Robust topology optimization formulation including local failure and load uncertainty using sequential quadratic program
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Robust topology optimization formulation including local failure and load uncertainty using sequential quadratic programming Kai Long . Xuan Wang . Yixian Du
Received: 25 March 2018 / Accepted: 3 August 2018 Springer Nature B.V. 2018
Abstract This paper introduces a new formulation of topology optimization for robust design including local failure and load uncertainty. In contrast to most studies, the focus has been on minimizing the total volume with multiple compliance constraints. With the introduction of the reciprocal intermediate variables, the topology optimization problem can be well posed as a sequential quadratic program with exact second-order information. Then, robust topology optimization is implemented within the framework of the suggested formulation, in which not only the randomness of the damage location but also the uncertainty of loading magnitude and direction are taken into account. Finally, several numerical examples are performed to verify the effectiveness and capability of the presented approach for robust design
considering local failure and load uncertainty. The effects that varying the input load magnitude and direction, damage location have upon the optimized designs are investigated by comparing those with deterministic design results.
K. Long (&) Beijing Key Laboratory of Energy Safety and Clean Utilization, North China Electric Power University, Beijing 102206, China e-mail: [email protected]
X. Wang State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China e-mail: [email protected]
K. Long State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China
Y. Du College of Mechanical and Power Engineering, China Three Gorges University, Yichang 443002, China e-mail: [email protected]
Keywords Topology optimization Reciprocal SIMP method Sequential quadratic programming Load uncertainty Fail-safe design
1 Introduction Since the prominent work of Bendsøe and Kikuchi (1988), topology optimization undergoes a
K. Long Key Laboratory of Safety Design and Reliability Technology for Engineering Vehicle, The Education Department of Hunan Province, Changsha University of Science and Technology, Changsha 410114, China
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tremendous progress and an amount of approaches emerge in chronological order including homogenization method (Bendsøe and Kikuchi 1988), Solid Isotropic Material with Penalization (SIMP) (Bendsøe 1989; Zhou and Rozvany 1991; Bendsøe and Sigmund 2004), Evolutionary Structural Optimization (ESO) and its later version-Bi-directional Evolutionary Structural Optimization (BESO) (Xie and Steven 1993; Huang and Xie 2010), level set method (Wang et al. 2003; Allaire et al. 2004) and phase field method (Wang and Zhou 2004). More recently, the moving morphable components (MMC) and moving morphable voids (MMV) concept
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