Constructal Design Associated with Genetic Algorithm to Minimize the Maximum Deflection of Thin Stiffened Steel Plates

This paper deals with the application of stochastic technique allied to the constructal design (CD) method and computational modeling for the optimization of composed plates reinforced by stiffeners. More specifically, it seeks to determine the optimal geometric configuration of the stiffened plate that minimizes its maximum deflection. For this purpose, a simply supported rectangular plate (with no stiffeners) was adopted as a reference. Then, a set of geometric configurations was proposed, through the application of CD method, by transforming a volume fraction (phi) of the reference plate into longitudinal and transverse stiffeners, maintaining the total volume, in-plane dimensions, boundary conditions, and loading. Regarding the optimization procedure, the genetic algorithm (GA) was chosen as the optimization method, and the geometric parameters considered as degrees of freedom were as follows: the number of longitudinal (N-ls) and transverse (N-ts) stiffeners; the thickness of the longitudinal (t(ls)) and transverse (t(ts)) stiffeners; and longitudinal and transverse stiffeners' heights ratio (h(ts)/h(ls)). Moreover, several values of phi were considered. Results indicated a great influence of the geometry on the mechanical behavior of the stiffened plates, as the optimal geometric configuration obtained here led to a reduction of over 98% in the maximum deflection in comparison with the reference plate.