Abstract A finite-element analysis is conducted to evaluate the symmetric behavior of single superelastic shape memory alloy (SE-SMA) rings with circular and elliptic shapes. The asymmetric behavior under pulling and pushing actions of the rings is due to the P-delta effect. In elastic zone, the P-delta effect is small with an elastic stiffness ratio of 1.1. The minor asymmetry is because of a relatively small displacement in elastic zone. However, the asymmetric behavior is more evident in pseudoelasticity zone and becomes significant in hardening zone. For the circular ring, the force response and tangent stiffness show asymmetric behavior affected by the thickness and inner diameter of the ring. The ratio between the tangent stiffness under pulling and pushing forces increases linearly when the dimension ratio, the ratio between the thickness and the inner diameter, is less than 0.12, and it shows a decreasing linear relationship at a higher dimension ratio. The stress response is also asymmetric, particularly when the stress is higher than the finishing stress of the upper plateau (σFASdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${sigma }_{F}^{AS}$$end{document}). The stress distributes unevenly in the circular case and is relatively high at the gripped points due to the concentration, making the circular ring fractured. Thus, the elliptic shape for the SE-SMA ring is proposed given its better symmetric behavior with less fracturing due to the lower corresponding stress. The higher the width-to-height (a/b) ratio is, the higher the symmetricity becomes. The tangent stiffness ratio is an exponential function of the a/b ratio. Moreover, the peak stress and difference peak stress are also presented as the exponential relationship of the a/b ratio.
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