Bi-directional evolutionary stress-based topology optimization of material nonlinear structures
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RESEARCH PAPER
Bi-directional evolutionary stress-based topology optimization of material nonlinear structures Bin Xu 1
&
Yongsheng Han 1 & Lei Zhao 1
Received: 22 May 2020 / Revised: 8 September 2020 / Accepted: 2 October 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Stress-based topology optimization and nonlinear structural topology optimization is gaining increasing attention in order to make topology optimization more realistic. Thus, this paper extends current concepts of topology optimization to the design of structures made of nonlinear materials. An extended bi-directional evolutionary structural optimization (BESO) method for stress minimization topology optimization of material nonlinear structures is proposed in this work. BESO method based on discrete variables can effectively avoid the well-known singularity problem in density-based methods with low-density elements. The maximum von Mises stress is approximated by the p-norm global stress. The sensitivity information for designing variable updates is derived in detail by adjoint method. As for the highly nonlinear stress behavior, the updated scheme takes advantages from two filters respectively of the sensitivity and topological variables to improve convergence. Moreover, the filtered sensitivity numbers are combined with their historical sensitivity information to further stabilize the optimization process. The effectiveness of the proposed method is demonstrated by several 2D benchmark design problems. Keywords Topology optimization . Material nonlinearity . Stress design . BESO method . Sensitivity analysis
1 Introduction Topology optimization, as a powerful structural design method, aims to find an optimized structural topology or material layout within a given design domain for specified objectives, constraints, and boundary conditions (Xu et al. 2020). Since Highlights • The stress-based topology optimization model of material nonlinearity is proposed. • The stress level of material nonlinear structures can be restrained using p-norm global stress. • The stress concentration problem of material nonlinear structures can be solved using p-norm global stress. • The maximal von Mises stress decreases and the stress distribution smoother with larger value p-norm. • The smaller value the initial yield stress σs0 takes, the lower the maximal von Mises stress is achieved. Responsible Editor: Emilio Carlos Nelli Silva * Bin Xu [email protected] 1
Institute of Structural Health Monitoring and Control, School of Mechanics, Civil Engineering & Architecture, Northwestern Polytechnical University, Xi’an 710072, China
the seminal paper by Bendsøe and Kikuchi (1988), topology optimization has attracted wide academic (Bendsøe and Sigmund 2003; Deaton and Grandhi 2014; Huang and Xie 2010) and industrial (Zhu et al. 2016) interests due to its huge potential in engineering applications and its intrinsic mathematical challenges. Various approaches have been presented in the literature, such as homogenization method (Bendsøe and
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