Analytical Study On Frictionless Contact Between Axisymmetrically-Deformed Circular Membrane And Rigid Plate

Membrane structures are widely used in many engineering fields.Membrane structure often works in a large deflection state and its deflection is much larger than the thickness under lateral load due to its flexibility.Therefore,membrane structure problem is uaually a large deflection deformation problem,which shows srtong geometric nonlinear characteristics and is difficult to analyze in many cases.However,since the analytical solution can show qualitative and quantitative relationships between variables,the analytical solution of membrane structure problem has always been pursued by scholars.In this paper,the existing analytical solutions to the problem of axisymmetric deformation of a peripherally fixed and uniformly loaded circular membrane are reviewed.Based on the existing analytical studies,the initial stress in membrane was taken into account and the small-rotation-angle assumption was given up,circular membrane problem is solved and a new analytical solution is given.After that,this paper summarizes the problem of frictionless contact between an axisymmetrically-deformed circular membrane and a rigid plate.Based on the existing analytical work of the frictionless contact problem,the contact problem is solved by considering the initial stress of the circular membrane and abandoning the small-rotation-angle assumption,and a new analytical solution to contact problem is given.The two new analytical solutions given in this paper are obtained by considering the initial stress of the circular membrane and abandoning the small-rotation-angle assumption.So the two new analytical solutions have higher calculation accuracy and can be applied for a wider range in comparison with the existing analytical solution.However,when the initial stress is zero and the slope angle of membrane is relatively small,the existing analytical solution is still applicable.In the results and discussion,by comparing the cacuation results obtained by the analytical solutions given in this paper and the existing analytical solutions when the initial stress is zero and the slope angle of membrane is small,it may be seen that the two cacuation results are very close to each other,which shows that the analytical solution presented here is reliable.In addition,by discussing the influence of the relevant parameters,it is found that the adoption of the small-rotation-angle assumption and the existence of the initial stress will make the deflection of membrane and the contact radius become smaller,and under the same uniformly distributed load,the contact radius will decrease with the increase of the initial stress.