热机载荷下形状记忆合金梁超静定问题分析

基于梁的弯曲变形理论及形状记忆合金材料的应力-应变关系,在考虑形状记忆合金材料相变临界应力与临界温度关系的情况下,分析了形状记忆合金超静定梁在非纯弯曲条件下的非线性力学行为.为了直观描述梁在拉压两侧相变的不对称性,引入拉压不对称系数,分析了各相变阶段横截面上的应力分布,通过求解平衡方程,得到了横截面中性轴位移、曲率以及相边界沿轴向的变化情况.结果表明:随着温度的升高,曲率减小;相边界不对称性越明显;中性轴最大位移在梁上的位置随之改变,且最大位移值不变.

Analysis of statically indeterminate problem of shape memory alloy beam under thermal and mechanical loads

Based on the bending deformation theory of beam and the stress-strain relationship of shape memory alloy, and further taking the relationship between critical stress and critical temperature of the shape memory alloy into account, the nonlinear mechanical behavior of statically indeterminate beam of shape memory alloy under the condition of impure bending is analyzed in this paper. In order to describe directly the asymmetry of phase transformation on both sides of the beam under tension or compression, a tension-compression asymmetry coefficient is hereby introduced. The stress distribution on cross section at each phase transformation stage is then analyzed. By solving the equilibrium equation, the displacement and curvature of neutral axis and the change of phase boundary along the axial direction are therefore obtained.