Decomposition Method and Regularized Newton’s Method Applied to Unconstrained Optimization: Laminated Thin Plates Fiber Orientation

AbstractThis work aims at the unconstrained optimization of laminate plate problems by introducing a methodology that uses a decomposition method along with regularized Newton method. The framework is applied to fiber orientation optimization in laminated thin plates regarding the minimization of the maximum displacement of specific plate regions. First, the problem’s domain is divided into isotropic and remainder parts, with the latter grouping laminar anisotropic behavior. This leads to an evaluation of the gradient and Hessian of the objective function in such fashion that inverses are defined only at the first step of the procedure and they are related to the isotropic part only, although the Hessian is updated each step. The fiber orientation sensibility on a plate’s solution can be evaluated separately, leading to an analytic and straightforward way of deriving the first and second derivatives of the design variables. The pb-2 Rayleigh-Ritz Method is used to approximate the solution space and to determine the problem’s semianalytical response. The results obtained are discussed and compared to those found in the literature.