BOUNDS AND EXTREMAL CONFIGURATIONS FOR THE TORSIONAL RIGIDITY OF COATED FIBER REINFORCED SHAFTS

Abstract. In this paper we derive bounds on the torsional rigidity for coated ber reinforced shafts. The bounds are used to assess the optimality or suboptimality of ber reinforcement cong-urations. This investigation focuses on coated ber reinforcements with circular cross section. It is shown how the eective antiplane shear modulus and torsional rigidity of each coated ber are used to determine whether the conguration provides reinforcement above or below that of a homogeneous shaft containing no coated bers. Simply connected shaft cross sections of arbitrary shape reinforced with any conguration of coated bers are considered. Precise conditions on the eective antiplane shear modulus and torsional rigidity of each coated ber are given under which the circular shaft reinforced with a single centered circular coated ber is either optimal or suboptimal