变刚度复材板壳结构优化及热环境下的屈曲

doi:10.7527/S1000-6893.2025.32473

Abstract

Abstract:

Variable-Stiffness （VS） composites have gained significant attention due to their tunable stiffness and strength properties. The instability issues of VS thin-walled structures in thermal environments cannot be ignored. The thermal buckling performance and geometric imperfection sensitivity of laminated plate and cylindrical shell structures with straight layups and manufacturable optimal curved fiber layups under different thermal environments are investigated. First， the optimal layup angles considering the minimum radius of curvature are obtained using an optimization algorithm based on a variable-fidelity Kriging surrogate model. Second， the thermal buckling problems of VS laminated plates and cylindrical shells are studied through static analysis and nonlinear buckling analysis considering thermal environments and initial imperfections. Comparisons are conducted between straight and curved fiber layup laminated plates and VS cylindrical shell considering their imperfection sensitivities. The results show that the linear buckling loads of the optimized VS structures are all greater than those of the straight layup laminated plates. Thermal stress leads to a reduction in the total instability load of VS laminated plates， while having a smaller impact on conventional straight layup laminated plates； for VS cylindrical shell structures， the total buckling load value increases slightly under thermal stress. Temperature has a minor effect on the imperfection sensitivity of laminated plates， while for cylindrical shell structures， temperature increases their compressive imperfection sensitivity.

Key words: Variable-Stiffness (VS) composites, variable-fidelity Kriging surrogate model, fiber angle optimization, thermal buckling, geometric imperfection sensitivity

CLC Number:

V214

Yuheng SUN, Yujie GUO, Shijie XIAO, Huiwen CUI, Hao YAN, Xiaohui WEI. Structure optimization of variable-stiffness composite shells and buckling in thermal environments[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(6): 232473.

Figures/Tables 24

Fig.1

Fig.2

Fig.3

Table 1

Fig.4

Fig.5

Fig.6

Fig.7

Table 2

Accuracy validation of Kriging surrogate model with variable-fidelity for VS-1 laminated plate

$T 0$ /（°）	$T 1$ /（°）	屈曲载荷/kN		R²	e_max/%	e_avg/%
$T 0$ /（°）	$T 1$ /（°）	FEA	代理模型	R²	e_max/%	e_avg/%
45	75	19.3	19.4	0.99	3.88	1.53
67.5	22.5	14.5	14.8
22.5	0	9.9	10.3
90	67.5	15.6	15.7
0	45	16.5	16.6

Table 2

Table 3

Accuracy validation of Kriging surrogate model with variable fidelity for VS-2 laminated plate

$T 01$ /（°）	$T 11$ /（°）	$T 02$ /（°）	$T 12$ /（°）	屈曲载荷/kN		R²	e_max /%	e_avg /%
$T 01$ /（°）	$T 11$ /（°）	$T 02$ /（°）	$T 12$ /（°）	FEA	代理模型	R²	e_max /%	e_avg /%
22.5	45	0	60	21.7	21.2	0.92	5.8	2.5
30	70	67.5	45	20.6	19.4
67.5	22.5	90	22.5	14.4	14.4
45	0	45	90	18.0	17.6
90	67.5	22.5	67.5	17.8	18.2

Table 3

Table 4

Accuracy validation of Kriging surrogate model with variable fidelity for VS-axial cylindrical shell

$T 01$ /（°）	$T 11$ /（°）	$T 02$ /（°）	$T 12$ /（°）	$T 03$ /（°）	$T 13$ /（°）	$T 04$ /（°）	$T 14$ /（°）	屈曲载荷/kN		R²	e_max /%	e_avg /%
$T 01$ /（°）	$T 11$ /（°）	$T 02$ /（°）	$T 12$ /（°）	$T 03$ /（°）	$T 13$ /（°）	$T 04$ /（°）	$T 14$ /（°）	FEA	代理模型	R²	e_max /%	e_avg /%
32.6	54.3	69.3	0.5	38.3	41.4	36.7	35.7	115.8	110.8	0.98	6.1	4.8
67.2	68.8	33.6	19.7	58.4	75.5	55.9	33.1	51.7	49.8
19.7	37.8	42.4	33.6	70.3	49.1	42.4	46.6	138.1	130.9
11.4	76.0	70.3	72.4	9.8	75.0	55.3	0.0	132.5	124.4
35.2	82.8	82.8	59.5	69.8	40.9	39.8	45.0	116.7	96.2

Table 4

Table 5

Accuracy validation of Kriging surrogate model with variable fidelity for VS-cir cylindrical shell

$T 01$ /（°）	$T 11$ /（°）	$T 02$ /（°）	$T 12$ /（°）	$T 03$ /（°）	$T 13$ /（°）	$T 04$ /（°）	$T 14$ /（°）	屈曲载荷/kN		R²	e_max /%	e_avg /%
$T 01$ /（°）	$T 11$ /（°）	$T 02$ /（°）	$T 12$ /（°）	$T 03$ /（°）	$T 13$ /（°）	$T 04$ /（°）	$T 14$ /（°）	FEA	代理模型	R²	e_max /%	e_avg /%
10.9	65.7	56.4	18.6	12.9	16.6	8.3	3.6	113.2	104.8	0.98	7.9	4.9
90.0	86.4	87.4	35.2	62.6	77.6	7.2	60.5	71.3	69.7
45.5	2.6	60.0	9.8	22.2	9.8	39.8	73.4	80.1	84.9
55.3	77.1	19.1	32.6	2.1	85.9	89.5	55.9	63.0	68.4
47.1	66.2	37.2	78.6	82.2	89.5	17.6	11.4	82.2	81.2

Table 5

Table 6

Table 7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

Fig.15

Fig.16

Fig.17

References 28

[1]	HYER M W， CHARETTE R F. Use of curvilinear fiber format in composite structure design［J］. AIAA Journal， 1991， 29（6）： 1011-1015.
[2]	郑广强，姚锋，周晓芹. 自动铺丝技术及其在A350制造过程中的应用［J］. 航空制造技术， 2017（16）： 76-82.
	ZHENG G Q， YAO F， ZHOU X Q. Application of automatic fiber placement technology in A350 manufacturing［J］. Aeronautical Manufacturing Technology， 2017（16）： 76-82 （in Chinese）.
[3]	GÜRDAL Z， OLMEDO R. In-plane response of laminates with spatially varying fiber orientations： Variable stiffness concept［J］. AIAA Journal， 1993， 31（4）： 751-758.
[4]	孔斌，顾杰斐，陈普会，等. 变刚度复合材料结构的设计、制造与分析［J］. 复合材料学报， 2017， 34（10）： 2121-2133.
	KONG B， GU J F， CHEN P H， et al. Design， manufacture and analysis of variable-stiffness composite structures［J］. Acta Materiae Compositae Sinica， 2017， 34（10）： 2121-2133 （in Chinese）.
[5]	IJSSELMUIDEN S T， ABDALLA M M， GÜRDAL Z. Optimization of variable-stiffness panels for maximum buckling load using lamination parameters［J］. AIAA Journal， 2010， 48（1）： 134-143.
[6]	WEAVER P， POTTER K， HAZRA K， et al. Buckling of variable angle tow plates： From concept to experiment： AIAA-2009-2509［R］. Reston： AIAA， 2009.
[7]	LOPES C S， CAMANHO P P， GÜRDAL Z， et al. Progressive failure analysis of tow-placed， variable-stiffness composite panels［J］. International Journal of Solids and Structures， 2007， 44（25/26）： 8493-8516.
[8]	冉庆波，肖鸿，杨富鸿，等. 含孔曲面自动铺丝轨迹规划算法［J］. 航空学报， 2022， 43（9）： 425602.
	RAN Q B， XIAO H， YANG F H， et al. Trajectory planning algorithm for automatic wire laying on perforated surface［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（9）： 425602 （in Chinese）.
[9]	BLOM A W， STICKLER P B， GÜRDAL Z. Optimization of a composite cylinder under bending by tailoring stiffness properties in circumferential direction［J］. Composites Part B： Engineering， 2010， 41（2）： 157-165.
[10]	ZHOU X Y， RUAN X， GOSLING P D. Thermal buckling optimization of variable angle tow fibre composite plates with gap/overlap free design［J］. Composite Structures， 2019， 223： 110932.
[11]	KHANI A， IJSSELMUIDEN S T， ABDALLA M M， et al. Design of variable stiffness panels for maximum strength using lamination parameters［J］. Composites Part B： Engineering， 2011， 42（3）： 546-552.
[12]	孙士平，张冰，邓同强，等. 复合载荷作用变刚度复合材料回转壳屈曲优化［J］. 复合材料学报， 2019， 36（4）： 1052-1061.
	SUN S P， ZHANG B， DENG T Q， et al. Buckling optimization of variable stiffness composite rotary shell under combined loads［J］. Acta Materiae Compositae Sinica， 2019， 36（4）： 1052-1061 （in Chinese）.
[13]	钟继凡. 基于代理模型的变刚度复合材料结构优化设计［D］. 武汉：华中科技大学， 2018.
	ZHONG J F. Optimization design of variable stiffness composite structure based on surrogate model［D］. Wuhan： Huazhong University of Science and Technology， 2018 （in Chinese）.
[14]	龚煜廉，张建国，吴志刚，等. 主动学习基自适应PC-Kriging模型的复合材料结构可靠度算法［J］. 航空学报， 2024， 45（8）： 228982.
	GONG Y L， ZHANG J G， WU Z G， et al. Reliability algorithm of composite structure based on active learning basis-adaptive PC-Kriging model［J］. Acta Aeronautica et Astronautica Sinica， 2024， 45（8）： 228982 （in Chinese）.
[15]	YI J X， LIU J， CHENG Y S. A fast forecast method based on high and low fidelity surrogate models for strength and stability of stiffened cylindrical shell with variable ribs［C］∥ 2018 IEEE 8th International Conference on Underwater System Technology： Theory and Applications. Piscataway： IEEE Press， 2018： 1-6.
[16]	HAO P， FENG S J， ZHANG K， et al. Adaptive gradient-enhanced Kriging model for variable-stiffness composite panels using isogeometric analysis［J］. Structural and Multidisciplinary Optimization， 2018， 58（1）： 1-16.
[17]	GUO Q， HANG J T， WANG S A， et al. Design optimization of variable stiffness composites by using multi-fidelity surrogate models［J］. Structural and Multidisciplinary Optimization， 2021， 63（1）： 439-461.
[18]	IJSSELMUIDEN S T， ABDALLA M M， GÜRDAL Z. Thermomechanical design optimization of variable stiffness composite panels for buckling［J］. Journal of Thermal Stresses， 2010， 33（10）： 977-992.
[19]	MANICKAM G， BHARATH A， DAS A N， et al. Thermal buckling behaviour of variable stiffness laminated composite plates［J］. Materials Today Communications， 2018， 16： 142-151.
[20]	DURAN A V， FASANELLA N A， SUNDARARAGHAVAN V， et al. Thermal buckling of composite plates with spatial varying fiber orientations［J］. Composite Structures， 2015， 124： 228-235.
[21]	VESCOVINI R， DOZIO L. Thermal buckling behaviour of thin and thick variable-stiffness panels［J］. Journal of Composites Science， 2018， 2（4）： 58.
[22]	MANICKAM G， HABOUSSI M， D’OTTAVIO M， et al. Nonlinear thermo-elastic stability of variable stiffness curvilinear fibres based layered composite beams by shear deformable trigonometric beam model coupled with modified constitutive equations［J］. International Journal of Non-Linear Mechanics， 2023， 148： 104303.
[23]	OLIVERI V， MILAZZO A， WEAVER P M. Thermo-mechanical post-buckling analysis of variable angle tow composite plate assemblies［J］. Composite Structures， 2018， 183： 620-635.
[24]	LIANG K， MU J Q， LI Z. Thermal-mechanical buckling analysis and optimization of the stringer stiffened cylinder using smeared stiffener based reduced-order models［J］. Computers & Mathematics with Applications， 2023， 143： 108-118.
[25]	ADITYA NARAYAN D， GANAPATHI M， PRADYUMNA B， et al. Investigation of thermo-elastic buckling of variable stiffness laminated composite shells using finite element approach based on higher-order theory［J］. Composite Structures， 2019， 211： 24-40.
[26]	CHEN X D， NIE G J， YANG X F. Thermal postbuckling analysis of variable angle tow composite cylindrical panels［J］. Journal of Thermal Stresses， 2021， 44（7）： 850-882.
[27]	张骏华. 导弹和运载火箭复合材料结构设计指南［M］. 北京：中国宇航出版社， 1999.
	ZHANG J H. Design guide for missile and launch vehicle composite structures［M］. Beijing： China Astronautic Publishing House， 1999 （in Chinese）.
[28]	HAO P， YUAN X J， LIU C， et al. An integrated framework of exact modeling， isogeometric analysis and optimization for variable-stiffness composite panels［J］. Computer Methods in Applied Mechanics and Engineering， 2018， 339： 205-238.

温度T/℃	密度 ρ/（kg·m^-³）	弹性模量		泊松比		剪切模量 G₁₂=G₂₃=G₁₃/GPa	热膨胀系数		比热容C_p /（J·（kg·℃）^-1）
温度T/℃	密度 ρ/（kg·m^-³）	E₁/GPa	E₂=E₃/GPa	μ₁₂	μ₂₃=μ₁₃	剪切模量 G₁₂=G₂₃=G₁₃/GPa	α₁/（10^-6·℃^-1）	α₂=α₃/（10^-6·℃^-1）	比热容C_p /（J·（kg·℃）^-1）
20	1 650	146	10.5	0.30	0.025	5.52	0.26	33.7	1 008
60		146	8.81	0.28	0.026	5.32	0.26	33.7	1 156
100		144	8.45	0.32	0.026	4.78	0.26	33.7	1 291
140		140	8.27	0.32	0.03	4.28	0.29	34.3	1 407
180		137	6.97	0.32	0.047	3.53	0.20	31.3	1 507
220		132	2.59	0.31	0.044	1.13	0.20	31.3	1 591
260		133	1.17	0.34	0.037	0.325	0.20	31.3	1 657
300		130	0.854	0.32	0.044	0.246	0.20	31.3	1 701

试件	全局最优解		考虑R_min后的最优解
试件	铺层形式	F_cr/kN	铺层形式	F_cr/kN
VS-1	［±<19.4，69.7>］_{6 s}	28.5	［±<39，52>］_{6 s}	24.1
VS-2	［±<28.1，50>/±<16.9，80.9>］_{3 s}	29.3	［±<33，45>/±<35，47>］_{3 s}	23.7

试件	优化铺层形式	F_cr/kN	F_QI-C/kN	F_CS-C/kN
VS-axial	［<37.6，16.5>/-<21，43.8>/<41.7，78.7>/-<87.1，50.2>］_s	203.9	160.2	199.32
VS-cir	［<6.3，24.6>/-<71.4，83.1>/<59.5，57.2>/-<35.1，16.9>］_s	172.9	160.2	199.32

Structure optimization of variable-stiffness composite shells and buckling in thermal environments

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References 28

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[1]	YANG Zhichun, LIU Liyuan, WANG Xiaochen. Analysis of aeroelastic vibro-acoustic response for heated panel of hypersonic vehicle [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(12): 3578-3587.
[2]	WU Zhenqiang, CHENG Hao, ZHANG Wei, LI Haibo, KONG Fanjin. Effects of Thermal Environment on Dynamic Properties of Aerospace Vehicle Panel Structures [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2013, 34(2): 334-342.
[3]	Sun Liangxin;Ma Lingjian. THERMAL BUCKLING OF ANTISYMMETRIC CROSS-PLY LAMINATED COMPOSITE PLATES [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1991, 12(12): 610-615.