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A Methodology for Optimal Design of Composite Laminates Using Polar Formalism

Published online by Cambridge University Press:  18 January 2016

M. Kazemi  and
G. Verchery
M. Kazemi*
Affiliation:
Environmental Sciences Research CenterDepartment of MechanicsEslamshahr BranchIslamic Azad UniversityEslamshahr, Iran
G. Verchery
Affiliation:
Institut Supérieur des Matériaux et Mécaniques Avancés Le Mans, France
*
*Corresponding author ([email protected])
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Abstract

An innovative optimization technique is presented for the design of composite laminated plates subjected to in-plane loads. A list of quasi-homogeneous laminates that can be used as angle-ply materials is proposed as a comprehensive solution for optimum lay-up. Two optimization procedures are performed: Dimensioning of the flexural stiffness and the elastic modulus, which provides the optimal orientations for the layers and offer highest in-plane resistance to composite laminated structures. The polar formalism for plane anisotropy is used to represent the flexural stiffness and elastic modulus tensors. Numerical examples are resolved for two materials with different elastic moduli.

Keywords

CompositeOptimizationQuasi-homogeneousAngle-ply
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 3 , June 2016 , pp. 255 - 266
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2016 

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References

1.Haftka, R. T., Gürdal, Z., Hajela, P., Design and Op timization of Laminated Composite Materials, John Wiley & Sons, New York, NY, U.S.A. (1999).Google Scholar
2.Miki, M., “Design of Laminated Fibrous Composite Plates with Required Flexural Stiffness,” Recent Advances in Composites in the United States and Japan, ASTM, Philadelphia (1985).Google Scholar
3.Barbero, E. J. and Tomblin, J., “A Damage Mechanics Model for Compression Strength of Composites,“ International Journal of Solids And Structures, 33, pp. 4379–4393 (1996).CrossRefGoogle Scholar
4.Khani, A., IJsselmuiden, S. T., Abdalla, M. M. and Gürdal, Z., “Design of Variable Stiffness Panels for Maximum Strength Using Lamination Parameters,“ Composites Part B: Engineering, 42, pp. 546–552 (2011).CrossRefGoogle Scholar
5.Setoodeh, S., Abdalla, M. M. and Gürdal, Z., “Design of Variable-Stiffness Laminates Using Lamination Parameters,” Composites Part B: Engineering, 37, pp. 301–309(2006).CrossRefGoogle Scholar
6.Liu, S., Hou, Y., Sun, X. and Zhang, Y., “A Two-Step Optimization Scheme for Maximum Stiffness Design of Laminated Plates Based on Lamination Parameters,” Composite Structures, 94, pp. 3529–3537 (2012).CrossRefGoogle Scholar
7.Nik, M. A., Fayazbakhsh, K., Pasini, D. and Lessard, L., “A comparative Study of Metamodeling Methods for the Design Optimization of Variable Stiffness Composites,” Composite Structures, 107, pp. 494–501 (2014).Google Scholar
8.Zuo, Z. H. and Xie, Y. M., “Maximizing the Effective Stiffness of Laminate Composite Materials,“ Computational Materials Science, 83, pp. 57–63 (2014).CrossRefGoogle Scholar
9.Vannucci, P., Riccardo, B. and Bennati, S., “Exact Optimal Flexural Design of Laminates,” Composite Structures, 90, pp. 337–345 (2009).CrossRefGoogle Scholar
10.Vannucci, P., “Influence of Invariant Material Parameters on the Flexural Optimal Design of Thin Anisotropic Laminates,” International Journal of Mechanical Sciences, 51, pp. 192–203 (2009).CrossRefGoogle Scholar
11.Verchery, G., “Design Rules for the Laminate Stiffness,” Mechanics of Composite Materials, 47, pp. 47–58 (2011).CrossRefGoogle Scholar
12.Verchery, G., “Les Invariants Des Tenseurs D'Ordre 4 Du Type De l'élasticité,” Mechanical Behavior of Anisotropic Solids/Comportment Méchanique des Solides Anisotropes, Editions du CNRS, Paris (1979).Google Scholar
13.Christensen, P. W. and Klarbring, A., An Introduction to Structural Optimization (Solid Mechanics and Its Applications), Springer, Linkoping (2008).Google Scholar
14.Jones, R. M., Mechanics of Composite Materials, CRC Press, Boca Raton (1998).Google Scholar
15.Vincenti, A., Vannucci, P. and Ahmadian, M. R., “Optimization of Laminated Composites by Using Genetic Algorithm and the Polar Description of Plane Anisotropy,” Mechanics of Advanced Materi als and Structures, 20, pp. 242–255 (2013).CrossRefGoogle Scholar
16.Vannucci, P., “Designing the Elastic Properties of Laminates as an Optimisation Problem: A Unified Approach Based on Polar Tensor Invariants,” Structural and Multidisciplinary Optimization, 31, pp. 378–387 (2006).CrossRefGoogle Scholar
17.Vannucci, P. and Verchery, G., “A Special Class of Uncoupled and Quasi-Homogeneous Laminates,“ Composites Science and Technology, 61, pp. 1465–1473 (2001).CrossRefGoogle Scholar
18.Vassilopoulos, A. P. and Keller, T., Fatigue of Fiber-Reinforced Composites, Springer, London (2011).CrossRefGoogle Scholar
19.Turvey, G. J. and Marshall, I. H., Buckling and Post-Buckling of Composite Plates, Chapman & Hall, London (1995).CrossRefGoogle Scholar
20.Kalamkarov, A. L. and Kolpakov, A. G., Analysis Design, and Optimization of Composite Structures, John Wiley & Sons, New York (1997).Google Scholar
21.Haftka, R. T. and Gurdal, Z., Elements of Structural Optimization, Kluwer Academic Publishers, Ordrecht (1992).CrossRefGoogle Scholar
22.Christensen, P. W. and Klarbring, A., An Introduction to Structural Optimization, Springer, Linkoping (2008).Google Scholar
23.Vannucci, P. and Verchery, G., “Designing with Anisotropy. Part 3: Quasi-Homogeneous Laminates,“ Comptes rendus de ICCM 12 (12th Inetrnational Conference on Composite Materials), Paris, France (1999).Google Scholar
24.Vannucci, P. and Verchery, G., “Anisotropy of Plane Complex Elastic Bodies,” International Journal of Solids and Structures, 47, pp. 1154–1166 (2010).CrossRefGoogle Scholar
25.Vannucci, P. and Verchery, G., “A New Method for Generating Fully Isotropic Laminates,” Composite Structures, 58, pp. 75–82 (2002).CrossRefGoogle Scholar
26.Montemurro, M., Vincenti, A. and Vannucci, P., “A Two-Level Procedure for the Global Optimum Design of Composite Modular Structures—Application to the Design of an Aircraft Wing,” Journal of Optimization Theory and Applications, 155, pp. 24–53 (2012).CrossRefGoogle Scholar
27.Vincenti, A., Vannucci, P. and Verchery, G., “Anisotropy and Symmetry for Elastic Properties of Laminates Reinforced by Balanced Fabrics,” Composites Part A: Applied Science and Manufacturing., 32, pp. 1525–153(2001).CrossRefGoogle Scholar
28.Agarwal, B. D. and Broutman, L. J., Analysis and Performance of Fiber Composites, John Wiley & Sons, New York (2006).Google Scholar
29.Miki, M., “Design of Laminated Fibrous Composite Plates with Required Flexural Stiffness,” Recent Advances in Composites in the United States and Japan, ASTM, Philadelphia (1985).Google Scholar
30.Kazemi, M., “A New Exact Semi-Analytical Solution for Buckling Analysis of Laminated Plates Under Biaxial Compression,” Archive of Applied Mechanics,pp. 1–11 (2015).Google Scholar