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PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Stacking Sequence Optimization for a Laminated Cylindrical Shell using the Simplex Algorithm
M.H. Yas1, M. Shakeri2 and R. Khaksar1
1Department of Mechanical Engineering, Razi University, Kermanshah, Iran
M.H. Yas, M. Shakeri, R. Khaksar, "Stacking Sequence Optimization for a Laminated Cylindrical Shell using the Simplex Algorithm", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 124, 2007. doi:10.4203/ccp.86.124
Keywords: optimization, composite, stacking sequence, vibration, frequency, simplex algorithm, Nelder-Mead.
Laminated cylindrical shells are widely used in industries as structural elements, and their vibration characteristics are important in view of the current interest in designing with composite materials. Laminated composite construction offers many opportunities for engineers and designers to optimize structures for a particular or even multiple tasks.
In this paper, the governing equations based on three-dimensional elasticity have been derived. The composite cylindrical shell has a finite length and simply supported conditions at both ends. The governing equations which are in the form of partial differential equations, are changed into ordinary differential ones by using a Fourier expansion in the axial direction and then analytical exact solution to these equations has been employed to compute the fitness function for the natural frequency. Then a hybrid method combining two algorithms is proposed for the global optimization. It is necessary to well explore the whole domain. When a promising area is detected, the appropriate tools must be used to exploit this area and obtain the optimum as accurately and quickly as possible. Both tasks are hardly performed through only one method. Thus first we perform the exploration with a tabu-search and then exploit with a Nelder-Mead simplex search. Finally the results are presented for a muli-layered composite cylindrical shell and compared with similar ones obtained earlier by the authors based on genetic algorithm based optimization .
It is concluded that the genetic algorithm is less accurate and handles a population well distributed within the solution space at the beginning of the search. It localizes the promising zones more quickly than tabu search, but its convergence towards the solutions is slower.