桁架结构拓扑优化的理论与应用研究

发布时间：2018-08-23 08:42

【摘要】：桁架结构具有自重轻、造价较低和施工简单等特点,在工程中得到广泛应用,其领域涉及工程机械,桥梁设计、施工支护、建筑结构以及水工渡槽、闸门支撑、输电网架等诸多方面,在工程建设中发挥着越来越重要的作用。以空间相机为例,目前国外的大中型空间光学相机主次镜间的结构多采用桁架式,其设计思想基于变构件受弯曲载荷为拉压载荷的结构优化设计原则,具有比刚度高、质量轻、适于长焦距光学系统布局等优点。此外,桁架结构还应用于飞机、卫星、空间站等航空航天结构设计中,具有广泛的应用领域。传统获取最优桁架布局的方法是利用连续体拓扑优化的类桁架结果近似,但是它存在着等效性不确定、尺寸参数未知等缺陷,而直接采用桁架拓扑优化则可有效避免这些问题。因此我们探寻将桁架拓扑优化方法应用于实际工程问题的有效途径。在此基础上,对经纬仪的关键部件结构进行桁架设计,即用桁架结构代替连续体结构,在保证其他性能不变的同时使总体结构重量最轻,以提供其量化设计方案。对此,论文主要进行了以下工作:构建任意形状设计区域的桁架基结构的研究:针对工程问题形状复杂、不规则的特点,扩展并完善了基于有限元网格构建桁架基结构的方法,通过结合图形碰撞检测技术,并利用离散逼近的思路,成功实现了包含任意数量凹形状的复杂设计区域的分级/满级连接基结构的构建。同时基于节点坐标差的途径,实现了重叠杆件快速、高效的查找。桁架基结构构建合理性的研究:根据力传递路径法,提出了通过求解设计区域在边界条件下的主应力迹线分布构建桁架节点的途径,可以得到包含更好拓扑结果的桁架基结构集合。其具有较少节点及杆件数量,并可优化得到与解析解十分接近的数值解。此外,通过结合分量载荷的叠加准则,成功地将此方法推广到多工况时的情况。大规模桁架塑性设计快速求解方法的研究:针对桁架满连接杆件数量大,计算耗时长的问题,对设计的传统加杆法进行改进完善。通过采用"从短到长"的逐级加杆的策略并限制迭代步增加杆数量的途径,降低了线性规划的规模及求解时间,同时降低了求解虚应变值时候选杆件的规模及内存分配。此外,通过结合主应力迹线法及合理的迭代终止条件,解决了传统加杆法中存在的"伪虚位移值"现象,使大规模桁架塑性设计的优化效率得到大幅度地提高。珩架弹性拓扑优化设计的研究:从半定规划入手,推导了桁架弹性设计中以最小重量为目标,柔顺度为约束的问题和以最大刚度为目标、体积为约束的问题的等效半定规划模型,从数值算例和理论推导两方面证明了二者拓扑优化结果的一致性。同时通过示例说明了桁架弹性设计和塑性设计在单、多工况下拓扑结果的差异性。光电经纬关键部件轻量化方案的研究:分析了光电经纬仪转台和四通的工作特点及与其他部件的连接关系,建立了合理的网格离散模型及桁架基结构,对其进行了桁架塑性与弹性拓扑优化。作为补充也进行了连续体拓扑优化。综合比较所得的各优化结果确立了桁架结构轻量化方案,然后对改进设计后的结构进行有限元分析验证,结果表明轻量化方案在满足各指标的同时大幅减轻了结构重量,实现了最初设计期望。
[Abstract]:Truss structure has the characteristics of light weight, low cost and simple construction. It has been widely used in engineering. Its fields include construction machinery, bridge design, construction support, building structure, aqueduct, gate support, transmission grid and so on. It is playing an increasingly important role in engineering construction. The main and secondary mirrors of large and medium-sized space optical cameras in foreign countries usually adopt truss structure. The design idea is based on the structural optimization design principle that the bending load is tension and compression load. The truss structure has the advantages of high specific stiffness, light weight and suitable for the layout of long focal length optical system. The traditional method to obtain the optimal truss layout is to use the approximate truss-like results of continuum topology optimization, but it has some shortcomings such as equivalence uncertainty, unknown size parameters and so on. The direct use of truss topology optimization can effectively avoid these problems. The truss topology optimization method is an effective way to apply to practical engineering problems. On this basis, the truss design of the key components of theodolite is carried out, that is, truss structure is used instead of continuum structure to ensure other performance unchanged while minimizing the overall structure weight to provide its quantitative design scheme. The following work: Research on the construction of truss foundation structure with arbitrary shape design area: In view of the complex and irregular shape of Engineering problems, the method of constructing truss foundation structure based on finite element mesh is extended and improved. By combining with graphic collision detection technology and using discrete approximation method, the method of containing arbitrary number of concave shapes is successfully realized. The construction of a hierarchical/full-level connection base structure for a complex design region with a shape is described. Based on the coordinate difference between nodes, the overlapping members can be found quickly and efficiently. In addition, by combining the superposition criterion of component loads, this method is successfully extended to the case of multi-load cases. Large-scale truss plastic design is fast. Research on the method of quick solution: Aiming at the problem of large number of truss full connecting rods and time-consuming calculation, the traditional method of adding rods is improved and perfected. In addition, by combining the principal stress trace method with the reasonable iterative termination conditions, the phenomenon of "pseudo-displacement" in the traditional method of adding bars is solved, which greatly improves the efficiency of plastic design of large-scale trusses. The equivalent semi-definite programming model of truss elastic design with minimum weight as the objective, flexibility as the constraint and maximum stiffness as the objective and volume as the constraint is deduced. The consistency of the two topological optimization results is proved by numerical examples and theoretical derivation. Research on the lightweight scheme of the key components of photoelectric theodolite: The working characteristics of the turntable and the four-way connection of the photoelectric theodolite and their connection with other components are analyzed. A reasonable mesh discrete model and truss base structure are established. The plastic and elastic topology optimization of the truss are carried out. As a supplement, continuum topology optimization is also carried out. The lightweight scheme of truss structure is established by comparing the results of optimization. Then the improved structure is verified by finite element analysis. The results show that the lightweight scheme not only meets the requirements, but also greatly reduces the weight of the structure and achieves the initial design expectations.
【学位授予单位】：中国科学院大学(中国科学院长春光学精密机械与物理研究所)
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TB21

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