基于变密度法的动载结构梁拓扑优化设计
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摘要
自动化流水线中吊臂搬运是比较常见的一种运输形式,吊臂导轨的承重梁在运输货物时承受垂直向下且位置随时间周期性变化的重力作用,造成周期性变化的形变。此形变对整个装置的稳定性、安全性和寿命具有重大影响。对承重梁在运输货物时受力进行分析,以位置变化的动载作为约束,建立基于变密度法的拓扑优化数学模型;引入通用性强的优化准则,采用以卷积方程为基础的过滤器,消除由于棋盘格和网络依赖所造成的不确定性;借用MATLAB建立相应的数学模型进行拓扑优化,根据优化结果建立相应的三维模型,将模型导入ANAYS进行静力变形分析;将试验数据与仿真结果进行对比,验证了仿真结果的可信度和拓扑优化方法的可行性。最终设计在屋顶窗吊装搬运装置中应用效果良好,为此类承重梁结构设计提供了参考。
The beam of roof window handing machine bears dynamic loads in operation. The rigidity of beam is the main factor that affects accuracy and stability of the whole machine. The stress analysis of beam was carried on firstly,then the mathematical model of topology optimization based on variable density method was established in which an additional constraint condition was taken part in. The iterative formula was deduced taking advantage of optimality criteria method and Lagrange multiplier was calculated using volume constraint. A filtering function was imported in order to solve checkerboard and mesh-independent. After the preparation of MATLAB program,3D model was created using the optimized cross section shape. Besides simulation of static stiffness was carried on to obtain the deformation with ANAYS,the test of static deformation also was implemented. The results of simulation and test were highly compatible to prove the accuracy and efficiency of the optimization and simulation. The final results are applied to the roof window handing machine and provide helpful instruction for similar optimization design.
The beam of roof window handing machine bears dynamic loads in operation. The rigidity of beam is the main factor that affects accuracy and stability of the whole machine. The stress analysis of beam was carried on firstly,then the mathematical model of topology optimization based on variable density method was established in which an additional constraint condition was taken part in. The iterative formula was deduced taking advantage of optimality criteria method and Lagrange multiplier was calculated using volume constraint. A filtering function was imported in order to solve checkerboard and mesh-independent. After the preparation of MATLAB program,3D model was created using the optimized cross section shape. Besides simulation of static stiffness was carried on to obtain the deformation with ANAYS,the test of static deformation also was implemented. The results of simulation and test were highly compatible to prove the accuracy and efficiency of the optimization and simulation. The final results are applied to the roof window handing machine and provide helpful instruction for similar optimization design.
引文
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[3]MLEJNEK H P,SCHIRRMACHER R.An Engineer’s Approach to Optimal Material Distribution and Shape Finding[J].Computer Methods in Applied Mechanics and Engineering,1993,106:1-26.
[4]HUANG X,XIE Y.Evolutionary Topology Optimization of Continuum Structures Methods and Applications[M].New York:John Wiley&Sons,2010.
[5]ZUO Z H,XIE Y M,HUANG X.Combining Genetic Algorithms with BESO for Topology Optimization[J].Structural and Multidisciplinary Optimization,2009,38(5):511-523.
[6]FOURIE P,GROENWOLD A.The Particle Swarm Optimization in Topology Optimization[M].Dalian:Liaoning Electronic Press,2001.
[7]LUH G C,LIN C Y.Structural Topology Optimization Using Ant Colony Optimization Algorithm[J].Applied Soft Computing,2009,9(4):1343-1353.
[8]左孔天.连续体结构拓扑优化理论与应用研究[D].武汉:华中科技大学,2004.
[9]陈艾荣,常成.渐进结构优化法在桥梁找型中的应用[J].同济大学学报(自然科学版),2012,40(1):8-13.CHEN A R,CHANG C.Evolutionary Structural Optimization in Form Finding of Bridges[J].Journal of Tongji University(Natural Science),2012,40(1):8-13.
[10]张宏博,薄瑞峰,游小红,等.基于拓扑优化的深孔钻床主轴箱的结构重构汽车车架的优化设计[J].机床与液压,2013,41(7):150-153.ZHANG H B,BO R F,YOU X H,et al.Structural Reconstruction of Spindle Box of Deep Hole Drilling Machine Based on Structural Topology Optimization[J].Machine Tool&Hydraulics,2013,41(7):150-153.
[11]葛文杰,黄杰,杨方.拓扑优化技术及其在汽车设计中的应用[J].机床与液压,2007,35(8):11-14.GE W J,HUANG J,YANG F.Topology Optimization Technology and Its Utility in Automotive Industry[J].Machine Tool&Hydraulics,2007,35(8):11-14.