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工程设计学报
Chinese Journal of Engineering Design  2005, Vol. 12 Issue (3): 140-147    DOI:
    
Shape optimization of two-dimensional continuum structures under displacement, stress and size constraints
 SUI  Yun-Kang, GUAN  Zhao, DU  Jia-Zheng, LI  Dong
Numerical Simulation Center for Engineering, Beijing University of Technology, Beijing 100022, China
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Abstract  Based on two-phase control theory, through establishing relation between design variables and coordinates of key points and relation between coordinates of key points and coordinates of nodes, relation between design variables and coordinates of nodes are acquired. According to the acquired relation, relation between objective function and design variables is constructed. By adopting finite difference method, restraint functions of stress and displacement are gained, and shape optimization model meeting stress, displacement and size restraints is established. The sequential quadratic programming is adopted to solve the shape optimization problem of two-dimensional continuum structures. Taking MSC/Nastran software as solver of structure analysis, program of two-dimensional continuum structures is developed with PCL language. In the process of program implementation, to effectively avoid iterative fluctuation and even divergence, the upper and lower bounds of design variables is adjusted by interval factor. The numerical examples show that the program and algorithm are robust, reliable and efficient.

Key words： shape optimization      two-dimensional continuum      two-phase control      sequential quadratic programming      interval factor     
Published: 28 June 2005
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SUI Yun-Kang
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SUI Yun-Kang, GUAN Zhao, DU Jia-Zheng, LI Dong. Shape optimization of two-dimensional continuum structures under displacement, stress and size constraints. Chinese Journal of Engineering Design, 2005, 12(3): 140-147.

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https://www.zjujournals.com/gcsjxb/     OR     https://www.zjujournals.com/gcsjxb/Y2005/V12/I3/140


位移、应力、尺寸约束下二维连续体的形状优化

以二级控制理论为切入点，通过构造设计变量与关键点坐标之间的关系和关键点坐标与节点坐标之间的关系，得到了设计变量和节点坐标之间的关系。根据这一关系建立了目标函数跟设计变量之间的关系，采用有限差分法得到应力和位移的约束函数，建立了满足应力、位移和尺寸约束的形状优化模型，并采用序列二次规划方法求解二维连续体的形状优化问题。以MSC/Nastran软件为结构分析求解器，借助PCL语言开发了二维连续体的形状优化程序。为了有效地避免约束近似造成的迭代振荡乃至发散，在程序实现中，采用了区间因子来调整设计变量的上下限。数值算例表明程序算法的可靠性、精确性、高效性。

关键词： 形状优化,  二维连续体,  二级控制,  序列二次规划,  区间因子 
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