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ADVANCES IN OPTIMIZATION FOR STRUCTURAL ENGINEERING
Edited by: B.H.V. Topping
Optimal Design of Laminated Composite Plates
G. Giambanco, S. Rizzo and R. Spallino
Department of Structural Engineering and Geotechnics, University of Palermo, Palermo, Italy
G. Giambanco, S. Rizzo, R. Spallino, "Optimal Design of Laminated Composite Plates", in B.H.V. Topping, (Editor), "Advances in Optimization for Structural Engineering", Civil-Comp Press, Edinburgh, UK, pp 143-147, 1996. doi:10.4203/ccp.40.6.2
To the optimal design (OD) problem of laminated composite plates many contributions have been already devoted. The problem takes its significance only if all the constraints stated by various serviceability and/or failure conditions are carefully accounted for. In this paper this OD problem is formulated as a constrained nonlinear mathematical programming (NLP) one. Despite of the fact the objective function has been assumed as linear combination of lamina1 thicknesses, which are the continuous design variables, nonlinearity is yielded by the implicit elastic formulation of composite laminates, and by the assumed maximum admissible failure criterion. Other linear constraints are also appended to the NLP approach, herein presented accounting for technological (minimum lamina thickness) requirements, and/or for assigned buckling load or first modal frequency, and for serviceability maximum displacement requirement. For this class of problems a method of solution, the directional derivative method, has been developed by the authors following the general criteria of the feasible direction method. The feasible directions method was preferred to the sequential unconstrained minimization techniques (SUMT) for the better performance exhibited, since SUMT often require a great number of function evaluation and are then computationally expensive. A feasible direction method possesses also the feature that each design point obtained throughout the optimization process is a feasible one, and that for each new design point the objective function will be reduced (or incremented in problems of maximization). A design point is called feasible if it lies in the feasible region, i.e., it does not violate any constraint of the problem. The unicity of the solution is assured if the problem is convex.
The OD procedure herein presented has been successfully tested by implementation to the optimal design of rectangular laminated composite plates with constraints on the center plate deflection. The numerical results obtained from a parametric study are presented and discussed.
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