【作者】 安晓敏；

【导师】 刘书田；

【作者基本信息】 大连理工大学 ， 工程力学， 2005， 硕士

【摘要】 现代工业、国防科技的迅猛发展,对产品结构提出了越来越高的要求。设计者希望运用更理性的手段设计新产品,这仅仅依靠设计者的经验远远不够。因此作为一种概念性设计手段,拓扑优化将起着越来越重要的作用。在航空航天领域,机翼常作为梁结构,其外形轮廓根据气动弹性剪裁设计确定,在结构设计阶段一般不作变动。因此为了减轻结构重量而进行的优化只能在机翼内部进行,其中很重要的一部分优化设计是机翼横截面内部加筋肋的确定。目前,有关梁的横截面拓扑优化设计的相关工作还不多见,但是这种设计思想对确定横截面上加筋肋方位十分有利,因此本文主要对这一问题进行了较详细地探讨和研究。具体工作如下: 1.简要综述了拓扑优化的发展现状,较详细地介绍了本文所应用的拓扑优化方法:拓扑优化的均匀化方法和密度惩罚法; 2.由于经典的Euler-Bernouilli梁理论和Timoshenko梁理论均假设梁截面在变形过程中保持为平面,不考虑截面的翘曲,这种假设不能满足工程实际的需要,因此本文引入并详细介绍了一种考虑翘曲变形的梁理论; 3.以梁的平均柔顺性最小化为目标函数,材料用量为约束条件建立了梁截面拓扑优化模型,编制程序实现了梁截面的拓扑优化技术,并通过典型算例验证了程序的可靠性; 4.进行了典型梁横截面的拓扑优化设计,并通过计算出平面翘曲位移的具体数值验证了:同等条件下,本文所得到的双工字梁截面比工程中常用的单工字梁截面翘曲程度小:并用ANSYS软件进行了进一步的验证。 5.实现了多工况下梁截面的拓扑优化设计,并且验证了结果的正确性。 6.针对典型问题的设计结果,比较了本文方法与为数不多的文献中提供的方法。发现本文的优化模型比文献(Yoon Young Kim, Tae Soo Kim. Topology optimization of beam cross sections. Int. J. Solids and Structures. 37(2000):477-493)中给出的模型具有更大的实用性。原因在于本文的优化方法能够将截面的所有刚度参数(剪切刚度,拉压刚度、弯曲刚度、扭转刚度)考虑在内,而文献则只考虑了弯曲刚度和扭转刚度; 7.对典型的飞机机翼横截面进行了拓扑优化设计,证明本文的方法能够有效地寻找到机翼剖面内加筋肋的方位。考虑翘曲变形的梁截面拓扑优化设计本文工作得到国家自然科学基金重点项目(编号:1 0332010)、重大研究计划项目(编号:90205029)以及教育部“新世纪优秀人才”培养计划(2 004)的资助。关键词:拓扑优化;梁;横截面;翘曲变形;柔顺性更多还原

【Abstract】 At present, the designers wish to utilize more rational methods to design the industrial, aeronautic and astronautic structures, so the designers’ experience is not enough. As a kind of rational conceptual designing method, the topology optimization technique is important more and more. Especially in the aeronautic and astronautic field, there is a sort of structure such as the airplane’s wing and the helicopter’s rotor blade, in the design of these structures, one of the important problems is to find the location and direction of stiffeners, because the external profile (the shape and dimension) of the cross section usually can not be modified due to the aeroelastic design requirement, only stiffening inside the beam’s cross section is allowed to modify. But now, topology optimization of beam cross sections is rarely found in literatures. Therefore, this paper focuses on this research work, including:1. Introduce the development about the topology optimization technique in short, and expatiate the method utilized in this paper: topology optimization based on Homogenization Method and SIMP (Solid Isotropic Material Penalization).2. Because of the shortcoming of the classical Euler-Bernouilli beam theory and Timoshenko beam theory which assume the cross section keeping plane during deforming and doesn’t consider the warping deformation, this paper introduce a beam theory which considers the cross-section’s warping deformation.3. The model of the topology optimization is presented: to minimize the average compliance is taken as the objective function, and the constraint is the material volume constraint. And the program is developed to realize the topology optimization technique.4. Several typical examples validate the program, and the warping displacement indicates that the II cross section has less warping deformation than the I cross section. And then, the software ANSYS is utilized to validate this paper’s results.5. Topology optimization design of beam cross section under multiple loading conditions is realized, and the validity of the results is confirmed in details.6. An example in past article (Yoon Young Kim, Tae Soo Kim. Topology optimization of beam cross sections. Int. J. Solids and Structures. 37 (2000):477-493) is repeatedusing the technique of this paper, and better results are obtained. This paper concludes that our optimization technique is more applicable than the past article. 7. Topology optimization technique of this paper can find the location and direction of stiffeners in the cross section, and an airfoil designing is realized.This research was supported by the Major Research Plan (90205029) and the Major Program (10332010) of the National Nature Science Foundation of China, the Excellent Young Teacher’s Program of MOE of China (2004). The financial supports are gratefully acknowledged.更多还原