Robust adaptive topology optimization of porous infills under loading uncertainties

• Published in: Structural and multidisciplinary optimization 2021-05, Vol.63 (5), p.2253-2266
• Main Authors: Hoang, Van-Nam, Pham, Trung, Tangaramvong, Sawekchai, Bordas, Stéphane P. A., Nguyen-Xuan, H.
• Format: Article
• Language: English
• Subjects: Bars; Computational Mathematics and Numerical Analysis; Design optimization; Engineering; Engineering Design; Finite element method; Loads (forces); Mathematical analysis; Optimization; Porosity; Research Paper; Robust design; Standard deviation; Theoretical and Applied Mechanics; Topology optimization; Uncertainty
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-020-02800-3

The majority of topology optimization methods for porous infill designs is based on the assumption of deterministic loads. However, in practice, quantities such as positions, weights, and directions of applied loads may change accidentally. Deterministic load-based designs might deliver poor structural performance under loading uncertainties. Such uncertain factors need to be taken into account in topological optimization to seek robust results. This paper presents a novel robust concurrent topology optimization method for the design of uniform/non-uniform porous infills under the accidental change of loads. A combination of moving morphable bars (MMBs) and loading uncertainties is proposed to directly model multiscale structures and seek robust designs. The macro- and microscopic structures can be simultaneously optimized through the minimization of the weighted sum of the expected compliance and standard deviation. The geometries of adaptive geometric components (AGCs) are straightforwardly optimized. The AGCs consist of two classes of geometric components: macroscopic bars describing the overall structure and microscopic bars describing the material microstructures. Automatic mesh-refinement is utilized to enhance computing efficiency. Numerical examples demonstrate that robust porous design can be obtained with only one global volume constraint while the material continuity of neighboring unit cells and the structural porosity can be maintained without additional constraints. The robust designs yield a more robust structural performance along with a smaller standard deviation compared with deterministic porous designs under loading uncertainties.