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 引用本文: 王选, 刘宏亮, 龙凯, 杨迪雄, 胡平. 基于改进的双向渐进结构优化法的应力约束拓扑优化[J]. 力学学报, 2018, 50(2): 385-394.
Wang Xuan, Liu Hongliang, Long Kai, Yang Dixiong, Hu Ping. STRESS-CONSTRAINED TOPOLOGY OPTIMIZATION BASED ON IMPROVED BI-DIRECTIONAL EVOLUTIONARY OPTIMIZATION METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2): 385-394.
 Citation: Wang Xuan, Liu Hongliang, Long Kai, Yang Dixiong, Hu Ping. STRESS-CONSTRAINED TOPOLOGY OPTIMIZATION BASED ON IMPROVED BI-DIRECTIONAL EVOLUTIONARY OPTIMIZATION METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2): 385-394.

## STRESS-CONSTRAINED TOPOLOGY OPTIMIZATION BASED ON IMPROVED BI-DIRECTIONAL EVOLUTIONARY OPTIMIZATION METHOD

• 摘要: 工程结构设计时经常需要限制最大名义应力,以避免发生断裂或疲劳破坏,一个有效的策略是采用拓扑优化方法. 常规的双向渐进结构优化法(bi-evolutionary structural optimization, BESO)不能有效求解应力约束拓扑优化问题,为此本文提出一种改进的双向渐进结构优化方法,处理体积和应力约束下的最小柔顺性问题. 引入基于K-S函数的全局应力度量,以减小大量局部应力约束引起的计算代价. 采用拉格朗日乘子法将应力约束函数引入到目标函数,然后由二分法确定合适的拉格朗日乘子的值使得应力约束得到满足. 而且,详细推导了基于BESO方法的应力约束拓扑优化模型及其灵敏度列式,最后通过三个典型拓扑优化算例验证改进方法的有效性. 为展示考虑应力约束的优点,将应力约束设计与传统的基于刚度的设计进行了比较. 结果表明, 改进的BESO方法优化迭代过程稳健,获得了边界灰度单元很少的清晰的拓扑构型,并实现了有效降低应力集中效应的设计.

Abstract: It is necessary to limit maximum nominal stress for engineering structural design generally, so as to avoid that the failure of fracture or fatigue occurs. Topology optimization approach is a feasible strategy. The conventional bi-evolutionary structural optimization (BESO) method cannot effectively address the topology optimization problem with stress constraint. To overcome this limitation, this paper suggests an improved BESO method for stress-constrained topology optimization, in which the minimum compliance design problem with volume and stress constraints is considered. A global stress measure based on the K-S function is introduced to reduce the computational cost associated with the local stress constraint. Meanwhile, the stress constraint function is added to the objective function by using the Lagrange multiplier method. Moreover, the appropriate value of the Lagrangian multiplier is then determined by a bisection method so that the stress constraint is satisfied. The model of BESO method for solving stress-constrained topology optimization and its sensitivity analysis are detailed. Finally, three typical topology optimization examples are performed to demonstrate the validity of the present method, in which the stress constrained designs are compared with the traditional stiffness based designs to illustrate the merit of considering stress constraint. The optimized results indicate that the improved BESO method, as a robust algorithm with stable iterative history, achieves an ambiguous topology with clearly defined boundaries, and realizes a design that effectively reduces stress concentration effect at the critical stress areas.

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