基于SIMP变密度法的结构拓扑优化及应用  

Structural topology optimization based on SIMP variable density method and its application

作　　者：于海 杨慧斌 茅健 闫娟 YU Hai;YANG Huibin;MAO Jian;YAN Juan(School of Mechanical and Automotive Engineering,Shanghai University of Engineering Science,Shanghai 201620,China)

机构地区：[1]上海工程技术大学机械与汽车工程学院,上海201620

出　　处：《工程塑料应用》2024年第10期91-99,共9页Engineering Plastics Application

摘　　要：在结构拓扑优化过程中,为了解决复杂结构计算速度慢、效率低的问题,提出了一种基于固体各向同性材料密度惩罚模型(SIMP)的步长自适应优化算法,该算法可根据SIMP惩罚因子P值自适应选择佳步长移动参数,并根据得到的目标函数的迭代值,自适应改变每次迭代的移动步长,在保证迭代精度的同时,以更快的速度逼近迭代目标,并利用经典MBB简支梁算例进行仿真实验,通过划分不同网格数量,横向对比分析另外三种步长迭代公式,得出最终迭代结果准确且迭代速度最快可提高100%的结论。此外,为满足汽车领域的轻量化需求,用拓扑优化技术,针对汽车油门支架结构进行重新优化设计,使优化后的模型体积减小35%;在此基础上,利用增材制造技术,采用双喷头连续纤维打印机,以长碳纤维体积分数为35%的复合材料(基体为短切碳纤维填充尼龙丝材)替代传统的铝合金材料进行增材制造,实现减重的目的,最终得到力学性能与原结构相当、质量减轻48%的油门支架结构,可进一步实现汽车的轻量化制造。In the process of topology optimization,in order to solve the problems of slow computation speed and low efficiency in complex structures,a step-size adaptive optimization algorithm based on the solid isotropic material with penalization(SIMP)model was presented.The proposed algorithm adaptively selects the optimal step size parameter according to the SIMP penalty factor P value and adjusts the step size for each iteration based on the objective function's iterative value.This approach ensures precision while accelerating convergence to the iteration target.Simulation experiments using the classical MBB simply supported beam case,with various mesh sizes,demonstrate that the proposed method achieves the most accurate results with up to a 100%improvement in iteration speed compared to three other step-size iteration formulas.Additionally,to address the lightweight requirements in the automotive industry,topology optimization was applied to redesign the throttle bracket structure.The optimized model volume is reduced by 35%.On this basis,using the additive manufacturing technology,the double-nozzle continuous fiber printer was used.The composite material with a long carbon fiber volume fraction of 35%(the matrix is a chopped carbon fiber filled nylon wire)replaced the traditional aluminum alloy material for additive manufacturing to achieve the purpose of weight reduction.Finally,the throttle bracket structure with mechanical properties equivalent to the original structure and a weight reduction of 48%were obtained,which can further realize the lightweight manufacturing of automobiles.

关 键 词：变密度法 自适应移动步长 拓扑优化 油门支架结构 增材制造 

分 类 号：TH122[机械工程—机械设计及理论]