefficient. To accurately calculate the material properties and stress distribution within fiber reinforced composite structures, the Gauss subdivision and the Tsai-Hill criterion combined with the P-norm function are introduced. Further, the critical loads leading to the worst structural performance are determined based on the weighted Sigmoid penalty of the stress constraint for balancing the performance requirements of high stiffness and high strength. Finally, the ITO model is solved by integrating all the proposed innovations with the Method of Moving Asymptotes (MMA). The validity and effectiveness of the proposed ITO method are validated by both numerical and engineering examples.

中文翻译：

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考虑应力约束和载荷不确定性的纤维增强复合材料结构等几何拓扑优化 （ITO）


针对纤维增强复合材料结构，提出了一种考虑应力约束和载荷不确定性的新型等几何拓扑优化 （ITO） 方法。首先，将非均匀有理 B 样条曲线 （NURBS） 控制点的密度和纤维取向定义为设计变量，而不确定外部载荷的大小和方向角定义为区间变量，构建纤维增强复合材料结构的 ITO 模型，在材料使用和全局失效系数的约束下最小化结构柔度。为了准确计算纤维增强复合材料结构内的材料性能和应力分布，引入了高斯细分和 Tsai-Hill 准则结合 P-norm 函数。此外，导致最差结构性能的临界载荷是根据应力约束的加权 Sigmoid 惩罚确定的，以平衡高刚度和高强度的性能要求。最后，通过将所有提出的创新与移动渐近线方法 （MMA） 集成来解决 ITO 模型。所提出的 ITO 方法的有效性和有效性通过数值和工程实例进行了验证。