STACER is a kind of widely used deployable mechanism on spacecraft, whose thin-wall steel strip is scrolled and eventually formed a spiral tube. Because the compressed tube can be extended dozens of times of its initial height;large deflection with large strain appears, and the deformation scope of the strip are continuously changed during the deployment, the deployment force is extremely difficult to solve even for numerical simulation. Here, using the variational method and the geometric characteristics of the deformation, a technique is proposed to solve the deployment force: at first the proper and possible shape function is constructed, and then the principal strain and the deformation energy are calculated by means of the shape function,finally the deployment force is carried out through the principle of minimum potential energy. This method makes the numerical procedure simplified and gives approached expression of the strip shape and the deployment force.%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。
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