GAO Xin-yue.Study on Small Deformation of Permeable Elastic Cantilever Thin Beam-Plate in a Cross-Flow[J].Science Technology and Engineering,2020,20(1):38-42.

Study on Small Deformation of Permeable Elastic Cantilever Thin Beam-Plate in a Cross-Flow

DOI：

 作者 单位 高欣悦 燕山大学理学院 郝亚娟 燕山大学理学院

采用相容拉格朗日-欧拉法,求解可渗透弹性悬臂梁式薄板在理想流体横向绕流下的小变形问题。假设弹性薄板的孔很小且均匀分布,不会对其弯曲刚度及外部流场产生影响,忽略小孔所造成的阻力。根据弹性薄壳理论和接触面动力学方程得到可渗透弹性梁式薄板的变形方程。利用线性渗透关系式及质量守恒定律求解薄板的阻滞压力。采用泰勒展开方法得到挠度函数和引起薄板变形的流体势函数待定参数的方程式,解方程求出待定参数,即得到薄板横向绕流发生小变形的挠度,进而可求出应力分量。通过具体算例,分析了流速、板的几何尺寸及渗透参数对可渗透弹性悬臂梁式薄板挠度、应力大小的影响。

The small deformation problem by united Lagrangian-Eulerian method for ideal fluid around a permeable elastic cantilever thin beam-plate is solved. Assuming that the holes of the elastic thin plate are small and uniformly distributed, the bending stiffness and external flow field of the plate will not be affected, and the resistance caused by the holes will be neglected. Based on the theory of elastic thin shell and kinetic equation of the interface , the deformation equation of permeable elastic thin beam-plate is gained.The blocking pressure of thin plate is solved by using the linear permeability relation and the law of conservation of mass. The equation of undetermined parameters of deflection function and of fluid potential function causing the deformation of thin plate is obtained by Taylor expansion method. The undetermined parameters are obtained by solving the equation. That is, the deflection for small deformation of the thin plate in the transverse flow can be given, and then the stress component can be obtained. The effects of flow velocity, geometric size and permeability parameters on the deflection and stress of a permeable elastic cantilever thin beam-plate are analyzed through a numerical example.

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