基于近似模型辅助智能算法的变截面点阵结构优化设计方法  

An optimization design method of variable cross-section lattice structures based on anapproximate model-assisted intelligent algorithm

作　　者：向艳 蒋国璋 张严[1,2,3] 徐曼曼 XIANG Yan;JIANG Guozhang;ZHANG Yan;XU Manman(Key Laboratory of Metallurgical Equipment and Control,Technology of Ministry of Education,Wuhan University of Science and Technology,Wuhan 430081,China;Key Laboratory of Mechanical Transmission and Manufacturing Engineering of Hubei Province,Wuhan University of Science and Technology,Wuhan 430081,China;Precision Manufacturing Institute,Wuhan University of Science and Technology,Wuhan 430081,China)

机构地区：[1]武汉科技大学冶金装备及其控制教育部重点实验室,武汉430081 [2]武汉科技大学机械传动与制造工程湖北省重点实验室,武汉430081 [3]武汉科技大学精密制造研究院,武汉430081

出　　处：《振动与冲击》2023年第16期181-188,208,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(52205280);中国博士后科学基金(2021M692486);数字制造装备与技术国家重点实验室开放基金(DMETKF2022017);武汉科技大学冶金装备及其控制教育部重点实验室开放基金。

摘　　要：桁架类点阵结构具有质量轻、比强度/比刚度高、减振吸能性好,且拓扑构型简单、增材成型可靠性高等优点,被广泛应用于航天器各关键承载部件设计。传统桁架类点阵设计大多囿于等截面设计约束,严重制约了优化设计的寻优潜能,难以满足航天器结构超轻质、高强度的性能要求。为突破传统点阵的等截面形状约束,构建基于显式拓扑描述函数的变截面几何描述模型,实现变截面点阵几何形状的自由描述;采用能量均匀化方法精确计算变截面点阵单胞宏观等效弹性张量,并建立变截面点阵几何描述参数关于其宏观等效弹性张量的近似响应模型;以变截面点阵的几何描述参数为设计变量,材料用量为约束条件,最大体积模量或最大剪切模量为目标函数,建立变截面点阵几何描述参数的优化数学模型,并采用基于近似模型辅助的粒子群优化算法实现上述优化模型的高效求解。数值算例表明,相较于等截面点阵,在相同材料用量下,优化后的变截面点阵的体积模量和剪切模量性能更优。所提方法进一步拓展了桁架类点阵的设计空间,有效提升其力学性能,在航天器结构轻量化设计方面具有应用推广前景。Truss lattice structures have the advantages of light weight,high specific strength/specific stiffness,good vibration and energy absorption,as well as simple topological configuration,high reliability of additive manufacturing,which have been widely used in the design of key load-bearing components of spacecrafts.The traditional truss lattice design is mostly limited by the constraint of constant cross-section,and the potential of optimization design method is also seriously restricted,which makes it difficult to meet the performance requirements of super light and high strength of spacecraft structures.In order to break through the constraint of constant cross-section shape of traditional lattice,a geometric description model of variable cross-section based on explicit topological description function was constructed to realize the free description of geometric shape of variable cross-section lattice.The macroscopic equivalent elastic tensor of the variable cross-section lattice unit cell was accurately calculated by using an energy-based homogenization method,and the approximate response model of geometric description parameters of the variable cross-section lattice about its macroscopic equivalent elastic tensor was established.Taking the geometric description parameters of variable cross-section lattice as design variables,material consumption as constraint conditions,and maximum bulk modulus or maximum shear modulus as objective functions,an optimization mathematical model of geometric description parameters of variable cross-section lattice is established,and the particle swarm optimization algorithm assisted by approximate model was adopted to realize the efficient solution of the above optimization model.Numerical examples show that compared with the lattice with constant cross-section,the optimized lattice with variable cross-section has better bulk modulus and shear modulus under the same material usage.The proposed method further expands the design space of truss lattice,and effectively improves its me

关 键 词：点阵结构 变截面 显式拓扑描述 能量均匀化 粒子群优化算法 

分 类 号：TB12[理学—工程力学]