The structural stability of a lightsail under the intense laser flux necessary for interstellar flight is studied analytically and numerically. A sinusoidal perturbation is introduced into a two-dimensional thin-film sail to determine if the sail remains stable or if the perturbations grow in amplitude. A perfectly reflective sail material that gives specular reflection of the laser illumination is assumed in determining the resulting loading on the sail, although other reflection models can be incorporated as well. The quasi-static solution of the critical point between shape stability and instability is found by equating the bending moments induced on the sail due to radiation pressure with the restoring moments caused by the strength of the sail material and the tension applied at the edges of the sail. From this quasi-static solution, analytical expressions for the critical value of elastic modulus and boundary tension magnitude are found as a function of sail properties (e.g., thickness) and the amplitude and wave number of the initial sinusoidal perturbation. These same expressions are also derived from a more formal variational energy (virtual work) approach. A numerical model of the complete lightsail dynamics is developed by discretizing the lightsail into rectangular finite elements. By introducing torsional and rectilinear springs between the elements into the numerical model, a hierarchy of models is produced that can incorporate the effects of bending and applied tension. The numerical models permit the transient dynamics of a perturbed lightsail to be compared to the analytic results of the quasi-static analysis, visualized as stability maps that show the rate of perturbation growth as a function of sail thickness, elastic modulus, and applied tension. The analytic theory is able to correctly predict the stability boundary found in the numerical simulations. The stiffness required to make a thin lightsail stable against uncontrolled perturbation growth appears to be unfeasible for known materials, however, a relatively modest tensioning of the sail (e.g., via an inflatable structure or spinning of the sail) is able to maintain the sail shape under all wavelengths and amplitudes of perturbations.

分析和数值研究了在星际飞行所需的强激光通量下光帆的结构稳定性。将正弦扰动引入二维薄膜帆以确定帆是否保持稳定或扰动的幅度是否增加。在确定帆上的最终载荷时，假定了一种完全反射的帆材料，该材料会产生激光照明的镜面反射，尽管也可以合并其他反射模型。通过将由辐射压力引起的帆上产生的弯矩与帆材料的强度和施加在边缘的张力引起的恢复力矩相等，找到形状稳定性和不稳定性之间临界点的准静态解。帆。从这个准静态解中，弹性模量和边界张力大小的临界值的解析表达式是作为帆特性（例如，厚度）和初始正弦扰动的幅度和波数的函数而找到的。这些相同的表达式也源自更正式的变分能量（虚拟功）方法。通过将光帆离散为矩形有限元来开发完整光帆动力学的数值模型。通过在数值模型中引入元素之间的扭转弹簧和直线弹簧，可以生成模型层次结构，其中可以包含弯曲和施加的张力的影响。数值模型允许将扰动光帆的瞬态动力学与准静态分析的分析结果进行比较，可视化为稳定性图，显示作为帆厚度、弹性模量和施加张力的函数的扰动增长速率。解析理论能够正确预测数值模拟中发现的稳定性边界。使薄光帆稳定以抵抗不受控制的扰动增长所需的刚度对于已知材料似乎是不可行的，但是，相对适度的帆张紧（例如，通过可充气结构或帆的旋转）能够保持帆的形状在所有波长和扰动幅度下。