The out-of-plane and in-plane deployment dynamics of a flexible space structure, namely, a solar sail quadrant consisting of a membrane attached to two support booms, are considered. The equations of motion of the system are obtained using a time-varying generalization of the extended Hamilton’s principle. They are then discretized via quasi-modal expansion of the deflections as truncated series involving both time- and space-dependent basis functions. Because all directions are accounted for and plate strains are used to capture the potentially significant effect of even a small stiffness on the dynamics, nonlinear terms appear in the discretized equations. To increase computational efficiency, coordinate transformations and linear algebraic manipulations are performed to make all spatial integrals time invariant. In addition, attempts are made to predict wrinkling using the Miller–Hedgepeth model: a coarse mesh is defined, the instantaneous state of each region is determined using a wrinkling criterion and averaged principal stresses, and constitutive relation of each region is adjusted based on its wrinkling state. Numerical simulations provide basic validation, sample deployment results, and a comparison against the results of an earlier linear model with only out-of-plane deflections. The stress predictions are also partially validated using previous results based on constant-size loaded membrane experiments.

考虑了灵活空间结构的平面外和平面内部署动力学，即由附着在两个支撑臂上的膜组成的太阳帆象限。系统的运动方程是使用扩展哈密顿原理的时变推广获得的。然后通过挠度的准模态展开将它们离散为截断序列，包括时间和空间相关的基函数。因为所有方向都被考虑在内，并且板应变被用来捕捉即使是很小的刚度对动力学的潜在显着影响，非线性项出现在离散方程中。为了提高计算效率，执行坐标变换和线性代数操作以使所有空间积分时间不变。此外，尝试使用 Miller-Hedgepeth 模型预测起皱：定义粗网格，使用起皱准则和平均主应力确定每个区域的瞬时状态，并根据其起皱状态调整每个区域的本构关系。数值模拟提供了基本验证、样本部署结果以及与早期仅具有平面外偏转的线性模型的结果的比较。使用先前基于恒定尺寸加载膜实验的结果也部分验证了应力预测。并根据其起皱状态调整每个区域的本构关系。数值模拟提供了基本验证、样本部署结果以及与早期仅具有平面外偏转的线性模型的结果的比较。使用先前基于恒定尺寸加载膜实验的结果也部分验证了应力预测。并根据其起皱状态调整每个区域的本构关系。数值模拟提供了基本验证、样本部署结果以及与早期仅具有平面外偏转的线性模型的结果的比较。使用先前基于恒定尺寸加载膜实验的结果也部分验证了应力预测。