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Structural Engineering and Mechanics
  Volume 76, Number 4, November25 2020 , pages 529-540

Robust concurrent topology optimization of multiscale structure under load position uncertainty
Jinhu Cai and Chunjie Wang

    Concurrent topology optimization of macrostructure and microstructure has attracted significant interest due to its high structural performance. However, most of the existing works are carried out under deterministic conditions, the obtained design may be vulnerable or even cause catastrophic failure when the load position exists uncertainty. Therefore, it is necessary to take load position uncertainty into consideration in structural design. This paper presents a computational method for robust concurrent topology optimization with consideration of load position uncertainty. The weighted sum of the mean and standard deviation of the structural compliance is defined as the objective function with constraints are imposed to both macro- and micro-scale structure volume fractions. The Bivariate Dimension Reduction method and Gauss-type quadrature (BDRGQ) are used to quantify and propagate load uncertainty to calculate the objective function. The effective properties of microstructure are evaluated by the numerical homogenization method. To release the computation burden, the decoupled sensitivity analysis method is proposed for microscale design variables. The bi-directional evolutionary structural optimization (BESO) method is used to obtain the black-and-white designs. Several 2D and 3D examples are presented to validate the effectiveness of the proposed robust concurrent topology optimization method.
Key Words
    load position uncertainty; robust concurrent topology optimization; homogenization method; Bivariate Dimension Reduction method; Gauss-type quadrature
Jinhu Cai: School of Mechanical Engineering and Automation, Beihang University, Beijing, China
Chunjie Wang : State Key Laboratory of Virtual Reality and Systems, Beihang University, Beijing, China

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