Reliability-based topology optimization of geometrically nonlinear structures considering non-probabilistic load parameter and geometric field uncertainties

• Published in: Structural and multidisciplinary optimization Vol. 68; no. 9; p. 187
• Main Authors: Zhan, Junjie, Wang, Mingyue, Chen, Jiayi, Xing, Jian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2025; Springer Nature B.V
• Subjects: Asymptotes; Computational Mathematics and Numerical Analysis; Engineering; Engineering Design; Epistemology; Load; Manufacturing; Neural networks; Optimization; Parameters; Research Paper; Structural reliability; Theoretical and Applied Mechanics; Topology optimization; Uncertainty; Geometrically nonlinear; Non-probabilistic reliability-based optimization; Bounded field model; Ellipsoid convex model
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-025-04136-2

This paper presents a geometrically nonlinear non-probabilistic reliability-based topology optimization (GN-NRBTO) method that addresses non-probabilistic load parameters and geometric field uncertainties. The changes in load parameter conditions are managed using an ellipsoid convex model, while geometric field uncertainties are handled through a bounded field model employing the threshold field function. Utilizing the concerned performance method, the GN-NRBTO model is formulated as a maximization problem of the performance function subject to constraints related to the volume of structures experiencing large displacements and reliability index considerations. The GN-NRBTO problem represents a nested optimization framework, with the inner-loop optimization dedicated to assessing structural reliability in the presence of uncertainties, while the outer-loop optimization focuses on determining the optimal material configurations for structures with significant displacements. Additionally, the additive hyperelasticity technique is employed to mitigate numerical instability in structures undergoing large displacements, while the gradient-based optimization algorithm known as the method of moving asymptotes (MMA) is utilized for solving the GN-NRBTO problem. The effectiveness and practicality of the proposed GN-NRBTO approach have been demonstrated through three numerical examples showcasing enhancements in the reliability of structures experiencing significant displacements.