Buckling of short column of superelastic shape memory alloy with tension compression asymmetry

Abstract

This numerical study is on the effect of tension-compression asymmetry of shape memory alloy on the response of a short column made of the same material. It incorporates superelastic SMA's highly nonlinear stress-strain relations. Primarily, a rectangular cross-section is selected for analysis of the column, loaded beyond the linear stress-strain relations. Then similar analysis is carried out for a different cross-section of equal area, namely, circle of the same area, for comparing the effect of cross-section. geometry on the response of the beam and column. Using the equations of static equilibrium, the variations of modulus of elasticity and bending moment for different equivalent cross-sections are presented. It is found that the reduced modulus of elasticity and the bending moment are functions of the stress-strain curve and cross-section geometry. Finite difference technique has been used to trace the equilibrium configuration path of the column with different end conditions. Thompson's two theorems are used to interpret the critical load for the column. Results are also obtained for the buckling load by using Timoshenko's method for inelastic buckling of a simple column. for comparison. Comparison shows good agreement between the present results offinite difference technique and those obtained from Timoshenko's method.