Multiobjective shape and material optimization of composite structures including damping

Abstract

A multiobjective optimal design methodology is developed for lightweight, low-cost composite structures of improved dynamic performance. The design objectives may include minimization of damped resonance amplitudes (or maximization of modal damping), weight, and material cost. The design vector includes micromechanics, laminate, and structural shape parameters. Constraints are imposed on static displacements, static and dynamic ply stresses, dynamic amplitudes, and natural frequencies. The effects of composite damping tailoring on the dynamics of the composite structure are incorporated. Applications on a cantilever composite beam and plate illustrate that only the proposed multiobjective formulation, as opposed to single objective functions, may simultaneously improve the objectives. The significance of composite damping in the design of advanced composite structures is also demonstrated, and the results indicate that the minimum-weight design or design methods based on undamped dynamics may fail to improve the dynamic performance near resonances. Nomenclature A = area [C],[c] = global and modal damping matrices, respectively E = normal modulus F(z) = objective functions / = frequency fd = damped frequency G = shear modulus G(z) = inequality constraints h = thickness [/£],[/:] = global and modal stiffness matrices, respectively k = volume ratio [M],[m] = global and modal mass matrices, respectively p^p = global and modal excitation force, respectively q — modal vector 5 = strength t = time U = dynamic amplitude u = displacement vector