STACER是一种航天器上广泛应用的伸展机构,其储能部件由薄壁钢带经冷加工涡卷最终成型为螺旋管状.由于伸展长度可达装载高度的几十倍,钢带在展开过程中呈现为大挠度、大应变形变,机构伸展力的计算必然涉及强非线性问题;同时,钢带的构型、边界条件在伸展过程中不断变化,这些因素又增加了问题的难度,致使常用的商业软件已无法直接处理此类问题.此研究工作应用变分方法的思想,以研究钢带变形的几何特性为基础,构造出钢带构型恰当的可能函数空间,并利用形状函数随伸展长度的变化规律求出钢带的主应变以及变形能,再利用势能极小原理,确定出钢带的真实构型以及相应的变形能,最终利用变形能和虚功原理得出伸展力.这一方法既可以简化计算又可以得到钢带形状函数、伸展力的近似解析式,为伸展力影响因素的定量分析提供了条件. STACER is a widely used extension mechanism on spacecraft whose energy storage components are made of thin-walled steel strip and finally formed into a spiral tube shape by the cold-formed scroll.Due to the extension length up to several tens of times the loading height, the strip appears in the unfolding process as Large deflection, large strain deformation, the calculation of mechanical expansion inevitably involves a strong nonlinear problem; the same time, strip configuration, the boundary conditions in the stretching process changes, these factors have increased the difficulty of the problem, resulting in commonly used commercial software It has been impossible to deal with such problems directly.In this work, based on the idea of ​​the variational method, based on the study of the geometric characteristics of the strip deformation, the appropriate possible function space of the strip configuration is constructed, and the change of the shape function with the extension length The law of the main strain of steel strip and deformation energy, and then use the principle of very small potential energy to determine the real configuration of steel strip and the corresponding deformation energy, the final use of deformation energy and virtual work principle derived stretching force.This method is both Which can simplify the calculation and obtain the approximate analytic formula of the shape function of the strip and the stretching force, which provides the conditions for the quantitative analysis of the influencing factors of the stretching force.