Study On The Deformation Problem Of Permeable Plate And Shell Under The Presence Of A Fluid

In recent years,with the rapid development of society,economy and industry,the fluidstructure interaction is widely used in various industrial research.Because there are many assumptions in solving the fluid-structure interaction,which can not be completely consistent with the actual engineering research,people pay more and more attention to the theoretical research of the fluid-structure interaction.The small deformation problem is targeted and solved using united Lagrangian-Eulerian method for ideal fluid around a permeable elastic cantilever thin beam-plate.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 could be ignored.Based on the theory of elastic thin shell and kinetic equation of the contact surface,the deformation equation of permeable elastic thin beam-plate is obtained.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.Therefore,the deflection for small deformation of the thin plate in the transverse flow can be given,and then the stress component and the bending moment of the thin plate can be obtained.The large deformation problem of a permeable elastic cylindrical shell under the ideal fluid is solved by using united Lagrangian-Eulerian method.It is assumed that the holes are dense and uniformly distributed along the generatrix direction of the shell,and the permeable direction of the fluid through the shell is consistent with the normal direction of the deformed surface of the shell.According to the internal pressure of the shell,the curvature change of the neutral planes,the interaction of membrane forces and other factors,the bending problem of the shell is deduced.Using the linear permeability relation and the law of conservation of mass,the blocking pressure of the shell is obtained,and then the curvature parameter equation of the cylindrical shell is given.The curvature parameters are obtained by solving the equation.According to the relationship among curvature parameters,flow velocity and deflection parameters,the deflection,tangential displacement and the bending moment of the cylindrical shell in the transverse flow deformation are obtained.Through the numerical example,the deflection and stress of permeable elastic cantilever thin beam-plate are caused by small deformation are analyzed by different flow velocity and elastomer parameters,the change of the bending moment of thin plate is discussed;the deflection and tangential displacement of permeable elastic cylindrical shell are caused by large deformation are analyzed by different flow velocity and elastomer parameters,and the change of the bending moment of cylindrical shell is discussed.