Closed-Form Formulas for the Optimum Design of Composite Laminates Under In-Plane Loading

The present work provides closed-form formulas for the optimum fiber orientation angle of symmetrically composite laminates under in-plane static loading. The formulation is based on the classical lamination theory. The optimization procedure is based on the classical approach where the strength ratio represents the objective function to be maximized while satisfying two failure criteria (Tsai–Wu and Tsai–Hill). The closed-form formulas were derived for three different composite materials, namely glass/epoxy, carbon/epoxy and aramid/epoxy. The design variables were the fiber orientation angles which were allowed to take any real value in the range of [-90∘,90∘] and their stacking sequence. The outcomes are presented graphically and in closed-form expressions suitable for design purposes. The accuracy of the proposed closed-form expressions was verified through comparison with existing results available in the literature.