Semianalytical Buckling Solution and Experimental Study of Variable–Cross Section Rods with Different Moduli

Abstract

Many civil-engineering materials and novel materials developed in recent years exhibit a property of different elastic moduli in tension and compression. One such material is graphene, a wonder material, which has the highest strength yet measured. However, the dominant failure of structures composed of this high-strength material is often attributed to buckling problems. Investigations on buckling problems for structures with different moduli are scarce. To address this new problem, the present paper develops a semianalytical method for the critical buckling loads of variable–cross section slender rods with different moduli. Based on the variational principle, a differential equation of the deflection of these structures is derived for the first time. By developing a nonlinear iterative program and using the variational iteration method, the critical buckling loads are obtained. Then, buckling tests and numerical simulation were conducted for slender rods made from graphite with different moduli. By comparing the semianalytical results with the laboratory tests and finite-element analysis results, the semianalytical model proposed in this paper was demonstrated to be accurate and reliable. The conclusion can be drawn that the characteristics of different moduli of materials have a significant influence on the buckling stability of structures. Therefore, it may lead to unsafe results if the classic theory is still adopted to determine the buckling loads of those rods composed of a material having different moduli. The proposed model could provide a novel approach for further investigation of nonlinear mechanical behavior for structures with different moduli.