飞机风挡鸟撞数值模拟研究进展

Research progress in numerical simulation of bird strike on aircraft windshields

摘要

风挡的抗鸟撞能力是飞机结构强度设计的重要评价指标。随着数值模拟方法的持续迭代与创新，当前该项技术已被广泛运用于飞机风挡的抗鸟撞设计。本文综述了近年来关于飞机风挡鸟撞数值模拟问题的研究成果，主要涵盖两大方向：一类是鸟体几何模型与力学行为、不同数值分析方法的优缺点与实际运用等鸟撞问题的共性研究；另一类是风挡材料的动态力学性能、高应变率条件下平板结构与全尺寸风挡的动态响应与失效模式等特性方面的研究。特别是，本文基于积木式方法的理念，从材料级、元件级到全尺寸结构级，逐层递进地阐述了飞机风挡材料与结构的动态性能与失效行为的研究成果。然而，当前研究仍面临跨尺度力学行为耦合机制不清、高精度仿真与计算效率难以平衡、模型构建与优化高度依赖经验试错等瓶颈。因此，提出未来的研究应重点关注多尺度数值仿真、无网格方法的标准化与先进技术的推广、机器学习技术在飞机风挡鸟撞问题中的应用等领域。

Abstract

The bird strike resistance of aircraft windshields is a critical evaluation index in the structural strength design of aircraft. With the continuous iteration and innovation of numerical simulation methods, this technology has been extensively applied in the bird strike resistance design of aircraft windshields. A comprehensive review of recent research achievements in numerical simulations of bird strikes on aircraft windshields based on emerging theories and methodologies is presented in this paper. The geometric modeling and mechanical behavior of bird bodies, as well as the advantages, disadvantages and practical applications of various numerical analysis methods are introduced as the general investigations. In another category of research, the dynamic mechanical properties of aircraft windshield materials, as well as the investigation of dynamic responses, failure modes and other associated mechanical behaviors of flat panel structures and full-scale windshields under high strain rate conditions are summarized. Specifically, with respect to the research findings on the dynamic properties and failure behaviors of aircraft windshield materials and structures, a progressive elaboration is presented from the material level, component level to the full-scale structural level based on the concept of the building block approach. However, bottlenecks are still encountered in current research, such as the unclear coupling mechanisms of multiscale mechanical behaviors, the challenge of balancing high simulation accuracy with efficiency, and the heavy reliance on experience-based trial and error in model construction and optimization. Therefore, key directions for future research are also proposed in this paper, including multiscale numerical simulation techniques that integrate macrostructural responses with microscale damage mechanisms, standardization of meshless methods and popularization of advanced technologies, and application of machine learning methods in mitigating bird strike risks on windshields.

关键词

数值模拟 / 鸟撞 / 风挡 / 层合玻璃 / 动态力学性能

Key words

numerical simulation / bird strike / windshield / laminated glass / dynamic mechanical property

参考文献

[1] 池福俭, 谭玉生, 罗鹏飞. 结构抗鸟撞强度分析技术研究[J].飞机设计, 2024, 44(6): 31-39.

[2] CHI F J, TAN Y S, LUO P F. Research on the strength analysis technique of structural bird strike resistance[J].Aircraft Design, 2024, 44(6): 31-39.

[3] 蔡明学, 王栋华. 机群鸟撞分析与修理对策[J].航空维修与工程, 2024(增刊 1): 98-100.

[4] CAI M X, WANG D H. Analysis and repair strategies for bird strikes in aircraft fleets[J].Aviation Maintenance & Engineering, 2024(Suppl 1): 98-100.

[5] 李俊杰, 柴象海, 金先龙, 等. 航空发动机鸟撞适航符合性数值模拟研究[J].振动与冲击, 2024, 43(10): 311-318.

[6] LI J J, CHAI X H, JIN X L, et al. Numerical simulation on the airworthiness compliance of aircraft engines during bird strikes[J].Journal of Vibration and Shock, 2024, 43(10): 311-318.

[7] 汪松柏, 牛潇, 霍嘉欣, 等. 航空发动机风扇转子叶片抗鸟撞改进设计[J].航空动力学报, 2024, 39(2): 20230494.

[8] WANG S B, NIU X, HUO J X, et al. Improved design for anti—bird impact of aero—engine fan rotor blades[J].Journal of Aerospace Power, 2024, 39(2): 20230494.

[9] 张海洋, 曹家洺, 韩立斌, 等. 宽弦空心风扇转子叶片鸟撞损伤数值仿真[J].航空发动机, 2024, 50(1): 94-101.

[10] ZHANG H Y, CAO J M, HAN L B, et al. Bird strike damage of wide—chord hollow fan rotor blades[J].Aeroengine, 2024, 50(1): 94-101.

[11] 何思, 刘存喜. 运输类飞机风挡抗鸟撞适航符合性验证方法[J].航空工程进展, 2016, 7(2): 186-190.

[12] HE S, LIU C X. A verification method of bird—strike resistance airworthiness for transport category airplane’s windshield[J].Advances in Aeronautical Science and Engineering, 2016, 7(2): 186-190.

[13] 刘信超, 徐亚芳, 王露晨, 等. 运输类飞机风挡鸟撞位置影响分析研究[J].振动与冲击, 2019, 38(17): 95-102.

[14] LIU X C, XU Y F, WANG L C, et al. Effects of bird strike position and boundary clamping component on transport airplane windshield safety[J].Journal of Vibration and Shock, 2019, 38(17): 95-102.

[15] 庞小强, 朱小龙, 荆雲杰, 等. 民机雷达罩的抗鸟撞非线性力学行为仿真研究[J].南京理工大学学报, 2024, 48(1): 62-73.

[16] PANG X Q, ZHU X L, JING Y J, et al. Simulation study of nonlinear mechanical behavior of civil aircraft radome against bird strike[J].Journal of Nanjing University of Science and Technology, 2024, 48(1): 62-73.

[17] 王富生, 张钧然, 刘洋, 等. 复合材料雷达罩耐鸟撞和电磁性能综合优化设计[J].振动与冲击, 2013, 32(13): 93-98.

[18] WANG F S, ZHANG J R, LIU Y, et al. Comprehensive optimization design of a composite radome for its anti—bird strike and electromagnetic performance[J].Journal of Vibration and Shock, 2013, 32(13): 93-98.

[19] 郭军, 李旭阳, 刘小川, 等. 变弯度机翼前缘结构抗鸟撞仿真与试验验证[J].振动与冲击, 2022, 41(24): 218-225.

[20] GUO J, LI X Y, LIU X C, et al. Simulation and experimental verification of anti—bird impact performance of a variable—bend wing leading edge structure[J].Journal of Vibration and Shock, 2022, 41(24): 218-225.

[21] 周涛, 申冲. 基于光滑粒子流体动力学的鸟撞机翼前缘动态响应分析[J].飞控与探测, 2025, 8(6): 48-62.

[22] ZHOU T, SHEN C. Dynamic response analysis of bird impact wing leading edge based on smooth particle fluid dynamics[J].Flight Control & Detection, 2025, 8(6): 48-62.

[23] 陈佳慧, 胡宇群, 陈川. 大型民用飞机风挡鸟撞的适航分析与数值仿真[J].航空计算技术, 2016, 46(4): 91-94.

[24] CHEN J H, HU Y Q, CHEN C. Airworthiness analysis and numerical simulation of bird impact on large civil aircraft windshield[J].Aeronautical Computing Technique, 2016, 46(4): 91-94.

[25] 郭琦, 赵青华, 邓晓伟. 快前沿强电磁脉冲作用下飞机风挡玻璃电磁屏蔽效能研究[J].飞机设计, 2025, 45(5): 71-75.

[26] GUO Q, ZHAO Q H, DENG X W. Research on electromagnetic shielding effectiveness of aircraft windshield in EMP environment with fast rise—time[J].Aircraft Design, 2025, 45(5): 71-75.

[27] 郭琦, 谭玉生, 孟要伟. 飞机风挡玻璃雷电间接效应[J].飞机设计, 2021, 41(5): 40-43.

[28] GUO Q, TAN Y S, MENG Y W. The indirect effect of lightning on windscreen of aircraft[J].Aircraft Design, 2021, 41(5): 40-43.

[29] 瑚洋, 林丽. 基于适航标准的飞机风挡加温系统控制方式研究[J].航空工程进展, 2020, 11(3): 414-421.

[30] HU Y, LIN L. Research on airworthiness—based control mode for aircraft windshield heating system[J].Advances in Aeronautical Science and Engineering, 2020, 11(3): 414-421.

[31] 于明, 刘永寿, 李磊, 等. 基于可靠性的飞机风挡抗鸟撞优化设计[J].航空制造技术, 2012, 55(11): 93-95.

[32] YU M, LIU Y S, LI L, et al. Reliability—based optimization design of aircraft windshield for resisting bird impact[J].Aeronautical Manufacturing Technology, 2012, 55(11): 93-95.

[33] 李玉龙, 石霄鹏. 民用飞机鸟撞研究现状[J].航空学报, 2012, 33(2): 189-198.

[34] LI Y L, SHI X P. Investigation of the present status of research on bird impacting on commercial airplanes[J].Acta Aeronautica et Astronautica Sinica, 2012, 33(2): 189-198.

[35] LIU Z X, XU Y K, HUANG F Z, et al. Test and numerical simulation on fragmentation behavior of an aircraft PMMA windshield under bird strike by using a novel coupled SPH—DEM method[J].Aerospace Science and Technology, 2026, 173: 111742.

[36] 刁斌. 飞机风挡鸟撞有限元模拟及撞击影响分析[D]. 南京: 南京航空航天大学,2017.

[37] DIAO B. Bird—strike finite element simulation to aircraft—windshield and impact analysis[D]. Nanjing: Nanjing University of Aeronautics and Astronautics,2017.

[38] 贾建东. 飞机典型结构抗鸟撞设计与分析[D]. 南京: 南京航空航天大学,2010.

[39] JIA J D. Bird impact resistance designing and analyzing for aircraft typical structures[D]. Nanjing: Nanjing University of Aeronautics and Astronautics,2010.

[40] KALAM S A, KUMAR R V, JANARDHANA G R. SPH high velocity impact analysis—influence of bird shape on rigid flat plate[J].Materials Today, 2017, 4(2): 2564-2572.

[41] 索涛, 李玉龙. 基于积木式方法的飞机结构抗鸟撞设计[J].航空学报, 2025, 46(5): 531524.

[42] SUO T, LI Y L. Anti—bird impact design of aircraft structure via bulding block approach[J].Acta Aeronautica et Astronautica Sinica, 2025, 46(5): 531524.

[43] MAO R H, MEGUID S A, NG T Y. Effects of incidence angle in bird strike on integrity of aero—engine fan blade[J].International Journal of Crashworthiness, 2009, 14(4): 295-308.

[44] ZHANG D H, FEI Q G. Effect of bird geometry and impact orientation in bird striking on a rotary jet—engine fan analysis using SPH method[J].Aerospace Science and Technology, 2016, 54: 320-329.

[45] 杜兴刚, 彭志军, 秦利军, 等. 无机脆性玻璃光窗抗鸟撞分析[J].教练机, 2016(2): 50-53.

[46] DU X G, PENG Z J, QIN L J, et al. Bird impact—resistant analysis on inorganic brittle glass window[J].Trainer, 2016(2): 50-53.

[47] HEDAYATI R, SADIGHI M, MOHAMMADI—AGHDAM M . On the difference of pressure readings from the numerical, experimental and theoretical results in different bird strike studies[J].Aerospace Science and Technology, 2014, 32(1): 260-266.

[48] 张俊红, 刘志远, 戴胡伟, 等. 撞击位置与风扇转速对鸟撞过程的影响[J].天津大学学报(自然科学与技术版), 2020, 53(5): 492-501.

[49] ZHANG J H, LIU Z Y, DAI H W, et al. Effect of impact position and fan rotational speed on bird—impact process[J].Journal of Tianjin University (Science and Technology), 2020, 53(5): 492-501.

[50] HEDAYATI R, ZIAEI—RAD S. New bird model for simulation of bird strike on various layups used in transparent components of rotorcrafts[J].Journal of Aerospace Engineering, 2014, 27(1): 76-85.

[51] DAR U A, AWAIS M, MIAN H H, et al. The effect of representative bird model and its impact direction on crashworthiness of aircraft windshield and canopy structure[J].Journal of Aerospace Engineering, 2019, 233(14): 5150-5163.

[52] 刘牧东, 熊欣, 崔韦. 直升机旋翼鸟撞研究现状与展望[J].应用力学学报, 2022, 39(5): 816-825.

[53] LIU M D, XIONG X, CUI W. Research status and advances in bird strike of helicopter rotor[J].Chinese Journal of Applied Mechanics, 2022, 39(5): 816-825.

[54] 张乐迪, 张显余. 基于 ANSYS Workbench 鸟撞飞机风挡有限元分析[J].飞机设计, 2014, 34(2): 13-16.

[55] ZHANG L D, ZHANG X Y. The finite element analysis of bird impact on aircraft front windshield based on ANSYS workbench[J].Aircraft Design, 2014, 34(2): 13-16.

[56] 王新军, 岳珠峰, 王富生, 等. 飞机风挡结构抗鸟撞动响应数值模拟[J].强度与环境, 2007, 34(1): 28-32.

[57] WANG X J, YUE Z F, WANG F S, et al. Numerical simulation of bird impact dynamic response for windshield[J].Structure & Environment Engineering, 2007, 34(1): 28-32.

[58] 霍雨佳. 鸟撞复合材料蜂窝夹芯平板动响应分析[J].航空材料学报, 2021, 41(6): 81-88.

[59] HUO Y J. Dynamic response analysis on bird impacted composite honeycomb sandwich structure[J].Journal of Aeronautical Materials, 2021, 41(6): 81-88.

[60] 倪磊, 杨荣, 白春玉, 等. 水陆两栖飞机尾翼抗鸟撞设计与验证方法研究[J].应用力学学报, 2022, 39(3): 452-461.

[61] NI L, YANG R, BAI C Y, et al. Design and verification of bird strike on amphibious aircraft tail[J].Chinese Journal of Applied Mechanics, 2022, 39(3): 452-461.

[62] 王金金, 李志刚, 杨海峰, 等. 光学玻璃材料动态冲击试验与鸟撞研究[J].振动与冲击, 2021, 40(7): 216-221.

[63] WANG J J, LI Z G, YANG H F, et al. Dynamic tests of optical glass material and bird impact[J].Journal of Vibration and Shock, 2021, 40(7): 216-221.

[64] 李振友, 朱书华, 周华闯, 等. 基于遗传算法的鸟体本构参数优化研究[J].航空计算技术, 2017, 47(1): 47-50.

[65] LI Z Y, ZHU S H, ZHOU H C, et al. Parameters optimization on constitutive model of bird based on genetic algorithm[J].Aeronautical Computing Technique, 2017, 47(1): 47-50.

[66] 刘军, 李玉龙, 石霄鹏, 等. 鸟体本构模型参数反演Ⅱ: 模型参数反演研究[J].航空学报, 2011, 32(5): 812-821.

[67] LIU J, LI Y L, SHI X P, et al. Parameters inversion on bird constitutive model part Ⅱ: study on model parameters inversion[J].Acta Aeronautica et Astronautica Sinica, 2011, 32(5): 812-821.

[68] 张永康, 李玉龙. 鸟体力学模型仿真研究[J].计算机仿真, 2011, 28(9): 67-70.

[69] ZHANG Y K, LI Y L. Numerical study on bird mechanical model[J].Computer Simulation, 2011, 28(9): 67-70.

[70] ZHANG Y L, ZHOU Y D. Evaluating constitutive models of smoothed particle hydrodynamics for bird—strike simulation[J].International Journal of Crashworthiness, 2024, 29(3): 547-556.

[71] LAVOIE M A, GAKWAYA A, ENSAN M N, et al. Bird’s substitute tests results and evaluation of available numerical methods[J].International Journal of Impact Engineering, 2009, 36(10/11):1276-1287.

[72] 刘小川, 郭军, 孙侠生, 等. 用于鸟撞试验的仿真鸟弹研究[J].实验力学, 2012, 27(5): 623-629.

[73] LIU X C, GUO J, SUN X S, et al. Investigation on the artificial bird projectile used in bird strike test[J].Journal of Experimental Mechanics, 2012, 27(5): 623-629.

[74] WILBECK J S, RAND J L. The development of a substitute bird model[J].Journal of Engineering for Power, 1981, 103(4): 725-730.

[75] 彭鸿博, 侯润峰, 李旭阳, 等. 一种适用宽速域冲击的明胶鸟弹数值建模方法[J].高压物理学报, 2024, 38(5): 054201.

[76] PENG H B, HOU R F, LI X Y, et al. A numerical modeling method of gelatin bird projectile suitable for wide—speed—range impact[J].Chinese Journal of High Pressure Physics, 2024, 38(5): 054201.

[77] HB 7084—2014 民用飞机结构抗鸟撞设计与试验通用要求[S].

[78] HB 7084—2014 General requirements for civil airplane bird—strike design and test[S].

[79] HEIMBS S. Computational methods for bird strike simulations: a review[J].Computers & Structures, 2011, 89(23/24): 2093-2112.

[80] BAUGHN T V, GRAHAM L W. Simulation of a bird—strike impact on aircraft canopy material[J].Journal of Aircraft, 1988, 25(7): 659-664.

[81] 白金泽, 孙秦. 基于神经网络方法的鸟撞飞机风挡冲击载荷反演[J].固体力学学报, 2005, 26(1): 77-82.

[82] BAI J Z, SUN Q. Neural—network based bird strike loadings inverse to aircraft windshield[J].Acta Mechanica Solida Sinica, 2005, 26(1): 77-82.

[83] 雷娜, 冯宇豪, 段君毅, 等. 有限元网格生成方法综述[J].电子科技大学学报, 2024, 53(6): 816-843.

[84] LEI N, FENG Y H, DUAN J Y, et al. A survey of finite element mesh generation methods[J].Journal of University of Electronic Science and Technology of China, 2024, 53(6): 816-843.

[85] 金峰, 刘璐璐, 朱信颖, 等. 钛合金包边复合材料风扇叶片的鸟撞数值仿真[J].航空发动机, 2024, 50(4): 107-113.

[86] JIN F, LIU L L, ZHU X Y, et al. Numerical simulation on bird impact of composite fan blade with titanium leading edge[J].Aeroengine, 2024, 50(4): 107-113.

[87] MEGUID S A, MAO R H, NG T Y. FE analysis of geometry effects of an artificial bird striking an aero—engine fan blade[J].International Journal of Impact Engineering, 2008, 35(6): 487-498.

[88] AIROLDI A, CACCHIONE B. Modelling of impact forces and pressures in Lagrangian bird strike analyses[J].International Journal of Impact Engineering, 2006, 32(10): 1651-1677.

[89] 宁义君, 顾洪宇, 朱东宇, 等. 迎风格式在水滴欧拉方程数值求解中的应用[J].航空科学技术, 2024, 35(1): 105-114.

[90] NING Y J, GU H Y, ZHU D Y, et al. Application of upwind scheme in numerical solution of Euler equation for water droplets[J].Aeronautical Science and Technology, 2024, 35(1): 105-114.

[91] JENQ S T, HSIAO F B, LIN I C, et al. Simulation of a rigid plate hit by a cylindrical hemi—spherical tip—ended soft impactor[J].Computational Materials Science, 2007, 39(3): 518-526.

[92] MATOS N, GOMES M, INFANTE V. Numerical modelling of soft body impacts: a review[J].Engineering Failure Analysis, 2023, 153: 107595.

[93] CHENG J Y, BINIENDA W K. Simulation of soft projectiles impacting composite targets using an arbitrary Lagrangian—eulerian formulation[J].Journal of Aircraft, 2006, 43(6): 1726-1731.

[94] 朱书华. 鸟撞飞机风挡动响应分析与仿真试验平台研究[D]. 南京: 南京航空航天大学,2009.

[95] ZHU S H. Study on dynamic responses of bird striking an aircraft windsheild and virtual test platform[D]. Nanjing: Nanjing University of Aeronautics and Astronautics,2009.

[96] 简成文, 李书. 民机机头复合材料风挡结构鸟撞分析[J].民用飞机设计与研究, 2015(1): 39-46.

[97] JIAN C W, LI S. Numerical study of bird impact on the aircraft windshield structure with composite material[J].Civil Aircraft Design and Research, 2015(1): 39-46.

[98] 张啸, 崔杰, 李明远, 等. 基于 CEL 法的破损边界附近气泡动力学特性研究[J].振动与冲击, 2024, 43(1): 99-106.

[99] ZHANG X, CUI J, LI M Y, et al. Dynamic characteristics of bubbles near damaged boundary based on CEL method[J].Journal of Vibration and Shock, 2024, 43(1): 99-106.

[100] SMOJVER I, IVANČEVIĆ D. Bird strike damage analysis in aircraft structures using Abaqus/Explicit and coupled Eulerian Lagrangian approach[J].Composites Science and Technology, 2011, 71(4): 489-498.

[101] 刘树森, 何小伟, 王文成, 等. 光滑粒子流体动力学流体仿真技术综述[J].软件学报, 2024, 35(1): 481-512.

[102] LIU S S, HE X W, WANG W C, et al. Survey on fluid simulation using smoothed particle hydrodynamics[J].Journal of Software, 2024, 35(1): 481-512.

[103] 王璐, 徐绯, 杨扬. 完全拉格朗日 SPH 在冲击问题中的改进和应用[J].力学学报, 2022, 54(12): 3297-3309.

[104] WANG L, XU F, YANG Y. Improvement of the total Lagrangian SPH and its application in impact problems[J].Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3297-3309.

[105] 龙思海, 滕春明, 张海东. 基于 abaqus 的 SPH 算法鸟撞分析研究[J].教练机, 2019(1): 23-26.

[106] LONG S H, TENG C M, ZHANG H D. Analysis and study of bird strike based on SPH algorithm of abaqus[J].Trainer, 2019(1): 23-26.

[107] 张景景, 谢洋, 刘志芳, 等. 碳纤维叶片的鸟弹冲击响应及损伤[J].爆炸与冲击, 2023, 43(12): 123301.

[108] ZHANG J J, XIE Y, LIU Z F, et al. Bird impact response and damage of carbon fiber blades[J].Explosion and Shock Waves, 2023, 43(12): 123301.

[109] 贾建东, 李志强, 杨建林, 等. 用 SPH 和有限元方法研究鸟撞飞机风挡问题[J].航空学报, 2010, 31(1): 136-142.

[110] JIA J D, LI Z Q, YANG J L, et al. A study of bird impact on aircraft windshield using SPH and finite element method[J].Acta Aeronautica et Astronautica Sinica, 2010, 31(1): 136-142.

[111] 刘军, 李玉龙, 徐绯. 基于 PAM—CRASH 的鸟撞飞机风挡动响应分析[J].爆炸与冲击, 2009, 29(1): 80-84.

[112] LIU J, LI Y L, XU F. Dynamic response analysis of bird—impact aircraft windshields based on PAM—CRASH[J].Explosion and Shock Waves, 2009, 29(1): 80-84.

[113] 陈贺贺, 原梅妮, 李立州, 等. DYB—3 航空有机玻璃风挡鸟撞数值模拟[J].中北大学学报(自然科学版), 2018, 39(3): 270-276.

[114] CHEN H H, YUAN M N, LI L Z, et al. Numerical simulation of DYB—3 aviation organic glass windshield under bird impact[J].Journal of North University of China (Natural Science Edition), 2018, 39(3): 270-276.

[115] HEDAYATI R, ZIAEI—RAD S, EYVAZIAN A, et al. Bird strike analysis on a typical helicopter windshield with different lay—ups[J].Journal of Mechanical Science and Technology, 2014, 28(4): 1381-1392.

[116] 张志春, 强洪夫, 高巍然. 一种新型 SPH—FEM 耦合算法及其在冲击动力学问题中的应用[J].爆炸与冲击, 2011, 31(3): 243-249.

[117] ZHANG Z C, QIANG H F, GAO W R. A new coupled SPH—FEM algorithm and its application to impact dynamics[J].Explosion and Shock Waves, 2011, 31(3): 243-249.

[118] 叶纪元, 杨扬, 徐绯, 等. 基于自适应 FEM—SPH 耦合算法的飞机典型部位破片冲击战伤的数值研究[J].爆炸与冲击, 2024, 44(6): 065101.

[119] YE J Y, YANG Y, XU F, et al. Numerical research on fragment impact damage of typical aircraft structures based on an adaptive FEM—SPH coupling algorithm[J].Explosion and Shock Waves, 2024, 44(6): 065101.

[120] CAO R J, CHEN J Y, SONG X Z, et al. Numerical simulation of the damage characteristics of carbon fiber—reinforced aluminum laminates under hypervelocity impact based on the FE—SPH adaptive method[J].Applied Composite Materials, 2025, 32(3): 817-847.

[121] 马明瑞, 陈福振, 严红, 等. 基于多分辨率 SPH—FEM 耦合方法的鸟撞问题数值模拟[J].航空学报, 2024, 45(21): 230116.

[122] MA M R, CHEN F Z, YAN H, et al. Numerical simulation of bird strike based on multi—resolution SPH—FEM coupling method[J].Acta Aeronautica et Astronautica Sinica, 2024, 45(21): 230116.

[123] ZHOU Y D, SUN Y C, HUANG T L, et al. SPH—FEM simulation of impacted composite laminates with different layups[J].Aerospace Science and Technology, 2019, 95: 105469.

[124] 林建鸿. 积木式方法与试验金字塔的历史沿革与发展趋势[J].航空工程进展, 2023, 14(5): 8-18.

[125] LIN J H. The historical developments and trendencies of building block approach and testing pyramid[J].Advances in Aeronautical Science and Engineering, 2023, 14(5): 8-18.

[126] 傅惠民, 李子昂, 付越帅. 航空发动机积木式可靠性评估方法[J].机电产品开发与创新, 2022, 35(3): 1-5.

[127] FU H M, LI Z A, FU Y S. Aero—engine building block reliability assessment method[J].Development & Innovation of Machinery & Electrical Products, 2022, 35(3): 1-5.

[128] 张英杰, 姚芬, 刘姗姗, 等. 中空钢化夹层玻璃的动态响应[J].高压物理学报, 2020, 34(5): 054101.

[129] ZHANG Y J, YAO F, LIU S S, et al. Dynamic response of hollow tempered laminated glass[J].Chinese Journal of High Pressure Physics, 2020, 34(5): 054101.

[130] CHEN X, WANG C Z, CHEN S W, et al. Characterization of the dynamic mechanical properties of low—iron float glass through Split—Hopkinson—Pressure—Bar tests[J].Construction and Building Materials, 2023, 365: 130083.

[131] MEYLAND M J, NIELSEN J H. High strain rate characterisation of soda—lime—silica glass and the effect of residual stresses[J].Glass Structures & Engineering, 2022, 7(4): 641-657.

[132] SHEIKH M Z, WANG Z, SUO T, et al. Dynamic failure of un—strengthened aluminosilicate glass[J].Theoretical and Applied Fracture Mechanics, 2019, 104: 102325.

[133] 江斌, 胡嘉奕, 郭亚洲, 等. 基于电磁 Hopkinson 杆的无机玻璃动态力学性能测试技术[J].科学通报, 2020, 65(31): 3475-3484.

[134] JIANG B, HU J Y, GUO Y Z, et al. A novel testing technique for dynamic mechanical properties of inorganic glass by electromagnetic Hopkinson bar[J].Chinese Science Bulletin, 2020, 65(31): 3475-3484.

[135] 王振, 张超, 王银茂, 等. 飞机风挡无机玻璃在不同应变率下的力学行为[J].爆炸与冲击, 2018, 38(2): 295-301.

[136] WANG Z, ZHANG C, WANG Y M, et al. Mechanical behaviours of aeronautical inorganic glass at different strain rates[J].Explosion and Shock Waves, 2018, 38(2): 295-301.

[137] 刘俊, 田宙, 钟巍. 冲击波作用下单层钢化玻璃应变阈值的数值模拟[J].爆炸与冲击, 2018, 38(3): 671-676.

[138] LIU J, TIAN Z, ZHONG W. Numerical simulation of strain threshold of monolithic tempered glass under blast wave[J].Explosion and Shock Waves, 2018, 38(3): 671-676.

[139] 刘浩, 贾彬, 孔德锋, 等. 钢化玻璃的动态力学性能及抗爆性能研究[J].应用数学和力学, 2025, 46(5): 600-610.

[140] LIU H, JIA B, KONG D F, et al. Study on dynamic mechanical properties and anti—explosion performances of tempered glass[J].Applied Mathematics and Mechanics, 2025, 46(5): 600-610.

[141] YATAĞAN M S. The effect of number of walls with different thickness on the properties of the polycarbonate panels[J].Health Sciences Quarterly, 2019, 3(4): 271-284.

[142] MOHAGHEGHIAN I, WANG Y, ZHOU J, et al. Deformation and damage mechanisms of laminated glass windows subjected to high velocity soft impact[J].International Journal of Solids and Structures, 2017, 109: 46-62.

[143] EL—QOUBAA Z, COLARD L, MATADI BOUMBIMBA R, et al. Experimental study and modelling of poly (methyl methacrylate) and polycarbonate compressive behavior from low to high strain rates[J].Journal of Dynamic Behavior of Materials, 2018, 4(2): 179-189.

[144] KLOSAK M, RUSINEK A, JANKOWIAK T, et al. Dynamic perforation and compression tests of PMMA for a wide range of temperatures—experimental and preliminary numerical analysis[C]//12th International Conference on the Mechanical and Physical Behaviour of Materials under Dynamic Loading. 2018, 183: 02055.

[145] MOY P, GUNNARSSON C A, WEERASOORIYA T, et al. Stress—strain response of PMMA as a function of strain—rate and temperature[C]//Dynamic Behavior of Materials, Volume 1. New York: Springer, 2011: 125-133.

[146] WANG F S, YUE Z F. Numerical simulation of damage and failure in aircraft windshield structure against bird strike[J].Materials & Design, 2010, 31(2): 687-695.

[147] WANG J, XU Y J, ZHANG W H. Finite element simulation of PMMA aircraft windshield against bird strike by using a rate and temperature dependent nonlinear viscoelastic constitutive model[J].Composite Structures, 2014, 108: 21-30.

[148] ABDULLAH T, KIRANE K. Continuum damage modeling of dynamic crack velocity, branching, and energy dissipation in brittle materials[J].International Journal of Fracture, 2021, 229(1): 15-37.

[149] DU Y M, PEI P H, SUO T, et al. Large deformation mechanical behavior and constitutive modeling of oriented PMMA[J].International Journal of Mechanical Sciences, 2023, 257: 108520.

[150] DAR U A, ZHANG W H. Polymer based aerospace structures under high velocity impact applications; experimental, constitutive and finite element analysis[J].Journal of Mechanical Science and Technology, 2015, 29(10): 4259-4265.

[151] 韩强, 于鹏, 姚小虎, 等. 聚碳酸脂本构方程及其在鸟撞风挡仿真中的应用[J].华南理工大学学报(自然科学版), 2013, 41(8): 99-102.

[152] HAN Q, YU P, YAO X H, et al. Constitutive equation of polycarbonate and its application to simulation of windshield under bird impact[J].Journal of South China University of Technology (Natural Science Edition), 2013, 41(8): 99-102.

[153] WANG H T, ZHOU H M, HUANG Z G, et al. Constitutive modeling of polycarbonate over a wide range of strain rates and temperatures[J].Mechanics of Time—Dependent Materials, 2017, 21(1): 97-117.

[154] WANG J, XU Y J, ZHANG W H, et al. A damage—based elastic—viscoplastic constitutive model for amorphous glassy polycarbonate polymers[J].Materials & Design, 2016, 97: 519-531.

[155] RUSINEK A, BERNIER R, BOUMBIMBA R M, et al. New devices to capture the temperature effect under dynamic compression and impact perforation of polymers, application to PMMA[J].Polymer Testing, 2018, 65: 1-9.

[156] GARCIA—GONZALEZ D, RUSINEK A, BENDARMA A, et al. Material and structural behaviour of PMMA from low temperatures to over the glass transition: quasi—static and dynamic loading[J].Polymer Testing, 2020, 81: 106263.

[157] 于鹏. 航空聚碳酸酯动态力学性能及本构关系研究[D]. 广州: 华南理工大学,2014.

[158] YU P. Investigation on the dynamic characteristics and constitutive model of polycarbonate of aircraft[D]. Guangzhou: South China University of Technology,2014.

[159] OSNES K, HOPPERSTAD O S, BØRVIK T. Rate dependent fracture of monolithic and laminated glass: experiments and simulations[J].Engineering Structures, 2020, 212: 110516.

[160] HA Y D. An extended ghost interlayer model in peridynamic theory for high—velocity impact fracture of laminated glass structures[J].Computers & Mathematics with Applications, 2020, 80(5): 744-761.

[161] GAO W, LIU X, CHEN S H, et al. A cohesive zone based DE/FE coupling approach for interfacial debonding analysis of laminated glass[J].Theoretical and Applied Fracture Mechanics, 2020, 108: 102668.

[162] 陈贺贺, 原梅妮, 李立州, 等. 基于光滑粒子流体动力学法的飞机风挡鸟撞失效破坏模拟[J].科学技术与工程, 2018, 18(7): 62-67.

[163] CHEN H H, YUAN M N, LI L Z, et al. Failure simulation of aircraft windshield under bird impact based on smoothed particle hydrodynamics[J].Science Technology and Engineering, 2018, 18(7): 62-67.

[164] DAR U A, ZHANG W H, XU Y J. FE analysis of dynamic response of aircraft windshield against bird impact[J].International Journal of Aerospace Engineering, 2013, 103: 171768.

[165] 苏艳, 缪奎宗, 张柱国, 等. 基于内聚力模型的飞机风挡与无人机碰撞仿真及试验验证[J].南京航空航天大学学报, 2023, 55(5): 839-850.

[166] SU Y, MIAO K Z, ZHANG Z G, et al. Simulation and test verification of collision between aircraft windshield and UAV based on cohesive zone model[J].Journal of Nanjing University of Aeronautics & Astronautics, 2023, 55(5): 839-850.

[167] 刘朋朋, 李玉龙, 刘军, 等. 飞机驾驶舱后观察窗抗鸟撞试验及数值模拟研究[J].振动与冲击, 2014, 33(8): 78-82.

[168] LIU P P, LI Y L, LIU J, et al. Tests and numerical simulation for bird’s impacting rear observation window of an aircraft cockpit[J].Journal of Vibration and Shock, 2014, 33(8): 78-82.

[169] KHOLOOSI F, NIA A A. Experimental and numerical investigation of the behavior of multi—layer windshield consisting of glass and polycarbonate against bird strike[J].International Journal of Impact Engineering, 2024, 194: 105092.

[170] REZAEI M, AREZOO B, ZIAEI—RAD S. Redesign an aircraft windshield to improve its mechanical resistance against simultaneous bird impacts[J].International Journal of Impact Engineering, 2024, 184: 104811.

[171] MOHAGHEGHIAN I, CHARALAMBIDES M N, WANG Y, et al. Effect of the polymer interlayer on the high—velocity soft impact response of laminated glass plates[J].International Journal of Impact Engineering, 2018, 120: 150-170.

[172] ZHANG X W, LIU H B, MAHARAJ C, et al. Impact response of laminated glass with varying interlayer materials[J].International Journal of Impact Engineering, 2020, 139: 103505.

[173] GRIMALDI A, SOLLO A, GUIDA M, et al. Parametric study of a SPH high velocity impact analysis—a bird—strike windshield application[J].Composite Structures, 2013, 96: 616-630.

[174] LIU L Z, MA Z Z, PANG S H, et al. Effect of polyurethane with different elastic modulus on the response of aircraft windshield against bird strike[J].Advanced Materials Research, 2012, 418/419/420: 179-184.