工程设计中一些形状优化问题的研究
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摘要
在工程设计中,形状优化设计方法,可以使工程设计的质量最轻、体积最小、承载力最大及利润最高等。在解决复杂工程优化设计问题时,形状优化设计方法可以从众多设计方案中寻找到最优设计方案。这样既能提高设计质量和设计效率,又能获得明显的经济效益和社会效益。
本文对工程中的一些形状优化设计问题,开展了优化研究,具体如下：
1)本文对发动机相关构件的形状优化设计方法进行了研究；对构件的受力进行了分析；研究了对称构件的形状优化设计方法；对解析敏度形状优化设计方法进行了研究。将对称形状优化设计方法和解析敏度形状优化设计方法融合起来,给出了一种对称解析敏度形状优化方法。用给出的优化方法,对具有对称性构件的形状进行了优化设计。用得到的最大应力值,与现有的最大值进行分析比较,其最大应力值降低了2.4%,证明本文给出的形状优化方法是正确的。
2)本文对发动机相关构件的带预测有效约束的形状优化设计方法和解析敏度形状优化设计方法进行了研究,将带预测有效约束的形状优化设计方法和解析敏度形状优化设计方法融合起来,提出了一种预测约束解析敏度形状优化方法。用提出的优化方法,优化设计了某构件的内孔形状。用优化得到的结构,与现有的结构进行分析比较,其最大计算值降低了6.4%,证明本文提出的形状优化方法是正确的。
3)本文推导了发动机相关对称构件形状优化设计方法和预测有效约束形状优化设计方法,研究了构件的解析敏度形状优化设计方法。将对称形状优化设计方法、带预测有效约束的形状优化设计方法和解析敏度形状优化设计方法融合起来,建立了一种预测约束对称解析敏度形状优化方法。用建立的优化方法,对某对称构件进行了优化设计。其计算结果与现有的结果进行分析比较,最大值降低了8.8%,证明本文建立的形状优化方法是正确的。
4)本文对磁驱动的机器鱼的尾鳍形状进行了优化研究。该机器鱼是在头部嵌入NdFeB永久磁铁为驱动器,在交变磁场的驱动下,头部产生微小振动就带动尾鳍摆动,将交变磁场能转换成机器鱼头部摆动的机械能,带动铜薄膜尾鳍产生波动并与液体耦合产生推力,模仿鱼类尾鳍的游动状态,实现仿生游动。
该微机器鱼的尾鳍是采用悬臂梁结构的变截面薄膜,固定在微机器鱼的头部。在对微机器鱼尾鳍形状进行优化设计时,提出了基于等面积条件,采用离散变量法对尾鳍的形状进行优化。本文优化的机器鱼最佳尾鳍形状,可以显著改善机器鱼的推进性能,理论分析与试验证明了提出的尾鳍形状离散优化方法行之有效,为深入进行鱼类仿生学的研究和仿生结构形状优化的研究奠定了基础。
5)本文开展了进退法优化设计算法研究,给出了一种在函数自身不能求一级导数情况下的精确进退法优化设计算法,即在每一次确定搜索区间时,精确进退法比进退法确定的搜索区间要小。在收敛精度一定的情况下,用精确进退法对优化目标函数求最优解,要比用进退法对同一个优化目标函数求最优解精度高、速度快。
In engineering design, the optimization of the shape is to be the lightest quality, smallest, largest and most profitable capacity and so on. In solving complex engineering optimization problems, the shape optimization method can find the optimal design from many designs. This will not only improve the design quality and design efficiency, but also achieve significant economic and social benefits.
In this thesis, several optimizations in engineering design are optimized as follows:
1) In this thesis, the optimization methods of the components related to engine are studied; The force of the components are analyzed; the optimization's methods of the components with symmetry are researched; analytical sensitivity analysis optimization methods are in-depth studied, the successful integration of the methods of Symmetric Optimal Design and the analytical sensitivity analysis optimization together. With the given optimization method, the symmetric shape of the component has been optimized design. The maximum stress value obtained is compared the results of the existing maximum value, the maximum stress value decreased by 2.4%, the shape of this optimization method is proved that it's correct.
2) In this thesis, a predicted effective constrained optimization and analytical sensitivity analysis optimization methods of the components related to engine are researched, the integration of the predicted effective constrained optimization and analytical sensitivity analysis optimization methods together, a predicted effective sensitivity analysis optimization methods is proposed. With this method, the design of the hole on the components is optimized. The maximum stress value decreased by 6.4%, compared with the existing maximum value, the shape of this optimization method is proved that it's correct.
3) In this thesis, the optimization methods of the components related to engine and a predicted effective constrained optimization is researched. Sensitivity analysis optimization method of the components is researched. The integration of the symmetry optimization's methods, the predicted effective constrained optimization and analytical sensitivity analysis optimization methods together, a predicted effective constrained symmetry sensitivity analysis optimization methods is proposed. With this method, the design of the hole on the components is optimized. The maximum stress value decreased by 8.8%, compared with the existing maximum value, the shape of this optimization method is proved that it's correct.
4) A robotic fish driven by magnetic is researched, the fish head is embedded the NdFeB permanent as magnet drive, the principle is that alternating magnetic field can be converted to machine swing the fish head of mechanical energy from changing the driving frequency of alternating magnetic field, driving the NdFeB magnetic drive embedded in the robotic fish head. Then they drive copper films caudal fin as volatility and produced thrust coupled with the liquid to achieve the above bionic swimming.
The micro-robot fish's caudal fin is the use of variable cross-section film like cantilever beam which is fixed at the micro-robot fish's head. The shape of Micro-Robotic Fish tail is optimized, the equal area conditions are proposed, and the discrete variable method is used to optimize the shape of the caudal fin. This optimization of the best fish tail shape of the machine, the machine can significantly improve the fish propulsion performance, theoretical analysis and experimental prove that the proposed discrete optimization method of the tail fin shape is effective, and it's laid the foundation for in-depth study of fish and bionic structural shape optimization research.
5) This retreat optimization methods are carried out. When the function itself is not a derivative case, an accurate retreat optimization methods is given. It means that the search range is determined every time, accurate method has the small search range than the retreat method. Convergence accuracy is certain, using accurate retreat optimization methods' objective function to get optimal solution, has high precision and speed than the retreat method.
本文对工程中的一些形状优化设计问题,开展了优化研究,具体如下：
1)本文对发动机相关构件的形状优化设计方法进行了研究；对构件的受力进行了分析；研究了对称构件的形状优化设计方法；对解析敏度形状优化设计方法进行了研究。将对称形状优化设计方法和解析敏度形状优化设计方法融合起来,给出了一种对称解析敏度形状优化方法。用给出的优化方法,对具有对称性构件的形状进行了优化设计。用得到的最大应力值,与现有的最大值进行分析比较,其最大应力值降低了2.4%,证明本文给出的形状优化方法是正确的。
2)本文对发动机相关构件的带预测有效约束的形状优化设计方法和解析敏度形状优化设计方法进行了研究,将带预测有效约束的形状优化设计方法和解析敏度形状优化设计方法融合起来,提出了一种预测约束解析敏度形状优化方法。用提出的优化方法,优化设计了某构件的内孔形状。用优化得到的结构,与现有的结构进行分析比较,其最大计算值降低了6.4%,证明本文提出的形状优化方法是正确的。
3)本文推导了发动机相关对称构件形状优化设计方法和预测有效约束形状优化设计方法,研究了构件的解析敏度形状优化设计方法。将对称形状优化设计方法、带预测有效约束的形状优化设计方法和解析敏度形状优化设计方法融合起来,建立了一种预测约束对称解析敏度形状优化方法。用建立的优化方法,对某对称构件进行了优化设计。其计算结果与现有的结果进行分析比较,最大值降低了8.8%,证明本文建立的形状优化方法是正确的。
4)本文对磁驱动的机器鱼的尾鳍形状进行了优化研究。该机器鱼是在头部嵌入NdFeB永久磁铁为驱动器,在交变磁场的驱动下,头部产生微小振动就带动尾鳍摆动,将交变磁场能转换成机器鱼头部摆动的机械能,带动铜薄膜尾鳍产生波动并与液体耦合产生推力,模仿鱼类尾鳍的游动状态,实现仿生游动。
该微机器鱼的尾鳍是采用悬臂梁结构的变截面薄膜,固定在微机器鱼的头部。在对微机器鱼尾鳍形状进行优化设计时,提出了基于等面积条件,采用离散变量法对尾鳍的形状进行优化。本文优化的机器鱼最佳尾鳍形状,可以显著改善机器鱼的推进性能,理论分析与试验证明了提出的尾鳍形状离散优化方法行之有效,为深入进行鱼类仿生学的研究和仿生结构形状优化的研究奠定了基础。
5)本文开展了进退法优化设计算法研究,给出了一种在函数自身不能求一级导数情况下的精确进退法优化设计算法,即在每一次确定搜索区间时,精确进退法比进退法确定的搜索区间要小。在收敛精度一定的情况下,用精确进退法对优化目标函数求最优解,要比用进退法对同一个优化目标函数求最优解精度高、速度快。
In engineering design, the optimization of the shape is to be the lightest quality, smallest, largest and most profitable capacity and so on. In solving complex engineering optimization problems, the shape optimization method can find the optimal design from many designs. This will not only improve the design quality and design efficiency, but also achieve significant economic and social benefits.
In this thesis, several optimizations in engineering design are optimized as follows:
1) In this thesis, the optimization methods of the components related to engine are studied; The force of the components are analyzed; the optimization's methods of the components with symmetry are researched; analytical sensitivity analysis optimization methods are in-depth studied, the successful integration of the methods of Symmetric Optimal Design and the analytical sensitivity analysis optimization together. With the given optimization method, the symmetric shape of the component has been optimized design. The maximum stress value obtained is compared the results of the existing maximum value, the maximum stress value decreased by 2.4%, the shape of this optimization method is proved that it's correct.
2) In this thesis, a predicted effective constrained optimization and analytical sensitivity analysis optimization methods of the components related to engine are researched, the integration of the predicted effective constrained optimization and analytical sensitivity analysis optimization methods together, a predicted effective sensitivity analysis optimization methods is proposed. With this method, the design of the hole on the components is optimized. The maximum stress value decreased by 6.4%, compared with the existing maximum value, the shape of this optimization method is proved that it's correct.
3) In this thesis, the optimization methods of the components related to engine and a predicted effective constrained optimization is researched. Sensitivity analysis optimization method of the components is researched. The integration of the symmetry optimization's methods, the predicted effective constrained optimization and analytical sensitivity analysis optimization methods together, a predicted effective constrained symmetry sensitivity analysis optimization methods is proposed. With this method, the design of the hole on the components is optimized. The maximum stress value decreased by 8.8%, compared with the existing maximum value, the shape of this optimization method is proved that it's correct.
4) A robotic fish driven by magnetic is researched, the fish head is embedded the NdFeB permanent as magnet drive, the principle is that alternating magnetic field can be converted to machine swing the fish head of mechanical energy from changing the driving frequency of alternating magnetic field, driving the NdFeB magnetic drive embedded in the robotic fish head. Then they drive copper films caudal fin as volatility and produced thrust coupled with the liquid to achieve the above bionic swimming.
The micro-robot fish's caudal fin is the use of variable cross-section film like cantilever beam which is fixed at the micro-robot fish's head. The shape of Micro-Robotic Fish tail is optimized, the equal area conditions are proposed, and the discrete variable method is used to optimize the shape of the caudal fin. This optimization of the best fish tail shape of the machine, the machine can significantly improve the fish propulsion performance, theoretical analysis and experimental prove that the proposed discrete optimization method of the tail fin shape is effective, and it's laid the foundation for in-depth study of fish and bionic structural shape optimization research.
5) This retreat optimization methods are carried out. When the function itself is not a derivative case, an accurate retreat optimization methods is given. It means that the search range is determined every time, accurate method has the small search range than the retreat method. Convergence accuracy is certain, using accurate retreat optimization methods' objective function to get optimal solution, has high precision and speed than the retreat method.
引文
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