基于常应变单元的空间薄膜结构动力学建模与分析

Dynamic modeling and analysis of space membrane structure based on constant strain element

为了保证薄膜结构构成的充气式可展开天线、网状可展开天线和太阳帆等航天器的表面精度、信号增益等工作性能,需要对空间薄膜结构的动力学展开性能进行分析。由有限元离散方法将整个薄膜反射面离散为众多常应变三角形单元,这些单元的节点可视作质点;考虑这些三角形单元的弹性势能,由最小势能原理得到三角形单元的平衡方程,从而实现单元上点的应变和单元三条斜边线应变之间的转换;最后,为了防止展开过程中单元间接触,建立接触模型,由薄膜反射面的离散拓扑组集结构的质量矩阵和刚度矩阵,并建立动力学方程。基于文中方法对具体算例进行计算和分析,结果表明,动力学模型能够很好的模拟薄膜的展开过程,可应用于薄膜结构的展开性能分析中。

It is necessary to analyze the dynamic deployment performance of space membrane structures for ensuring the surface accuracy and signal gain of spacecraft composed of thin membrane structure,such as inflatable deployable antennas,mesh deployable antennas,and solar sails.The whole thin membrane reflector was discretized into many constant strain triangular elements of which the nodes could be regarded as particles by using the finite element method.Under the premise of considering the elastic potential energy of the triangular element,the equilibrium equation of the triangular element was obtained by the principle of minimum potential energy,so as to realize the transformation between the strain of the point on the element and the strain of the three oblique edges of the element.Finally,the contact model was established to prevent the contact between elements in the deployment process from happening,and the mass matrix and stiffness matrix of the structure were assembled by the discrete topology of the thin membrane reflector,and the dynamic equation was established.Based on the results the dynamic model can simulate the deployment of the membrane accurately,and can be applied to analyzing the deployment performance of the membrane structure.