【作者】 王强；

【导师】 刘湃； 罗阳军；

【作者基本信息】 大连理工大学 ， 航空宇航科学与技术， 2023， 硕士

【摘要】 在航空航天结构的服役过程中,惯性载荷的作用十分普遍,例如飞行器加速飞行时的推力。针对航空航天等领域的承载结构及关键部件,采用拓扑优化方法对惯性载荷作用下结构的拓扑构型进行设计,能够有效提升结构设计的刚度等力学性能。同时,多材料结构因能够充分发挥各材料的性能优势,已被广泛应用于航空航天、汽车工程等领域。针对惯性载荷作用下的多材料结构,采用拓扑优化方法对其拓扑构型和材料分布进行优化设计,获得满足性能要求的概念设计,对提高拓扑优化引导的航空航天多材料结构设计水平具有重要意义。本文基于上述背景,主要进行了如下工作:(1)针对惯性载荷作用下的连续体结构拓扑优化问题,采用材料场级数展开(Material-Field Series-Expansion,MFSE)拓扑优化方法描述结构拓扑,通过考虑材料场函数的空间相关性显著降低拓扑优化问题的设计变量数目,并提供清晰的结构边界描述。进一步,将材料场函数值映射为各单元的材料用量,通过分别采用有理近似模型(Rational Approximation Material Properties,RAMP)与线性模型表征单元的弹性模量与惯性载荷对材料用量的依赖关系,消除拓扑相关惯性载荷优化问题中结构灰度区域的寄生效应(parasitic effects)数值问题。利用MFSE方法中拓扑表征与有限元分析网格相互独立的特性,针对三维设计问题采用了动态全局网格加密方案提高优化求解效率。基于伴随变量法推导了MFSE方法框架下的惯性载荷结构拓扑优化问题的灵敏度信息,并采用数学规划算法求解拓扑优化问题。数值算例研究了考虑自重载荷的二维及三维结构拓扑优化问题,讨论了集中力与拓扑相关自重载荷共同作用下结构拓扑设计规律。数值算例显示本文所提出的设计方法显著降低了设计变量的数目,有效避免了惯性载荷下结构拓扑优化中的寄生效应,并获得了与已有文献相接近的设计性能。(2)针对惯性载荷作用下的多材料结构拓扑优化问题,建立了基于多个材料场表征的多材料拓扑描述及力学性能插值模型,并开展了多材料结构的拓扑优化设计。具体来说,该方法首先采用一个材料场函数表征结构的拓扑(即区分孔洞区与材料区),并额外引入多个材料场函数用于表征结构材料区内的多材料布局。进而,将拓扑表征材料场映射为各有限单元的拓扑描述变量,并基于有理近似模型(RAMP)对多材料结构的孔洞区及材料区的材料用量进行插值。进一步,将描述多材料的场函数映射为各单元的材料用量,结合多材料的实体各向同性材料惩罚法(Solid Isotropic Material with Penalization,SIMP)与上述RAMP插值模型对材料区内各材料的力学性能进行插值。综上,该多材料场函数表征与插值模型能够有效地避免考虑拓扑相关载荷的多材料拓扑设计中的寄生效应,同时能够显著降低多材料结构拓扑优化中设计变量的数目。数值算例研究了含双材料及三材料的二维及三维多材料结构拓扑优化问题,讨论了多材料的刚度与密度对优化结果的影响规律。数值算例显示本文建立的多材料插值模型有效避免了寄生效应,并获得了清晰的多材料设计布局。更多还原

【Abstract】 In the service process of aerospace structures,the role of inertial loads is very common,such as the thrust of accelerated flight of aircraft.For the load-bearing structures and key components in aerospace and other fields,topology optimization methods are used to design the topological configuration of structures under inertial loads,which can effectively improve the mechanical properties of structural design such as stiffness.At the same time,multi-material structures have been widely used in aerospace and automotive engineering fields because they can fully utilize the performance advantages of each material.The topology optimization method is used to optimize the topological configuration and material distribution of multi-material structures under inertial loads to obtain a conceptual design that meets the performance requirements,which is important to improve the design of aerospace multi-material structures guided by topology optimization.In this paper,based on the above background,the following work is carried out:(1)For the topology optimization of continuum structures under inertial load,the material-field series-expansion(MFSE)topology optimization method is used to describe the topology of the structure,which significantly reduces the number of design variables in the topology optimization problem by considering the spatial correlation of the material-field functions and provides a clear description of the structural boundaries.Further,the material field function values are mapped to the material usage of each element,and the numerical problem of parasitic effects in the gray area of the structure in the topology-dependent inertia load optimization problem is eliminated by using the rational approximation material properties(RAMP)and linear model to characterize the dependence of Elastic modulus of the element and inertia load on the material usage,respectively.The topological representation and FEA mesh are independent of each other in the MFSE method,and a dynamic global mesh encryption scheme is adopted to improve the efficiency of the optimization solution for the Three-dimensional design problem.The sensitivity information of the topology optimization problem of inertial load structure in the framework of MFSE method is derived based on the adjoint-variable method,and the topology optimization problem is solved by mathematical programming algorithm.Numerical cases investigate the optimization of two-dimensional and three-dimensional structural topology considering self-weight loads,and discuss the structural topology design law under the combined effect of concentrated force and topologically related self-weight loads.The numerical cases show that the proposed design method significantly reduces the number of design variables,effectively avoids parasitic effects in structural topology optimization under inertial loads,and achieves design performance comparable to that of the existing literature.(2)For the topology optimization of the multi-material structure under inertial load,a multi-material topology description and mechanical property interpolation model based on multiple material-field characterization is developed,and the topology optimization design of the multi-material structure is carried out.Specifically,the method first uses one material field function to characterize the topology of the structure(i.e.,to distinguish the void area from the solid area),and introduces multiple additional material field functions to characterize the multi-material layout within the solid area of the structure.Further,the topologically characterized material fields are mapped to the topological descriptive variables of each finite element,and the material amounts in the void and solid area of the multi-material structure are interpolated based on the rational approximation material properties(RAMP).Further,the field function describing the multi-material is mapped to the material usage of each element,and the mechanical properties of each material within the solid area are interpolated by combining the Solid Isotropic Material with Penalization(SIMP)method for multi-materials with the RAMP interpolation model described above.In summary,the multi-material field function characterization and interpolation model can effectively avoid parasitic effects in the design of multi-material topologies considering topology-related loads,and can significantly reduce the number of design variables in the topology optimization of multi-material structures.Numerical examples are presented to study the optimization of two-and three-dimensional multi-material topologies with two solid materials and three solid materials,and the influence of the stiffness and density of the multi-materials on the optimization results is discussed.The numerical examples show that the multi-material interpolation model established in this paper effectively avoids parasitic effects and obtains a clear multi-material design layout.更多还原