对角受拉方膜褶皱变形幅值的理论预测及实验验证

THEORETICAL PREDICTION AND EXPERIMENTAL VERIFICATION OF WRINKLE AMPLITUDE IN A SQUARE MEMBRANE SUBJECTED TO DIAGONAL TENSION

柔性薄膜结构广泛应用于航天飞行器的关键部件.形面平整度是影响薄膜结构性能的主要因素之一.褶皱幅值是评价薄膜反射面天线形面平整度的重要指标.褶皱幅值的大小与垂直于褶皱方向的横向应变密切相关.本文基于薄板稳定性理论,针对对角受拉方形薄膜建立了一个能够准确预测其褶皱变形幅值的理论模型.该模型考虑了横向拉伸力对薄膜变形的影响,将垂直于褶皱方向的位移分解为由泊松效应造成的横向收缩位移、由面外变形造成的褶皱位移以及由横向拉伸力造成的拉伸位移三个部分,重新推导了褶皱幅值的理论公式.基于数字图像相关技术,对受拉方形薄膜进行了散斑实验测试.利用双目视觉三维测量系统,测量了方形薄膜的三维位移场,获得了薄膜的三维变形形貌和褶皱波形图,研究了褶皱幅值与拉伸载荷之间的非线性关系.与已有理论模型相比,该模型进一步提高了褶皱幅值的计算精度,与实验结果吻合良好.本文呈现的理论研究可为精确数值模型的建立及算法实现提供有意义的指导.

Flexible membrane structures are widely used in the key parts of aerospace vehicles.Surface flatness is one of the main factors affecting the performances of membrane structures.Wrinkle amplitude is an important factor for evaluating the surface flatness of membrane reflector antennas.Wrinkle amplitude is strongly related with the transverse strain,perpendicular to wrinkling direction.Based on the stability theory of thin plates,a theoretical model is proposed to predict the wrinkle amplitude in a square membrane subjected to diagonal tension.The effect of transverse tensile force on the membrane deformation is taken into account.The displacement perpendicular to wrinkling direction is decomposed into three parts:the transverse displacement induced by Poisson’s effect,the wrinkling displacement induced by out-of-plane deformation,and the tensile displacement induced by transverse tensile force.The formulation of wrinkle amplitude is reworked.Based on digital image correlation(DIC)technology,speckle experiment is carried out for a square membrane subjected to diagonal tension.The three-dimensional displacement of square membrane is measured by the binocular vision three-dimensional measurement system.The three-dimensional deformed shapes and wrinkle waveforms of membrane are obtained.We study the nonlinear relationship between wrinkle amplitudes and tensile loads.Compared with an existing model,our model greatly improves the accuracy of prediction to wrinkle amplitude,which is in good agreement with experimental results.The theoretical research presented in this paper can provide valuable guidance for the establishment of a fine numerical model and the implementation of algorithm.