【作者】 刘磊；

【导师】 刘书田； 殷德政；

【作者基本信息】 大连理工大学 ， 机械， 2024， 硕士

【摘要】 薄壁结构因其具有重量轻,承载效率高等优点被广泛应用于运载火箭、宇宙飞船、深海潜艇等高端工业装备中,但其稳定性较差,易产生大变形的缺陷限制着其在工程领域中性能的发挥。在薄壁结构上布置加筋已成为改善其结构性能所应用的最为普遍的一种方式。现有的薄壁结构的加筋优化设计,主要从确定加筋的布置位置、数量、形状与尺寸参数三个方面入手,对平面薄壁结构进行性能提升设计。然而针对曲面薄壁结构加筋优化设计的研究工作相对较少,并且现有工作大多只对上述三个方面中的某一方面进行优化,极大限制了寻求最优设计的可能。此外,曲面薄壁结构中既有规则曲面又包含复杂曲面,在考虑薄壁结构形式多样性前提下,能够对加筋布局和尺寸要素进行协同优化设计的拓扑优化方法的亟需进一步研究。在此背景下,本文基于变密度法拓扑优化方法,开展了从平面薄壁结构到简单曲面薄壁结构再到复杂曲面薄壁结构的加筋优化设计工作,实现了多种形式的薄壁结构加筋布局与加筋高度的协同优化设计。详细的内容和成果如下:1)平面薄壁结构加筋布局与高度协同优化方法。以一种基于Heaviside函数的定向生长拓扑描述参数化方法为基础,在变密度法的框架下实现了平面薄壁结构上加筋布局与加筋高度的协同拓扑优化。所提方法引入了两个设计变量分别描述加筋的有无和加筋的高度,以结构柔顺性为目标建立了优化问题的列式,并推导了目标函数对两个设计变量的灵敏度。通过两个数值算例验证了所提方法对于多种载荷形式下平面薄壁结构加筋布局与高度协同优化设计的有效性,得到了具有合理布局且高度可变的全新加筋形式。2)规则曲面薄壁结构加筋布局与高度协同优化方法。通过规则曲面的参数化表达式建立起参数空间和物理空间的映射关系,基于参数平面与曲面之间的一一映射关系,简述了两个空间内有限元模型的构建方法,将曲面上加筋的优化问题转化为平面上的优化问题,在平面薄壁结构加筋布局与高度协同拓扑优化方法基础上,实现这类规则曲面薄壁结构上加筋的优化设计。通过圆柱和圆锥曲面两类规则曲面对所提方法进行了验证,得到了规则曲面薄壁结构上具有合理布局且高度可变的加筋形式。3)复杂曲面薄壁结构加筋布局与高度协同优化方法。通过获取已知复杂曲面控制点,使用MATLAB对NURBS复杂曲面进行精确表达并建立复杂曲面薄壁结构有限元模型,根据NURBS的空间映射关系将物理空间曲面上的优化问题转化为参数平面上的优化问题,优化所得的结构再通过映射关系转换到曲面结构上,实现了复杂曲面薄壁结构上加筋布局与高度的协同优化设计。最后以马鞍型复杂曲面为例验证了本章所提方法的有效性,得到了具有可变高度和清晰布局的加筋形式。更多还原

【Abstract】 Thin-walled structure is widely used in high-end industrial equipment such as carrier rocket,spacecraft and deep-sea submarine due to its advantages of light weight and high bearing efficiency,but its poor stability and easy to produce large deformation limit its performance in the engineering.The placement of reinforcement on thin-walled structures has become the most common way to improve their structural properties.The existing reinforcement optimization design on thin-walled structures mainly starts from the three aspects of determining the stiffener layout position,quantity,shape and size parameters,and carries on the performance improvement design of the flat thin-walled structure.However,there are relatively few researches on the reinforcement optimization design of general curved thin-wall structure,and most of the existing works only optimize one of the above three aspects,which greatly limits the possibility of seeking the optimal design.In addition,curved surface thin-walled structures contain both regular surfaces and complex surfaces.Considering the diversity of thin-walled structures,topological optimization methods that can co-optimize the design of reinforcement layout and size elements need to be further studied.Against this background,this dissertation carried out the stiffener optimization design from flat thin-walled structure to regular curved surface thin-walled structure and then to complex curved surface thin-walled structure basing on the topology optimization method of variable density method,and realized the concurrent optimization design of stiffener’s layout and heights on various forms of thin-walled structures.The detailed contents and achievements are as follows:1)Concurrent optimization method of stiffener’s layout and heights of flat thinwalled structure.On the basis of a parametric method of directional growth topology description based on the Heaviside function,the collaborative topology optimization of stiffener layout and heights on flat thin-wall structures is realized under the framework of SIMP.In the proposed method,two design variables are introduced to describe the presence or absence of reinforcement and the height of reinforcement respectively.The optimization problem is presented with the objective of structural compliance,and the sensitivity of the objective function is derived.Two numerical examples are given to verify the effectiveness of the proposed method for the ribs layout and heights cooperative optimization design of planar thinwalled structures under various load forms,and a new reinforcement form with a reasonable layout and heght field is obtained.2)Concurrent optimization method of stiffener’s layout and heights of regular cuved surface thin-walled structure.The mapping relationship between parametric space and physical space is established through the parametric expression of regular surface.Based on the one-to-one mapping relationship between parameter plane and curved surface,the construction method of finite element model in the two spaces is briefly described.The optimization problem of ribs on curved surface is transformed into an problem on plane.Based on the reinforcement layout and heights on flat thin-wall structure cooperative topology optimization method,the optimization design of this kind of regular curved surface thin-wall structure is realized.The proposed method is verified by two types of regular surfaces,cylindrical and conical,and the stiffening form of regular curved surface with reasonable layout and variable height on thinwall structure is obtained.3)Concurrent optimization method of stiffener’s layout and heights of complex cuved surface thin-walled structure.By obtaining the control points of known complex surfaces,MATLAB is used to accurately express the NURBS complex surfaces and establish the finite element model of the complex surfaces thin-walled structure.The optimization problem is transformed from the physical space curved-surface to the parameter plane according to the spatial mapping relationship of NURBS,and the optimized structure is then transformed into the curved surface structure through the mapping relationship.The concurrent optimization design of stiffener layout and heights on complex curved surface thin-wall structure is realized.Finally,a saddle surface is taken as an example to verify the effectiveness of the proposed method,and a stiffened structure with variable height and clear layout is obtained.更多还原