面向新一代运载火箭的网格加筋柱壳结构优化研究
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摘要
由于较高的比强度和比刚度,加筋柱壳结构已广泛应用于运载火箭中的燃料贮箱和级间段等部段。加筋柱壳的轻量化设计理论与方法是保证火箭运载能力不可回避的需求。本文首先提出了两种基于等效刚度模型和精细模型的加筋柱壳混合优化方法,然后发展了适合多变量加筋柱壳优化问题的高效优化方法,继而系统地研究了加筋柱壳的缺陷敏感性问题,发展了最不利多点扰动载荷搜索方法。此外,本文还提出了面向低缺陷敏感性的加筋柱壳设计理念,建立了两种低缺陷敏感层级加筋柱壳构型,并构造了计及缺陷敏感度的优化模型。最后将加筋柱壳的前期分析优化经验集成固化为基于ABAQUS的快速设计软件。
本文主要内容如下：
(1)研究了两种基于等效模型和精细模型的加筋柱壳混合优化方法。面向我国新一代运载火箭和未来重型运载火箭箭体设计,针对加筋柱壳后屈曲分析计算成本较大的现状,首先对于均匀轴压工况,提出了加筋柱壳尺寸布局两步优化方法。对于非均匀轴压工况,本文还提出了同一壁板结构参数相同、不同壁板结构参数不同的分区设计理念,进而发展了一种基于等效刚度模型和精细模型的代理模型混合优化方法。算例结果表明两种优化方法的优化效益显著。
(2)面向发射阶段承受非均匀分布轴压荷载的助推器液氧贮箱设计需求,提出了基于自适应抽样方法并考虑设计偏好的代理模型优化方法。通过变量分组和定义合适的变量敏感性指标,发展了一套能够考虑设计偏好的自适应抽样方法,可理性地缩减设计空间,从而大大提高优化效率。三维刚架算例结果表明：该方法能够极大提高计算效率,且优化结果十分接近全局最优解。助推器液氧贮箱算例证明：该方法能以更少的计算成本,获得更为优异的结构设计。
(3)针对火箭薄壁结构中具有高发概率的凹陷缺陷,提出了最不利多点扰动载荷搜索方法。首先研究了不同类型加筋柱壳对不同类型缺陷的敏感性,然后以单点凹陷为例系统地研究了凹陷方向和发生位置对结构屈曲临界载荷的影响规律,继而提出一种多点凹陷组合模型,用于考察凹陷间的交互作用及其对结构承载能力的影响。在这些研究成果基础上,进一步发展了最不利多点扰动载荷搜索方法,用以寻找限定缺陷幅度的最不利缺陷工况及其对应的结构轴压承载力下限,并为新一代运载火箭及未来重型运载火箭的薄壁结构设计提供改进的折减因子。
(4)提出了面向低缺陷敏感性的加筋柱壳设计理念,建立了两种低缺陷敏感层级加筋柱壳结构构型,并构建了计及缺陷敏感度的优化模型。针对提出的双曲母线加筋柱壳和双向多级加筋柱壳构型,深入地研究了其优异性能的力学本质。双曲母线加筋柱壳算例的数值分析结果表明：对于弹性屈曲加筋柱壳,外凸双曲母线既可提高完善结构轴压承载力,又可大大提高非完善加筋柱壳的承载性能；对于塑性屈曲加筋柱壳,内凹双曲母线可小幅提高完善结构承载力,但外凸双曲母线则可大大提高非完善加筋柱壳的承载性能,表现为结构对整体型和局部型缺陷的低敏感性。双向多级加筋柱壳算例的数值分析结果表明：此类结构可将缺陷引发的初始局部出平面变形尽量限制在主筋格栅中,减缓了其向整体失稳模式的演化,降低了对初始几何缺陷的敏感性。基于这两种新型加筋柱壳结构构型,本文构建了计及缺陷敏感度的加筋柱壳优化模型,并完成数值算例验证。
(5)开发了完美(善)与非完美(善)加筋柱壳强度稳定性分析软件,以及基于ABAQUS的有限元模型质量检查软件等4个辅助设计软件,形成了一系列能够体现后续优化设计意图、实现整箭整弹的积木式模块化建模的专用模板,为弹箭体结构设计提供了更加方便快捷的设计工具。上述软件已应用于我国运载火箭及导弹型号的一线研发中。
本博士论文得到大连理工大学优秀博士学位论文特别资助基金、973项目青年科学家专题“计及缺陷敏感性的网格加筋筒壳结构轻量化设计理论与方法”(批准号：2014CB049000,2014-2019年)、国家自然科学基金重大研究计划重点基金项目“面向近空间飞行器多功能超轻质结构设计优化理论”(批准号：90816025,2009-2012年)、总装预研重点项目“航天箭体结构优化减重设计的关键技术”(批准号：625010345,2011-2014年)、中央高校基本科研业务费重点资助项目“X体典型筒壳结构轻量化设计方法与应用”(批准号：DUT11ZD (G)04,2011-2012年)及多项国防课题的资助,在此一并表示感谢。
Due to high specific strength and stiffness, stiffened shells have been widely used in the fuel tanks and interstages of launch vehicles. Lightweight design methodology of stiffened shells becomes unavoidable to guarantee the carrying capacity of launch vehicles. Firstly, two hybrid optimization methods based on equivalent stiffness model and exact model were proposed. Then, another efficient optimization method was developed for multi-variable optimization of stiffened shells. Subsequently, imperfection sensitivity of stiffened shells was investigated systematically, and Worst Multiple Perturbation Loads Approach (WMPLA) was studied. Futhermore, two concepts of hierarchical stiffened shells with low imperfection sensitivity were proposed, together with the corresponding optimization formulations considering imperfection sensitivity. Finally, several rapid design softwares based on ABAQUS were developed, taking the previous analysis and optimization experiences into account.
The main works of this dissertation are given as follows:
(1) Two hybrid optimization methods based on equivalent model and exact model were investigated. With regard to China's new generation and future heavy-lift launch vehicles, due to the high computational cost of post-buckling analysis for stiffened shells, a bi-step size-layout optimization framework was presented for uniform axial compression, while a concept of partition design was utilized for non-uniform axial compression, and then a surrogate-based hybrid optimization framework was further developed. Results indicated that the optimization benefits of these two methods were significant.
(2) Motivated by the design requirement of liquid oxygen tanks in the boosters of launch vehicles under non-uniform axial compression during ascent, a surrogate-based optimization framework with adaptive sampling allowing for user's preference was proposed. Based on variable category and various sensitivity indices, an adaptive sampling method allowing for user's preference was further developed, by which design space could be reduced rationally, and thus optimization efficiency was improved. Results of a three-dimensional rigid frame showed that the optimization efficiency was improved significantly, and the optimum result was proved to be potentially close to the global optimum. Results of a liquid oxygen tank model indicated that a more superior design could be achieved with less computation cost.
(3) Based on dimple-shape imperfections, which probably occurs in thin-walled structures of launch vehicles, WMPLA was proposed. Firstly, the sensitivities to imperfections with various forms were studied in detail for various types of stiffened shells. Then the influence of a single dimple-shape imperfection on the load-carrying capacity of cylindrical shells was investigated by varying the amplitudes, directions and positions of imperfections. Further, a combined dimpe-shape imperfection was developed to investigate the interaction of dimples and the reduction of the load-carrying capacity. Finally, WMPLA was presented to find the worst imperfection and lower bound of load-carrying capacity, aiming at providing a reference for improving knockdown factors of thin-walled structures in China's new generation and future heavy-lift launch vehicles.
(4) The concept of stiffened shells for low imperfection sensitivity was put forward, and two configurations of hierarchical stiffened shells with low imperfection sensitivity were proposed herein. Further, two optimization formulations considering imperfection sensitivity were also developed. For stiffened shells with hyperbolic generatrix shape and bi-directional hierarchical stiffened shells, and the mechanical essences of their low imperfection sensitivities were studied. Numerical results showed that the outward hyperbolic generatrix shape could improve the load-carrying capacities of both perfect and imperfect elastic-buckling stiffened shells, while for the plastic-buckling stiffened shell, the inward hyperbolic generatrix shape could increase the collapse loads of perfect structures in a small amplitude, and the outward hyperbolic generatrix shape could improve the load-carrying capacities of imperfect structures significantly, reflected as the low sensitivity to global-and local-pattern imperfections. Numerical results also indicated that the existence of major stiffeners in hierarchical stiffened shell had the ability to restrict the development of the initial out-of-plane deformation, thus the evolution to the global-pattern deformation was slowed down, and the imperfection sensitivity was further decreased. Furthermore, two optimization formulations considering imperfection sensitivity were proposed to search for the hierarchical optimum design. Finally, the effectiveness of the proposed optimization formulations was validated.
(5) Strength and stability analyses software of perfect and imperfect stiffened shells was developed, together with another four design-aided softwares, including quality verification software of FEM model based on ABAQUS, etc., which formed a series of modular softwares for the modeling of whole launch vehicle and missile, and also provided a convenient design tool for structural designs of launch vehicle and missile. The above softwares have been successfully utilized in the developments of new launch vehicles and missiles in China.
The research of this dissertation was supported by the Excellent Doctoral Dissertation Sustentation Fund of Dalian University of Technology, the973program (2014CB049000,2014-2019), the National Natural Science Foundation of China (90816025,2009-2012), the Advanced Research Project of Equipment Department (625010345,2011-2014), the Fundamental Research Funds for the Central Universities (DUT11ZD(G)04,2011-2012) and several national defense projects. The financial contributions are gratefully acknowledged.
本文主要内容如下：
(1)研究了两种基于等效模型和精细模型的加筋柱壳混合优化方法。面向我国新一代运载火箭和未来重型运载火箭箭体设计,针对加筋柱壳后屈曲分析计算成本较大的现状,首先对于均匀轴压工况,提出了加筋柱壳尺寸布局两步优化方法。对于非均匀轴压工况,本文还提出了同一壁板结构参数相同、不同壁板结构参数不同的分区设计理念,进而发展了一种基于等效刚度模型和精细模型的代理模型混合优化方法。算例结果表明两种优化方法的优化效益显著。
(2)面向发射阶段承受非均匀分布轴压荷载的助推器液氧贮箱设计需求,提出了基于自适应抽样方法并考虑设计偏好的代理模型优化方法。通过变量分组和定义合适的变量敏感性指标,发展了一套能够考虑设计偏好的自适应抽样方法,可理性地缩减设计空间,从而大大提高优化效率。三维刚架算例结果表明：该方法能够极大提高计算效率,且优化结果十分接近全局最优解。助推器液氧贮箱算例证明：该方法能以更少的计算成本,获得更为优异的结构设计。
(3)针对火箭薄壁结构中具有高发概率的凹陷缺陷,提出了最不利多点扰动载荷搜索方法。首先研究了不同类型加筋柱壳对不同类型缺陷的敏感性,然后以单点凹陷为例系统地研究了凹陷方向和发生位置对结构屈曲临界载荷的影响规律,继而提出一种多点凹陷组合模型,用于考察凹陷间的交互作用及其对结构承载能力的影响。在这些研究成果基础上,进一步发展了最不利多点扰动载荷搜索方法,用以寻找限定缺陷幅度的最不利缺陷工况及其对应的结构轴压承载力下限,并为新一代运载火箭及未来重型运载火箭的薄壁结构设计提供改进的折减因子。
(4)提出了面向低缺陷敏感性的加筋柱壳设计理念,建立了两种低缺陷敏感层级加筋柱壳结构构型,并构建了计及缺陷敏感度的优化模型。针对提出的双曲母线加筋柱壳和双向多级加筋柱壳构型,深入地研究了其优异性能的力学本质。双曲母线加筋柱壳算例的数值分析结果表明：对于弹性屈曲加筋柱壳,外凸双曲母线既可提高完善结构轴压承载力,又可大大提高非完善加筋柱壳的承载性能；对于塑性屈曲加筋柱壳,内凹双曲母线可小幅提高完善结构承载力,但外凸双曲母线则可大大提高非完善加筋柱壳的承载性能,表现为结构对整体型和局部型缺陷的低敏感性。双向多级加筋柱壳算例的数值分析结果表明：此类结构可将缺陷引发的初始局部出平面变形尽量限制在主筋格栅中,减缓了其向整体失稳模式的演化,降低了对初始几何缺陷的敏感性。基于这两种新型加筋柱壳结构构型,本文构建了计及缺陷敏感度的加筋柱壳优化模型,并完成数值算例验证。
(5)开发了完美(善)与非完美(善)加筋柱壳强度稳定性分析软件,以及基于ABAQUS的有限元模型质量检查软件等4个辅助设计软件,形成了一系列能够体现后续优化设计意图、实现整箭整弹的积木式模块化建模的专用模板,为弹箭体结构设计提供了更加方便快捷的设计工具。上述软件已应用于我国运载火箭及导弹型号的一线研发中。
本博士论文得到大连理工大学优秀博士学位论文特别资助基金、973项目青年科学家专题“计及缺陷敏感性的网格加筋筒壳结构轻量化设计理论与方法”(批准号：2014CB049000,2014-2019年)、国家自然科学基金重大研究计划重点基金项目“面向近空间飞行器多功能超轻质结构设计优化理论”(批准号：90816025,2009-2012年)、总装预研重点项目“航天箭体结构优化减重设计的关键技术”(批准号：625010345,2011-2014年)、中央高校基本科研业务费重点资助项目“X体典型筒壳结构轻量化设计方法与应用”(批准号：DUT11ZD (G)04,2011-2012年)及多项国防课题的资助,在此一并表示感谢。
Due to high specific strength and stiffness, stiffened shells have been widely used in the fuel tanks and interstages of launch vehicles. Lightweight design methodology of stiffened shells becomes unavoidable to guarantee the carrying capacity of launch vehicles. Firstly, two hybrid optimization methods based on equivalent stiffness model and exact model were proposed. Then, another efficient optimization method was developed for multi-variable optimization of stiffened shells. Subsequently, imperfection sensitivity of stiffened shells was investigated systematically, and Worst Multiple Perturbation Loads Approach (WMPLA) was studied. Futhermore, two concepts of hierarchical stiffened shells with low imperfection sensitivity were proposed, together with the corresponding optimization formulations considering imperfection sensitivity. Finally, several rapid design softwares based on ABAQUS were developed, taking the previous analysis and optimization experiences into account.
The main works of this dissertation are given as follows:
(1) Two hybrid optimization methods based on equivalent model and exact model were investigated. With regard to China's new generation and future heavy-lift launch vehicles, due to the high computational cost of post-buckling analysis for stiffened shells, a bi-step size-layout optimization framework was presented for uniform axial compression, while a concept of partition design was utilized for non-uniform axial compression, and then a surrogate-based hybrid optimization framework was further developed. Results indicated that the optimization benefits of these two methods were significant.
(2) Motivated by the design requirement of liquid oxygen tanks in the boosters of launch vehicles under non-uniform axial compression during ascent, a surrogate-based optimization framework with adaptive sampling allowing for user's preference was proposed. Based on variable category and various sensitivity indices, an adaptive sampling method allowing for user's preference was further developed, by which design space could be reduced rationally, and thus optimization efficiency was improved. Results of a three-dimensional rigid frame showed that the optimization efficiency was improved significantly, and the optimum result was proved to be potentially close to the global optimum. Results of a liquid oxygen tank model indicated that a more superior design could be achieved with less computation cost.
(3) Based on dimple-shape imperfections, which probably occurs in thin-walled structures of launch vehicles, WMPLA was proposed. Firstly, the sensitivities to imperfections with various forms were studied in detail for various types of stiffened shells. Then the influence of a single dimple-shape imperfection on the load-carrying capacity of cylindrical shells was investigated by varying the amplitudes, directions and positions of imperfections. Further, a combined dimpe-shape imperfection was developed to investigate the interaction of dimples and the reduction of the load-carrying capacity. Finally, WMPLA was presented to find the worst imperfection and lower bound of load-carrying capacity, aiming at providing a reference for improving knockdown factors of thin-walled structures in China's new generation and future heavy-lift launch vehicles.
(4) The concept of stiffened shells for low imperfection sensitivity was put forward, and two configurations of hierarchical stiffened shells with low imperfection sensitivity were proposed herein. Further, two optimization formulations considering imperfection sensitivity were also developed. For stiffened shells with hyperbolic generatrix shape and bi-directional hierarchical stiffened shells, and the mechanical essences of their low imperfection sensitivities were studied. Numerical results showed that the outward hyperbolic generatrix shape could improve the load-carrying capacities of both perfect and imperfect elastic-buckling stiffened shells, while for the plastic-buckling stiffened shell, the inward hyperbolic generatrix shape could increase the collapse loads of perfect structures in a small amplitude, and the outward hyperbolic generatrix shape could improve the load-carrying capacities of imperfect structures significantly, reflected as the low sensitivity to global-and local-pattern imperfections. Numerical results also indicated that the existence of major stiffeners in hierarchical stiffened shell had the ability to restrict the development of the initial out-of-plane deformation, thus the evolution to the global-pattern deformation was slowed down, and the imperfection sensitivity was further decreased. Furthermore, two optimization formulations considering imperfection sensitivity were proposed to search for the hierarchical optimum design. Finally, the effectiveness of the proposed optimization formulations was validated.
(5) Strength and stability analyses software of perfect and imperfect stiffened shells was developed, together with another four design-aided softwares, including quality verification software of FEM model based on ABAQUS, etc., which formed a series of modular softwares for the modeling of whole launch vehicle and missile, and also provided a convenient design tool for structural designs of launch vehicle and missile. The above softwares have been successfully utilized in the developments of new launch vehicles and missiles in China.
The research of this dissertation was supported by the Excellent Doctoral Dissertation Sustentation Fund of Dalian University of Technology, the973program (2014CB049000,2014-2019), the National Natural Science Foundation of China (90816025,2009-2012), the Advanced Research Project of Equipment Department (625010345,2011-2014), the Fundamental Research Funds for the Central Universities (DUT11ZD(G)04,2011-2012) and several national defense projects. The financial contributions are gratefully acknowledged.
引文
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