板系结构拓扑优化及其在液压机底座设计中的应用研究
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摘要
面对全球工业化的高度发展和世界能源危机,如何最有效的利用资源是当前亟待解决的问题。为此,针对液压机底座这类重量很大的箱形板系结构开展以重量最轻为目标,以材料的合理分配为手段的结构拓扑优化具有重要的现实意义。同时,研究实用、可靠和有效的拓扑优化方法,对于发展液压机本体结构的设计理论具有推动作用和理论价值。目前,压机结构拓扑优化研究尚属空白,为此本文以基结构法为基本研究方法,以压机底座为研究对象,对这类箱形板系结构的拓扑优化进行了系统研究。
论文提出用于结构拓扑优化的压机底座板系基结构设计。并根据液压机底座的功能、载荷及结构特点,提出其基结构的建立原则。在已建立的底座板系基结构基础上,给出了结构拓扑优化数学模型。
为提高底座结构拓扑优化的效率,本文对基于三层BP网络的结构近似分析方法进行了系统研究。提出应用遗传算法确定三层BP神经网络隐层节点数的方法,即通过建立以BP神经网络的训练误差为目标函数,以隐层节点数为设计变量的优化数学模型,使隐层节点数的确定具有理论依据。
提出用于训练BP网络的教师样本集D-最优设计方法,即用一个无交叉耦合项的二次回归方程近似描述构成底座的各板厚度与挠度的关系。在给定样本总量的条件下,建立以挠度的回归方差最小为目标的最优因素组合的优化问题。求解该优化问题,可以获得使BP网络误差最小的最优教师样本集。
本文提出基于三层BP神经网络结构近似分析方法的压机底座板系结构拓扑优化问题的遗传算法。在该算法中,采用拒绝策略处理约束,即采用三层BP网络结构近似分析方法处理位移约束,以提高优化效率;采用有限元屈曲分析对每一代种群中的最优个体进行稳定性检验,以保证最优解满足稳定性约束条件。
本文对压机底座板系结构进行了拓扑优化,得到了六种重量较轻,形式较新颖的底座拓扑结构。
本文制作了两个1:5的金属模型,对技术参数相同、结构性能相近,而拓扑形式(其中之一为最优拓扑结构)和重量不同的底座模型进行了实验对比。实验表明,本文提出的算法具有实用性、可靠性和有效性。
With the fast development of global industrialization and the crisis of world energy sources, currently how to utilize the sources efficiently is a key problem to be resolved. Therefore, aiming at the base frame, which is a kind of heavy box section plate’s structure, of the hydraulic press, it is very important to carry out the structural topology optimization with the lightest weight as the objective. At the same time, that research on the practical, reliable and effective topology optimization method has a promote effect and theoretical value for the development of the design theory of the structure of the hydraulic press. Currently, topology optimization research on the structure of the hydraulic press has not been found with the best knowledge of the author. Therefore, with the ground structure method as a basic research method and with the press’base frame as the research objective, a systematical research on the topological optimization of the box section plate’s structure was carried out in this work.
The ground structures of press base frame were firstly set up to be used to topology optimization. On the base of analyzing function, load and structure features of press base frame, the basic principles of building ground structure was proposed. The mathematical models for the topology optimization were proposed as well.
To increase effective of structural topology optimizing a whole research on the approximate analysis method with three layers BP neural network was underway. A rational method to decide the nodal number of the hidden layer of the three layers of BP neural net based on the genetic algorithm was firstly proposed. The D-optimization method of BP network teaching sample design was firstly proposed. The method is that using a quadratic regression equation without cross items approximate express the relation of plates’thickness and flexibility of press base frame. Under the condition of the sample quantity was given, the optimization problem was set up which aim is to minimum the regression variance of flexibility of base frame. By solving the problem the optimum teaching sample was obtained with most minimum regression variance of flexibility.
A genetic algorithm was proposed to solve the problem of structural topology optimization of press base frame using structural approximate analysis with three layers BP network. In that algorithm, a rejecting strategy for treating constrains was used, which means that all individuals’displacement constrains are treat by BP network and only the optimum individuals’stability constrain was check by FEM buckling analysis.
Two discontinuous phenomena in the topology optimization of the box section plate’s system structure were firstly proposed. It was pointed out that the two mutational phenomena were the reason inducing that the structural approximate analysis method based on the BP neural net was difficult to be applied on the topology optimization. Therefore, the D-optimization design strategy of the teacher’s sample was set up, which makes the trained BP neural net can be applied on the approximate quick computation of the structural displacement constraint. The method, which combined the mechanical initial check and the finite element buckling analysis, was utilized to deal with the stability constraints.
The structural topology optimization was firstly implemented for the base frame of the hydraulic press in this work. Six optimum topological base frame structures light in weight and novel in layout were obtained.
Finally, two 1:5 metal models, which technical parameter and performance is same, but topology and weight is different, as well as one of which is optimum base frame, were manufactured to do the experimental comparison, The experiments showed that the algorithm that was proposed by this work is practical, reliable and valid.
论文提出用于结构拓扑优化的压机底座板系基结构设计。并根据液压机底座的功能、载荷及结构特点,提出其基结构的建立原则。在已建立的底座板系基结构基础上,给出了结构拓扑优化数学模型。
为提高底座结构拓扑优化的效率,本文对基于三层BP网络的结构近似分析方法进行了系统研究。提出应用遗传算法确定三层BP神经网络隐层节点数的方法,即通过建立以BP神经网络的训练误差为目标函数,以隐层节点数为设计变量的优化数学模型,使隐层节点数的确定具有理论依据。
提出用于训练BP网络的教师样本集D-最优设计方法,即用一个无交叉耦合项的二次回归方程近似描述构成底座的各板厚度与挠度的关系。在给定样本总量的条件下,建立以挠度的回归方差最小为目标的最优因素组合的优化问题。求解该优化问题,可以获得使BP网络误差最小的最优教师样本集。
本文提出基于三层BP神经网络结构近似分析方法的压机底座板系结构拓扑优化问题的遗传算法。在该算法中,采用拒绝策略处理约束,即采用三层BP网络结构近似分析方法处理位移约束,以提高优化效率;采用有限元屈曲分析对每一代种群中的最优个体进行稳定性检验,以保证最优解满足稳定性约束条件。
本文对压机底座板系结构进行了拓扑优化,得到了六种重量较轻,形式较新颖的底座拓扑结构。
本文制作了两个1:5的金属模型,对技术参数相同、结构性能相近,而拓扑形式(其中之一为最优拓扑结构)和重量不同的底座模型进行了实验对比。实验表明,本文提出的算法具有实用性、可靠性和有效性。
With the fast development of global industrialization and the crisis of world energy sources, currently how to utilize the sources efficiently is a key problem to be resolved. Therefore, aiming at the base frame, which is a kind of heavy box section plate’s structure, of the hydraulic press, it is very important to carry out the structural topology optimization with the lightest weight as the objective. At the same time, that research on the practical, reliable and effective topology optimization method has a promote effect and theoretical value for the development of the design theory of the structure of the hydraulic press. Currently, topology optimization research on the structure of the hydraulic press has not been found with the best knowledge of the author. Therefore, with the ground structure method as a basic research method and with the press’base frame as the research objective, a systematical research on the topological optimization of the box section plate’s structure was carried out in this work.
The ground structures of press base frame were firstly set up to be used to topology optimization. On the base of analyzing function, load and structure features of press base frame, the basic principles of building ground structure was proposed. The mathematical models for the topology optimization were proposed as well.
To increase effective of structural topology optimizing a whole research on the approximate analysis method with three layers BP neural network was underway. A rational method to decide the nodal number of the hidden layer of the three layers of BP neural net based on the genetic algorithm was firstly proposed. The D-optimization method of BP network teaching sample design was firstly proposed. The method is that using a quadratic regression equation without cross items approximate express the relation of plates’thickness and flexibility of press base frame. Under the condition of the sample quantity was given, the optimization problem was set up which aim is to minimum the regression variance of flexibility of base frame. By solving the problem the optimum teaching sample was obtained with most minimum regression variance of flexibility.
A genetic algorithm was proposed to solve the problem of structural topology optimization of press base frame using structural approximate analysis with three layers BP network. In that algorithm, a rejecting strategy for treating constrains was used, which means that all individuals’displacement constrains are treat by BP network and only the optimum individuals’stability constrain was check by FEM buckling analysis.
Two discontinuous phenomena in the topology optimization of the box section plate’s system structure were firstly proposed. It was pointed out that the two mutational phenomena were the reason inducing that the structural approximate analysis method based on the BP neural net was difficult to be applied on the topology optimization. Therefore, the D-optimization design strategy of the teacher’s sample was set up, which makes the trained BP neural net can be applied on the approximate quick computation of the structural displacement constraint. The method, which combined the mechanical initial check and the finite element buckling analysis, was utilized to deal with the stability constraints.
The structural topology optimization was firstly implemented for the base frame of the hydraulic press in this work. Six optimum topological base frame structures light in weight and novel in layout were obtained.
Finally, two 1:5 metal models, which technical parameter and performance is same, but topology and weight is different, as well as one of which is optimum base frame, were manufactured to do the experimental comparison, The experiments showed that the algorithm that was proposed by this work is practical, reliable and valid.
引文
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