Constrained thickness optimization of rectangular orthotropic fiber-reinforced plate for fundamental frequency maximization

Abstract

This paper addresses the thickness optimization of rectangular orthotropic fiber-reinforced composite plates by using mathematical programming theory of nonlinear constrained optimization. We optimize the thickness distribution of various composite plates for reaching a maximum in the plate natural frequency, subject to an equality constraint in a plate volume and a number of inequality constraints on the lower and upper bounds of allowable range of thicknesses. For the modeling part of our optimization algorithm, we formulate the kinematical hypothesis of the classical plate theory (CPT), reduced plane stress theory of linearized elasticity, and Hamilton’s principle. For the solution part, we implement the Rayleigh-Ritz semi-analytical solution technique to spatially discretize the weak form of the plate partial differential equation (PDE), and transforming it to a generalized algebraic eigen-problem. For the design optimization part, we use a conjugate Rosen’s gradient projection method. The design variables of the optimization design space are thicknesses of an arbitrary but rectangular partition of the plate into constant-thickness subdivisions. After simulating our algorithm, we noticed many interesting and impressive results, and tried to justify them. The most impressive finding is that, as the fiber orientation of the composite plate rotates, the plate thickness distribution rotates also in the same way, but with different manifestations for different boundary conditions. For parametric studies, we analyze the sensitivity of the algorithm against parameters, like, the degree of fineness in the number of plate partitions into constant-thickness sub-plates, the degree of plate anisotropy, the fiber orientation, the rectangular plate aspect ratio, the upper to lower bounds of allowable thickness ratio, and boundary conditions.