机翼颤振模型主盒段的优化方法研究
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摘要
飞机在飞行过程中会出现颤振现象,造成机体的损坏。为避免颤振的发生,需要对飞机的颤振特性加以研究,风洞试验是验证飞机在动载荷作用下振动特性的可靠手段。大量的研究实例证明,颤振模型与原结构的相似程度决定了风洞试验数据的准确程度。因此,如何设计包含外形相似、刚度相似和质量相似的颤振模型是一个值得研究的问题。
研究表明,拓扑优化、尺寸优化和形状优化技术是解决颤振模型设计的有效手段。机翼的内部结构复杂,采用缩比方法设计颤振模型时,由于模型与原结构的尺寸相差很大,往往出现微小结构,导致颤振模型的可制造性差。同时由于微小结构的弹性差,会引起非线性问题。主盒段是机翼颤振模型的主要承力结构,其质量和刚度的相似程度是解决机翼颤振模型相似性的基础。本文结合拓扑优化和尺寸优化,在外形相似的基础上,提出了实现质量和刚度相似的盒段优化方法,主要工作如下：
首先,利用APDL语言构建主盒段骨架有限元模型,以柔度为结构的设计目标,以梁或者肋存在状态为设计变量,建立骨架的优化模型。基于梁或者肋对目标函数的灵敏度分析,再运用MATLAB软件,从而编写了结构的修改程序,实现骨架的拓扑优化；
其次,在骨架的拓扑构型确定的情况下,将骨架的特征参数优化分段进行,以每一段选取点的柔度为目标,以对应梁的特征参数为设计变量,采用ISIGHT软件中的多岛遗传算法和序列二次规划法,实现了骨架的参数修改,在每次分段优化结束后,将得到的参数值去余,调整厚度,对应为骨架材料每层厚度的整数倍；
再次,在骨架结构的基础上建立蒙皮结构,以盒段每一段的柔度为设计目标,对应段的蒙皮厚度为设计变量。在每次分段优化结束后,将得到的厚度值去余,调整厚度,对应为蒙皮材料每层厚度的整数倍；
最后,为了和真实结构的质量分布相似,在优化模型的相应位置加配重,以配重为设计变量,实现以频率为目标的优化。
某盒段的优化算例证明,该方法不仅实现了固有频率相似,而且.实现了固有振型的相似,即很好的实现了与原结构的质量和刚度相似,同时提高的结构的效率,为机翼颤振模型的优化奠定了基础。
During the flight, aircraft flutter is always appearing, which can lead to the destruction To avoid the happening of the flutter, study should be done for the flutter characteristics of the plane. The wind tunnel test is a reliable method to verify vibration characteristics of the plane which is on the moving load. A lot of research examples show that the precision of test data is applied to the similarity of the model with the original structure. So how to design flutter model, including shape elastic, mass similarity and stiffness similarity, is a problem worth studying.
Research shows that topological optimization, size optimization and shape optimization is a effective method to solve the flutter model design. Because of the internal complexity of the wing structure, it is easy to make subtle structure for the design of flutter model. The subtle structure is bad for the manufacturing of flutter model. And because of bad elastic characteristics, the subtle structure can cause nonlinear problems. The mayor box is the main load-carrying structure of wing flutter model. The mass and stiffness similarity of the box is the base of resolving the similarity of wing flutter model. Combined with the topology optimization and size optimization, based on the shape similarity, a optimization method of box to achieve structural and elastic similarity is proposed. Work is as follows:
First, with APDL,the finite element model of the box framework is built. Then using flexibility as target and exits state of beams or ribs as design variables, optimization model of framework is established. Based on the analysis of sensitivity for the beam or rib with the objective, by using MATLAB software, modify program of the structure is made to conduct the structural optimization.
Second, when topology configuration of the framework is fixed on, the characteristic parameters of the beam are regarded as design variables and the structural optimization of the framework is conducted with different segmentations. The parameters of framework is modified in multi-island genetic algorithm method and sequential quadratic programming method. After optimization, the arithmetical compliment of the parameter is removed and the thickness of framework is adjusted at integer multiples of each layer thickness.
Third, the skin structure of the box is established on the framework structure, thus the optimization is developed as follows:the thickness of the skin is used as a design variable and the flexibility of the box is used as a design target. After optimization, the arithmetical compliment of the parameter is removed and the thickness of the skin is adjusted at integer multiples of each layer thickness.
At last, the counterweight is added on the corresponding place of the box for the similarity with the mass distribution of the real structure. The optimization is developed with frequency as a design target and counterweight as a design variable.
This optimization method is applied to a box model. Results show that the proposed approach is feasible to achieve given natural frequency and natural vibration. In other words, both of the mass and stiffness similarity with the real structure are ensured. Meanwhile the method improve the efficiency of the structure, so it provides a useful reference for the design of wing flutter models.
研究表明,拓扑优化、尺寸优化和形状优化技术是解决颤振模型设计的有效手段。机翼的内部结构复杂,采用缩比方法设计颤振模型时,由于模型与原结构的尺寸相差很大,往往出现微小结构,导致颤振模型的可制造性差。同时由于微小结构的弹性差,会引起非线性问题。主盒段是机翼颤振模型的主要承力结构,其质量和刚度的相似程度是解决机翼颤振模型相似性的基础。本文结合拓扑优化和尺寸优化,在外形相似的基础上,提出了实现质量和刚度相似的盒段优化方法,主要工作如下：
首先,利用APDL语言构建主盒段骨架有限元模型,以柔度为结构的设计目标,以梁或者肋存在状态为设计变量,建立骨架的优化模型。基于梁或者肋对目标函数的灵敏度分析,再运用MATLAB软件,从而编写了结构的修改程序,实现骨架的拓扑优化；
其次,在骨架的拓扑构型确定的情况下,将骨架的特征参数优化分段进行,以每一段选取点的柔度为目标,以对应梁的特征参数为设计变量,采用ISIGHT软件中的多岛遗传算法和序列二次规划法,实现了骨架的参数修改,在每次分段优化结束后,将得到的参数值去余,调整厚度,对应为骨架材料每层厚度的整数倍；
再次,在骨架结构的基础上建立蒙皮结构,以盒段每一段的柔度为设计目标,对应段的蒙皮厚度为设计变量。在每次分段优化结束后,将得到的厚度值去余,调整厚度,对应为蒙皮材料每层厚度的整数倍；
最后,为了和真实结构的质量分布相似,在优化模型的相应位置加配重,以配重为设计变量,实现以频率为目标的优化。
某盒段的优化算例证明,该方法不仅实现了固有频率相似,而且.实现了固有振型的相似,即很好的实现了与原结构的质量和刚度相似,同时提高的结构的效率,为机翼颤振模型的优化奠定了基础。
During the flight, aircraft flutter is always appearing, which can lead to the destruction To avoid the happening of the flutter, study should be done for the flutter characteristics of the plane. The wind tunnel test is a reliable method to verify vibration characteristics of the plane which is on the moving load. A lot of research examples show that the precision of test data is applied to the similarity of the model with the original structure. So how to design flutter model, including shape elastic, mass similarity and stiffness similarity, is a problem worth studying.
Research shows that topological optimization, size optimization and shape optimization is a effective method to solve the flutter model design. Because of the internal complexity of the wing structure, it is easy to make subtle structure for the design of flutter model. The subtle structure is bad for the manufacturing of flutter model. And because of bad elastic characteristics, the subtle structure can cause nonlinear problems. The mayor box is the main load-carrying structure of wing flutter model. The mass and stiffness similarity of the box is the base of resolving the similarity of wing flutter model. Combined with the topology optimization and size optimization, based on the shape similarity, a optimization method of box to achieve structural and elastic similarity is proposed. Work is as follows:
First, with APDL,the finite element model of the box framework is built. Then using flexibility as target and exits state of beams or ribs as design variables, optimization model of framework is established. Based on the analysis of sensitivity for the beam or rib with the objective, by using MATLAB software, modify program of the structure is made to conduct the structural optimization.
Second, when topology configuration of the framework is fixed on, the characteristic parameters of the beam are regarded as design variables and the structural optimization of the framework is conducted with different segmentations. The parameters of framework is modified in multi-island genetic algorithm method and sequential quadratic programming method. After optimization, the arithmetical compliment of the parameter is removed and the thickness of framework is adjusted at integer multiples of each layer thickness.
Third, the skin structure of the box is established on the framework structure, thus the optimization is developed as follows:the thickness of the skin is used as a design variable and the flexibility of the box is used as a design target. After optimization, the arithmetical compliment of the parameter is removed and the thickness of the skin is adjusted at integer multiples of each layer thickness.
At last, the counterweight is added on the corresponding place of the box for the similarity with the mass distribution of the real structure. The optimization is developed with frequency as a design target and counterweight as a design variable.
This optimization method is applied to a box model. Results show that the proposed approach is feasible to achieve given natural frequency and natural vibration. In other words, both of the mass and stiffness similarity with the real structure are ensured. Meanwhile the method improve the efficiency of the structure, so it provides a useful reference for the design of wing flutter models.
引文
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[2]郭润江,王利京.颤振模型设计中的质量和刚度影响[J].飞机工程,2002,1：15-19.
[3]Cho J S, Chang Y H, Supersonic flutter analysis of wings using an unsteady 3D panel method [J]. Computers& Flu-ids,2001,30(3):237-256.
[4]AIAA. Development of reduced-order models for aeroelastic analysis and flutter prediction using the CFI.3D v6.0 code, A0228399 [R]. New York:AIAA,2002.
[5]Davenport, Alan G., Past. present and future of wind engineering. Journal of Wind Engineering and Industrial Aerodynamics,2002, Vol.90, No.12-15, pp1371-1380.
[6]AIAA. Weight reduction through optimal arrangement of force-carrying components within wing box structures. [R]. U.S.:AIAA,2004.
[7]邓扬晨,张卫红,章怡宁.基于分级优化的飞机翼面结构布局综合技术研究[J].强度与环境,2005,32(1)：27-36.
[8]杨乃宾,章怡宁.复合材料飞机结构设计[M].航空工业出版社,2002.
[9]Martin Carlsson. Aeroelastic model design using an integrated optimization approach[J]. Journal of Aircraft,2004,41 (6):152321526.
[10]刘成玉,王利京.T尾低速颤振模型设计[J].飞机工程,2005,2：18-21.
[11]李少华,杨智春,谷迎松.一种复合材料跨声速颤振模型的部分结构相似设计方法[J].机械强度,2009,31(2)：339-343.
[12]吕斌,刘德广,谢长川等.机翼低速风洞试验颤振模型优化设计方法[J].北京航空航天大学学报,2006,32(2)：163-166.
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