Stress-based shape and topology optimization with cellular level set in B-splines
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RESEARCH PAPER
Stress-based shape and topology optimization with cellular level set in B-splines Yelin Song 1 & Qingping Ma 2 & Yu He 2 & Mingdong Zhou 1 & Michael Yu Wang 2 Received: 26 November 2019 / Revised: 9 April 2020 / Accepted: 15 April 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A parametric level set approach based on B-splines is developed for the stress-based shape and topology optimization of cellular structures. In this method, the whole design domain is divided into a set of non-overlapping sub-domains, within each of which the structure is represented by an implicit B-spline level set function. This parameterization scheme ensures that the adjacent cells can be smoothly connected. The stress value of the structure is computed by using a p-norm function-based aggregation. The extended finite element method is implemented to calculate the structural stress. Moreover, a new optimization strategy based on a two-field formulation is proposed to eliminate numerical instability in the optimization process. A continuity scheme based on the least square method is proposed to guarantee the high-order connectivity at the adjacent cell boundary. In addition, optimized cellular structures with different cell partitions are obtained and discussed. Several numerical examples are presented to illustrate the applicability of the approach. Keywords Topology optimization . Cellular structures . Level set method . Stress minimization . Stress constraints
1 Introduction The structural strength is a critical factor in structural design since a large local stress will lead to structural failures such as fracture, fatigue and creep (Andkjær & Sigmund, 2011). Topology optimization is an effective structural design approach that satisfies design requirements by rationally distributing materials. In recent years, many scholars have attempted to apply the topology optimization to stress-related structural designs. Duysinx and Bendsøe (Duysinx & Bendsøe, 1998) introduced stress constraints into structural topology optimization. Similar to SIMP (solid isotropic material with penalization)
Responsible Editor: Zhen Luo * Mingdong Zhou [email protected] 1
Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
2
Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Kowloon 999077, Hong Kong
method, they proposed a stress interpolation with ε-relaxation approach to solve the so-called singularity issue (Cheng & Guo, 1997) of the stress constraints in structural topology optimization. The stress is a local feature of structures, which implies that the stress in every material point of the structure needs to be constrained. This will result in a large number of local stress constraints. Generally, an integrated stress constraint function is used to aggregate the local stress constraints, such as the p-norm function (Duysinx & Sigmund, 1998) and
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