热机载荷下形状记忆合金梁超静定问题分析

兰州理工大学学报 ›› 2021, Vol. 47 ›› Issue (1): 158-163.

热机载荷下形状记忆合金梁超静定问题分析

杨静宁, 王永祥, 唐健

兰州理工大学理学院, 甘肃兰州 730050

收稿日期:2019-11-18 出版日期:2021-02-28 发布日期:2021-03-11
作者简介:杨静宁(1969-),男,甘肃静宁人,副教授.
基金资助:
国家自然科学基金(11862012)

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

YANG Jing-ning, WANG Yong-xiang, TANG Jian

School of Science, Lanzhou Univ. of Tech., Lanzhou 730050, China

Received:2019-11-18 Online:2021-02-28 Published:2021-03-11

摘要/Abstract

摘要： 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.

关键词: 形状记忆合金, 超静定, 相边界, 非线性

Abstract: 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.

Key words: shape memory alloy, statically indeterminate, phase boundary, nonlinear

中图分类号:

O343

杨静宁, 王永祥, 唐健. 热机载荷下形状记忆合金梁超静定问题分析[J]. 兰州理工大学学报, 2021, 47(1): 158-163.

YANG Jing-ning, WANG Yong-xiang, TANG Jian. Analysis of statically indeterminate problem of shape memory alloy beam under thermal and mechanical loads[J]. Journal of Lanzhou University of Technology, 2021, 47(1): 158-163.

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