Concurrent Lamination and Tapering Optimization of Cantilever Composite Plates under Shear
Abstract
:1. Introduction
2. Materials and Methods
2.1. Cantilever Laminated Plate
2.2. Stiffness Formulation
2.3. Finite Element Analysis
2.4. Optimization
3. Results and Discussion
4. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
QI-R | Quasi-isotropic and rectangular |
QI-T | Quasi-isotropic and tapered |
ST-R | Stiffness-tailored and rectangular |
ST-T | Stiffness-tailored and tapered |
Nomenclature
A | Plate area |
Constitutive matrix for in-plane deformation | |
Constitutive matrix for transverse shear deformation | |
Longitudinal modulus | |
Transverse modulus | |
In-plane shear modulus | |
, | Transverse shear moduli |
F | Tip shear force |
f | Nodal force vector |
K | Nodal stiffness matrix |
l | Plate length |
N | Number of layers |
t | Plate thickness |
Layer thicknesses | |
Material invariants | |
u | Nodal displacement vector |
, | Lamination parameters |
w | Plate width |
Taper angle | |
Major Poisson’s ratio | |
Layer angles |
References
- Wang, G.; Wereley, N.M. Free Vibration Analysis of Rotating Blades with Uniform Tapers. AIAA J. 2004, 42, 1531–1541. [Google Scholar] [CrossRef]
- Kim, T.U.; Hwang, I.H. Optimal design of composite wing subjected to gust loads. Comput. Struct. 2005, 83, 1546–1554. [Google Scholar] [CrossRef]
- Dado, M.; Al-Sadder, S. A new technique for large deflection analysis of non-prismatic cantilever beams. Mech. Res. Commun. 2005, 32, 692–703. [Google Scholar] [CrossRef]
- Ansari, M.Z.; Cho, C.; Kim, J.; Bang, B. Comparison between Deflection and Vibration Characteristics of Rectangular and Trapezoidal profile Microcantilevers. Sensors 2009, 9, 2706–2718. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Plaut, R.H.; Virgin, L.N. Optimal design of cantilevered elastica for minimum tip deflection under self-weight. Struct. Multidisc. Optim. 2011, 43, 657–664. [Google Scholar] [CrossRef]
- Kien, N.D.; Gan, B.S. Large deflections of tapered functionally graded beams subjected to end forces. Appl. Math. Model. 2014, 38, 3054–3066. [Google Scholar]
- Zhao, Z.; Feng, C.; Dong, Y.; Yang, J. Geometrically nonlinear bending of functionally graded nanocomposite trapezoidal plates reinforced with graphene platelets (GPLs). Int. J. Mech. Mater. Des. 2019, 15, 791–800. [Google Scholar] [CrossRef]
- Kılıc, O.; Aktas, A.; Dırıkolu, M.H. An investigation of the effects of shear on the deflection of an orthotropic cantilever beam by the use of anisotropic elasticity theory. Compos. Sci. Technol. 2001, 61, 2055–2061. [Google Scholar] [CrossRef]
- Thinh, T.I.; Ngoc, L.K. Static behavior and vibration control of piezoelectric cantilever composite plates and comparison with experiments. Comput. Mater. Sci. 2010, 49, s276–s280. [Google Scholar] [CrossRef]
- Vo, T.P.; Thai, H.-T. Static behavior of composite beams using various refined shear deformation theories. Compos. Struct. 2012, 94, 2513–2522. [Google Scholar] [CrossRef] [Green Version]
- Doeva, O.; Masjedi, P.K.; Weaver, P.M. Static deflection of fully coupled composite Timoshenko beams: An exact analytical solution. Eur. J. Mech. A Solids 2020, 81, 103975. [Google Scholar] [CrossRef]
- Bouadjadja, S.; Tati, A.; Guerira, B. Analytical and experimental investigations on large deflection analysis of composite cantilever beams. Mech. Adv. Mater. Struct. 2020, 1–9. [Google Scholar] [CrossRef]
- Franco Correia, V.M.; Mota Soares, C.M.; Mota Soares, C.A. Design sensitivity analysis and optimal design of composite structures using higher order discrete models. Eng. Optim. 1997, 29, 85–111. [Google Scholar] [CrossRef]
- Mota Soares, C.M.; Mota Soares, C.A.; Franco Correia, V.M. Optimization of multilaminated structures using higher-order deformation models. Comput. Methods. Appl. Mech. Eng. 1997, 149, 133–152. [Google Scholar]
- Kim, C.-G.; Hong, C.-S. Practical design of tapered composite structures using the manufacturing cost concept. Compos. Struct. 2001, 51, 285–299. [Google Scholar] [CrossRef]
- Öztürk, H.; Sabuncu, M. Stability analysis of a cantilever composite beam on elastic supports. Compos. Sci. Technol. 2005, 65, 1982–1995. [Google Scholar] [CrossRef]
- Karaagac, C.; Öztürk, H.; Sabuncu, M. Lateral dynamic stability analysis of a cantilever laminated composite beam with an elastic support. Int. J. Struct. Stab. Dyn. 2007, 7, 377–402. [Google Scholar] [CrossRef]
- Blasques, J.P.; Stolpe, M. Maximum stiffness and minimum weight optimization of laminated composite beams using continuous fiber angles. Struct. Multidisc. Optim. 2011, 43, 573–588. [Google Scholar] [CrossRef]
- Albazzan, M.A.; Harik, R.; Tatting, B.F.; Gürdal, Z. Efficient design optimization of nonconventional laminated composites using lamination parameters: A state of the art. Compos. Struct. 2019, 209, 362–374. [Google Scholar] [CrossRef]
- Serhat, G.; Faria, T.G.; Basdogan, I. Multi-objective optimization of stiffened, fiber-reinforced composite fuselages for mechanical and vibro-acoustic requirements. In Proceedings of the 17th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Washington, DC, USA, 13–17 June 2016. [Google Scholar]
- Serhat, G.; Basdogan, I. Effect of aspect ratio and boundary conditions on the eigenfrequency optimization of composite panels using lamination parameters. In Proceedings of the 11th ASMO-UK/ISSMO/NOED2016 International Conference on Numerical Optimisation Methods for Engineering Design, Munich, Germany, 18–20 July 2016. [Google Scholar]
- Serhat, G.; Basdogan, I. Multi-objective optimization of composite plates using lamination parameters. Mater. Design 2019, 180, 107904. [Google Scholar] [CrossRef]
- Serhat, G.; Basdogan, I. Comparison of vibro–acoustic performance metrics in the design and optimization of stiffened composite fuselages. In Proceedings of the 45th International Congress and Exposition on Noise Control Engineering (INTER–NOISE 2016), Hamburg, Germany, 21–24 August 2016. [Google Scholar]
- Serhat, G.; Basdogan, I. Design of curved composite panels for optimal dynamic response using lamination parameters. Compos. Part B Eng. 2018, 147, 135–146. [Google Scholar] [CrossRef]
- Hammer, V.B.; Bendsøe, M.P.; Lipton, R.; Pedersen, P. Parametrization in laminate design for optimal compliance. Int. J. Solids Struct. 1997, 34, 415–434. [Google Scholar] [CrossRef]
- Liu, S.; Hou, Y.; Sun, X.; Zhang, Y. A two-step optimization scheme for maximum stiffness design of laminated plates based on lamination parameters. Compos. Struct. 2012, 94, 3529–3537. [Google Scholar] [CrossRef]
- Setoodeh, S.; Abdalla, M.M.; Gürdal, Z. Design of variable–stiffness laminates using lamination parameters. Compos. Part B Eng. 2006, 37, 301–309. [Google Scholar] [CrossRef]
- Demir, E.; Yousefi-Louyeh, P.; Yildiz, M. Design of variable stiffness composite structures using lamination parameters with fiber steering constraint. Compos. Part B Eng. 2019, 165, 733–746. [Google Scholar] [CrossRef]
- Hong, Z.; Peeters, D.; Turteltaub, S. An enhanced curvature-constrained design method for manufacturable variable stiffness composite laminates. Comput. Struct. 2020, 238, 106284. [Google Scholar] [CrossRef]
- El Said, B.; Hallett, S.R. Multiscale surrogate modelling of the elastic response of thick composite structures with embedded defects and features. Compos. Struct. 2018, 200, 781–798. [Google Scholar] [CrossRef] [Green Version]
- Peeters, D.; van Baalen, D.; Abdallah, M. Combining topology and lamination parameter optimisation. Struct. Multidisc. Optim. 2015, 52, 105–120. [Google Scholar] [CrossRef]
- Tsai, S.W.; Hahn, H.T. Introduction to Composite Materials, 1st ed.; Technomic: Lancaster, UK, 1980; pp. 123–131. [Google Scholar]
- Grenestedt, J.L. Layup optimization and sensitivity analysis of the fundamental eigenfrequency of composite plates. Compos. Struct. 1989, 12, 193–209. [Google Scholar] [CrossRef]
- Fukunaga, H.; Vanderplaats, G.N. Stiffness optimization of orthotropic laminated composites using lamination parameters. AIAA J. 1991, 29, 641–646. [Google Scholar] [CrossRef]
- Gürdal, Z.; Haftka, R.T.; Hajela, P. Design and Optimization of Laminated Composite Materials, 1st ed.; John Wiley & Sons: New York, NY, USA, 1999; p. 140. [Google Scholar]
- Fukunaga, H.; Sekine, H.; Sato, M. Optimal design of symmetric laminated plates for fundamental frequency. J. Sound Vibrat. 1994, 171, 219–229. [Google Scholar] [CrossRef]
- Serhat, G.; Basdogan, I. Lamination parameter interpolation method for design of manufacturable variable-stiffness composite panels. AIAA J. 2019, 57, 3052–3065. [Google Scholar] [CrossRef]
- Serhat, G.; Bediz, B.; Basdogan, I. Unifying lamination parameters with spectral-Tchebychev method for variable-stiffness composite plate design. Compos. Struct. 2020, 242, 112183. [Google Scholar] [CrossRef]
- Diaconu, C.G.; Sato, M.; Sekine, H. Layup optimization of symmetrically laminated thick plates for fundamental frequencies using lamination parameters. Struct. Multidisc. Optim. 2002, 24, 302–311. [Google Scholar] [CrossRef]
- Serhat, G.; Anamagh, M.R.; Bediz, B.; Basdogan, I. Dynamic analysis of doubly curved composite panels using lamination parameters and spectral-Tchebychev method. Comput. Struct. 2020, 239C, 106294. [Google Scholar] [CrossRef]
- Liu, G.R.; Quek, S.S. The Finite Element Method: A Practical Course, 1st ed.; Butterworth-Heinemann: London, UK, 2003; pp. 180–184. [Google Scholar]
- Reddy, J.N. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed.; CRC Press: Boca Raton, FL, USA, 2003; p. 112. [Google Scholar]
- Grenestedt, J.L. Composite plate optimization only requires one parameter. Struct. Optim. 1990, 2, 29–37. [Google Scholar] [CrossRef]
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Serhat, G. Concurrent Lamination and Tapering Optimization of Cantilever Composite Plates under Shear. Materials 2021, 14, 2285. https://doi.org/10.3390/ma14092285
Serhat G. Concurrent Lamination and Tapering Optimization of Cantilever Composite Plates under Shear. Materials. 2021; 14(9):2285. https://doi.org/10.3390/ma14092285
Chicago/Turabian StyleSerhat, Gokhan. 2021. "Concurrent Lamination and Tapering Optimization of Cantilever Composite Plates under Shear" Materials 14, no. 9: 2285. https://doi.org/10.3390/ma14092285
APA StyleSerhat, G. (2021). Concurrent Lamination and Tapering Optimization of Cantilever Composite Plates under Shear. Materials, 14(9), 2285. https://doi.org/10.3390/ma14092285