Keywords: multiobjective, genetic algorithm, vibrations, strength, panel, anisotropic.

In this paper the multi-objective design of anisotropic laminated cylindrical panels for maximum fundamental frequency and strength under transverse loading is described. Cylindrical panel is simply supported at four sides. The natural frequency and the stress (objective function) are obtained using the finite element method. The design objective is optimized using the Genetic Algorithm method.

Design optimizations involving more than one objective can be handled by a multi-objective approach leading to designs which are balanced from an overall strength viewpoint. Adali et al. [1] presented the multi-objective optimization of laminated plates for maximum prebuckling, buckling and post buckling strength. A multi-objective approach was used to design laminated cylindrical shells for maximum pressure and buckling load [2]. These papers show that compromise designs can perform in a satisfactory manner under different loading conditions [3]. Recent studies have shown that genetic algorithms (GAs) are highly suitable for the solution of the composite laminate design problems, with discrete design variables. The solution of such problems by the GA is possible because the method does not require gradient or Hessian information [4]. A few researchers have combined multi-objective design with genetic algorithms. Crossely et al [5] used a two-branch tournament genetic algorithm for multi-objective design while Obayashi [6] used a multi-objective genetic algorithm for multidisciplinary design of a transonic wing plan form. Rudenko [7] used a multi-objective evolutionary algorithm for car front end design and Coello et al [8] used a new GA-based multi-objective optimization technique for the design of robot arms. Walker and Smith [3] described a technique for using GAs to determine both the mass and deflection of laminated composite plates with stress constraints. Maximum frequency problems are of practical importance in the design of composite laminates against resonance due to external excitation. The frequency of an external excitation can be placed either between zero and the fundamental frequency or in a gap between two consecutive higher-order frequencies depending on its magnitude. In the case of discrete set of ply angles the optimal stacking sequence is to be determined such that the fundamental frequency or the frequency separation is maximized.

In general, quadratic failure criteria such as the Tsai-Hill and Tsai-Wu theories have been widely used to predict the failure of composite materials. There is an inconsistency, however, in the application of Tsai-Wu theory to stacking sequence optimization [9]. Therefore, in the present work Tsai-Hill failure criterion is used as the strength criterion.

1

S. Adali, M. Walker and V.E. Verijenkov, "Multi-objective optimization of laminated plates for maximum prebuckling , buckling and postbuckling strength using continuous and discrete ply angles", Compos Struct, 35, 117-30, 1996. doi:10.1016/0263-8223(96)00030-X

2

S. Adali, A. Richester and V.E. Verijenko, "Multi-objective design of laminated cylindrical shells for maximum pressure and buckling load", Microcomput Civil Eng, 10, 269-79, 1995. doi:10.1111/j.1467-8667.1995.tb00289.x

3

M. Walker, R.E. Smith, "A technique for multi-objective optimization of laminated composite structures using genetic algorithm and finite element analysis", Compos Struct, 62, 123-128, 2003. doi:10.1016/S0263-8223(03)00098-9

4

V.B. Gantovink, Z. Gurdal and L.T. Watson, "A genetic algorithm with memory for optimal design of laminated sandwich composite panels", Compos Struct, 58, 513-520, 2002. doi:10.1016/S0263-8223(02)00128-9

5

W.A. Crossley, A.M. Cook and D.W. Fanjoy, "Structural mechanics ad materials-using the two-branch tournament genetic algorithm for multi-objective design", AIAA, 37,261, 1999. doi:10.2514/2.699

6

S. Obayashi, Y. Yamagushi and T. Nakamura, "Multi-objective genetic algorithm for multidisciplinary design of transonic wing planform", J Aircraft, 34(5), 690, 1997. doi:10.2514/2.2231

7

O. Rudenko and et al, "A multi-objective evolutionary algorithm for car front end design", In: Lecture notes in computer science 2310, 205-18, 2002. doi:10.1007/3-540-46033-0_17

8

C.A. Coello, A.D. Christiansen and A.H. Aguirre, "Using a new GA-based multi-objective optimization technique for the design of robot arms", Robotica, 16(4), 401-14, 1998. doi:10.1017/S0263574798000034

9

J.H. Park and et al, "Stacking sequence deign of composite laminates for maximum strength using genetic algorithms", Compos Struct, 52, 217-231, 2001. doi:10.1016/S0263-8223(00)00170-7

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