Solid Mechanics and Vehicle Conceptual Design

An equivalent⁃deformation⁃modulus algorithm for fast optimization of anisotropic material distribution in thin plates

  • Mi XU ,
  • Zebei MAO ,
  • Bo WANG ,
  • Tong LI
Expand
  • State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian 116024,China
E-mail: tong@dlut.edu.cn

Received date: 2023-07-06

  Revised date: 2023-07-24

  Accepted date: 2023-08-08

  Online published: 2023-08-24

Supported by

National Natural Science Foundation of China(12172077);Dalian High-Level Talent Innovation Support Program(2019RD04);Dalian Science and Technology Innovation Fund(2020JJ25CY011)

Abstract

Anisotropic materials widely exist in load-bearing components for various mechanical devices. Unlike isotropic materials, the distribution and orientation of different material phases in anisotropic materials can sensitively mediate the mechanical output of these components according to the loading conditions. In this paper, an optimization method for anisotropic material distribution, named Equivalent-Deformation-Modulus (EDM) algorithm, is proposed to efficiently optimize the load-bearing ability of anisotropic thin plates. This EDM algorithm will play an important role in the aviation, for it enables the multi-modal co-optimization for the buckling resistance of thin plates, and solves the problem of overlapping eigenvalue in traditional optimization algorithm. Taking the optimization of fiber orientation in short fiber reinforced polymer thin plate as an example, without changing the mass and shape of the plate, this EDM algorithm can improve the critical buckling load by 28.9% and reduce the computational cost by 98.1%, compared to traditional optimization algorithm. The EDM method was also applied to designing a load-bearing component in the airframe with an irregular shape by increasing the critical buckling load by 27.2%-30.8%.

Cite this article

Mi XU , Zebei MAO , Bo WANG , Tong LI . An equivalent⁃deformation⁃modulus algorithm for fast optimization of anisotropic material distribution in thin plates[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2024 , 45(10) : 229273 -229273 . DOI: 10.7527/S1000-6893.2023.29273

References

1 WENK H R, VAN HOUTTE P. Texture and anisotropy[J]. Reports on Progress in Physics200467(8): 1367-1428.
2 DHARMAVARAPU P, M B S S R. Aramid fibre as potential reinforcement for polymer matrix composites: A review[J]. Emergent Materials20225(5): 1561-1578.
3 LI T, WANG Z X, ZHANG H, et al. Effect of aramid nanofibers on interfacial properties of high performance fiber reinforced composites[J]. Composite Interfaces202229(3): 312-326.
4 MORAMPUDI P, NAMALA K K, GAJJELA Y K, et al. Review on glass fiber reinforced polymer composites[J]. Materials Today: Proceedings202143: 314-319.
5 SATHISHKUMAR T P, SATHEESHKUMAR S, NAVEEN J. Glass fiber-reinforced polymer composites?A review[J]. Journal of Reinforced Plastics and Composites201433(13): 1258-1275.
6 LI Y G, LI N Y, GAO J. Tooling design and microwave curing technologies for the manufacturing of fiber-reinforced polymer composites in aerospace applications[J]. The International Journal of Advanced Manufacturing Technology201470(1): 591-606.
7 LI Y G, LI N Y, ZHOU J, et al. Microwave curing of multidirectional carbon fiber reinforced polymer composites[J]. Composite Structures2019212: 83-93.
8 AN Q L, CHEN J, CAI X J, et al. Thermal characteristics of unidirectional carbon fiber reinforced polymer laminates during orthogonal cutting[J]. Journal of Reinforced Plastics and Composites201837(13): 905-916.
9 KIM J W, KIM H S. Study on fibre orientation and fibre content of glass fibre reinforced polymer[J]. Materials Research Innovations201418(sup2): S2-482-S2-487.
10 KIM J W, KIM H S, LEE D G. Study on fibre orientation of weld line parts during injection moulding of fibre reinforced plastic by image processing[J]. Materials Research Innovations201115(sup1): s303-s306.
11 DO T T, LEE D J. Analysis of tensile properties for composites with wrinkled fabric[J]. Journal of Mechanical Science and Technology201024(2): 471-479.
12 ZARUTSKII V A, SIVAK V F. Experimental analysis of the natural vibrations and stability of cylindrical shells reinforced with rectangular plates[J]. International Applied Mechanics200844(5): 562-564.
13 HADJILOIZI D A, KALAMKAROV A L, GEORGIA DES A V. Plane stress analysis of magnetoelectric composite and reinforced plates: Applications to wafer- and rib-reinforced plates and three-layered honeycomb shells[J]. ZAMM - Journal of Applied Mathematics and Mechanics201797(7): 786-814.
14 WANG Z G. Recent advances in novel metallic honeycomb structure[J]. Composites Part B: Engineering2019166: 731-741.
15 ZHANG L, LIU B, GU Y, et al. Modelling and characterization of mechanical properties of optimized honeycomb structure[J]. International Journal of Mechanics and Materials in Design202016(1): 155-166.
16 HAMM C E, MERKEL R, SPRINGER O, et al. Architecture and material properties of diatom shells provide effective mechanical protection[J]. Nature2003421(6925): 841-843.
17 STUDART A R. Biological and bioinspired composites with spatially tunable heterogeneous architectures[J]. Advanced Functional Materials201323(36): 4423-4436.
18 ZANNONI C, MANTOVANI R, VICECONTI M. Material properties assignment to finite element models of bone structures: A new method[J]. Medical Engineering & Physics199920(10): 735-740.
19 REZNIKOV N, SHAHAR R, WEINER S. Bone hierarchical structure in three dimensions[J]. Acta Biomaterialia201410(9): 3815-3826.
20 PARSONS A J, AHMED I, HAN N, et al. Mimicking bone structure and function with structural composite materials[J]. Journal of Bionic Engineering20107: S1-S10.
21 ROPER S W K, LEE H, HUH M, et al. Simultaneous isotropic and anisotropic multi-material topology optimization for conceptual-level design of aerospace components[J]. Structural and Multidisciplinary Optimization202164(1): 441-456.
22 MARíN J C, GRACIANI E. Normal stress flow evaluation in composite aircraft wing sections by strength of material models[J]. Composite Structures2022282: 115088.
23 CHEN J Y, LIU X J, TIAN Y J, et al. 3D-printed anisotropic polymer materials for functional applications[J]. Advanced Materials202234(5): e2102877.
24 LUND E. Discrete material and thickness optimization of laminated composite structures including failure criteria[J]. Structural and Multidisciplinary Optimization201857(6): 2357-2375.
25 SJ?LUND J H, PEETERS D, LUND E. A new thickness parameterization for discrete material and thickness optimization[J]. Structural and Multidisciplinary Optimization201858(5): 1885-1897.
26 NIU B, SHAN Y, LUND E. Discrete material optimization of vibrating composite plate and attached piezoelectric fiber composite patch[J]. Structural and Multidisciplinary Optimization201960(5): 1759-1782.
27 DUAN Z Y, YAN J, LEE I, et al. Discrete material selection and structural topology optimization of composite frames for maximum fundamental frequency with manufacturing constraints[J]. Structural and Multidisciplinary Optimization201960(5): 1741-1758.
28 DUAN Z Y, YAN J, LEE I, et al. A two-step optimization scheme based on equivalent stiffness parameters for forcing convexity of fiber winding angle in composite frames[J]. Structural and Multidisciplinary Optimization201959(6): 2111-2129.
29 DUAN Z Y, YAN J, LEE I, et al. Integrated design optimization of composite frames and materials for maximum fundamental frequency with continuous fiber winding angles[J]. Acta Mechanica Sinica201834(6): 1084-1094.
30 YAN J, DUAN Z Y, LUND E, et al. Concurrent multi-scale design optimization of composite frame structures using the Heaviside penalization of discrete material model[J]. Acta Mechanica Sinica201632(3): 430-441.
31 TIAN S M, WANG M, QI W C. Effects of elastically supported boundaries on flutter characteristics of thin-walled panels[J]. Energies202215(19): 7088.
32 ZAWADA-MICHA?OWSKA M, PIE?KO P, JóZWIK J, et al. A comparison of the geometrical accuracy of thin-walled elements made of different aluminum alloys[J]. Materials202114(23): 7242.
33 LIU C N, CHENG H, ZHANG K F, et al. An efficient trans-scale and multi-stage approach for the deformation analysis of large-sized thin-walled composite structure in aircraft assembly[J]. The International Journal of Advanced Manufacturing Technology2022120(9): 5697-5713.
34 XU F F, LI H, ZHANG D X. A study on dynamic characteristics of thin-walled cylindrical cavities with a large aspect ratio[J]. Aerospace20229(4): 174.
35 ABRAMIAN A, VIROT E, LOZANO E, et al. Nondestructive prediction of the buckling load of imperfect shells[J]. Physical Review Letters2020125(22): 225504.
36 JIAO P, CHEN Z P, MA H, et al. Buckling behaviors of thin-walled cylindrical shells under localized axial compression loads, Part 2: Numerical study[J]. Thin-Walled Structures2021169: 108330.
37 ROZYLO P, FERDYNUS M, DEBSKI H, et al. Progressive failure analysis of thin-walled composite structures verified experimentally[J]. Materials202013(5): 1138.
38 SZKLAREK K, GAJEWSKI J. Optimisation of the thin-walled composite structures in terms of critical buckling force[J]. Materials202013(17): 3881.
39 ERKMEN R E. Elastic buckling analysis of thin-walled beams including web-distortion[J]. Thin-Walled Structures2022170: 108604.
40 LUO Y J, ZHAN J J. Linear buckling topology optimization of reinforced thin-walled structures considering uncertain geometrical imperfections[J]. Structural and Multidisciplinary Optimization202062(6): 3367-3382.
41 PRATO A, AL-SAYMAREE M S M, FEATHERST ON C A, et al. Buckling and post-buckling of thin-walled stiffened panels: Modelling imperfections and joints[J]. Thin-Walled Structures2022172: 108938.
42 SUN Y, TIAN K, LI R, et al. Accelerated Koiter method for post-buckling analysis of thin-walled shells under axial compression[J]. Thin-Walled Structures2020155: 106962.
43 WANG Q N, QIAN C F, WU Z W. Research on the rational design method of strength reinforcement for thin-walled structure based on limit load analysis[J]. Applied Sciences202212(4): 2208.
44 SIRAJUDEEN R S, SEKAR R. Buckling analysis of pultruded glass fiber reinforced polymer (GFRP) angle sections[J]. Polymers202012(11): 2532.
45 KASIVISWANATHAN M, UPADHYAY A. Global buckling behavior of blade stiffened compression flange of FRP box-beams[J]. Structures202132: 1081-1091.
46 ARRANZ S, SOHOULI A, SULEMAN A. Buckling optimization of variable stiffness composite panels for curvilinear fibers and grid stiffeners[J]. Journal of Composites Science20215(12): 324.
47 ZHANG W H, JIU L P, MENG L. Buckling-constrained topology optimization using feature-driven optimization method[J]. Structural and Multidisciplinary Optimization202265(1): 37.
48 LIU Y R, WANG L, GU K X, et al. Artificial Neural Network (ANN)-Bayesian Probability Framework (BPF) based method of dynamic force reconstruction under multi-source uncertainties[J]. Knowledge-Based Systems2022237: 107796.
49 SCHITTKOWSKI K. NLPQL: A fortran subroutine solving constrained nonlinear programming problems[J]. Annals of Operations Research19865(1): 485-500.
50 LI Z Y, LIU Z, LEI Z, et al. An innovative computational framework for the analysis of complex mechanical behaviors of short fiber reinforced polymer composites[J]. Composite Structures2021277: 114594.
51 ZHANG L, LI Z Y, ZHANG H Y, et al. Fatigue failure mechanism analysis and life prediction of short fiber reinforced polymer composites under tension-tension loading[J]. International Journal of Fatigue2022160: 106880.
52 RITZ W. über eine neue methode zur l?sung gewisser variationsprobleme der mathematischen physik[J]. Journal für die reine und angewandte Mathematik20091909(135): 1-61 (in German).
53 ?IT?AN P. The Rayleigh-Ritz method still competitive[J]. Journal of Computational and Applied Mathematics199454(3): 297-306.
54 NEVES M M, RODRIGUES H, GUEDES J M. Generalized topology design of structures with a buckling load criterion[J]. Structural Optimization199510(2): 71-78.
55 DU J B, OLHOFF N. Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps[J]. Structural and Multidisciplinary Optimization200734(2): 91-110.
56 MA Z D, KIKUCHI N, CHENG H C, et al. Topological optimization technique for free vibration problems[J]. Journal of Applied Mechanics199562(1): 200-207.
57 MA Z D, KIKUCHI N, CHENG H C. Topological design for vibrating structures[J]. Computer Methods in Applied Mechanics and Engineering1995121(1-4): 259-280.
58 TADJBAKHSH I, KELLER J B. Strongest columns and isoperimetric inequalities for eigenvalues[J]. Journal of Applied Mechanics196229(1): 159.
59 ZHENG J C, ZHANG P W, ZHANG D H, et al. A multi-scale submodel method for fatigue analysis of braided composite structures[J]. Materials202114(15): 4190.
60 ARAI K, YODO K, OKADA H, et al. Ultra-large scale fracture mechanics analysis using a parallel finite element method with submodel technique[J]. Finite Elements in Analysis and Design2015105: 44-55.
61 SUN Y T, ZHAI J J, ZHANG Q, et al. Research of large scale mechanical structure crack growth method based on finite element parametric submodel[J]. Engineering Failure Analysis2019102: 226-236.
Outlines

/