A Study Of Wrinkling And Modal Analysis Of In-space Planar Membrane Structures

In-space membrane structures have been widely studied in recent years. It is indicated that the prediction and controlling of membrane wrinkling and modal analysis of the membrane structure are very difficult scientific problems and needed to be solved whether from applications or theoretical analysis of membrane structures. In this thesis, the plane membrane structure is our subject to be researched. We study the generation mechanism of membrane wrinkling, calculate the characteristics of wrinkling and analyze the development of wrinkling. At the same time, we conduct a modal analysis and calculate the frequency of a membrane which has a circular boundary consisted in a slope-membrane structure.Wrinkling analysis is usually divided into two categories, depending on whether the wrinkling model considers the small flexural rigidity of membrane material. In the first category, the model ignores the flexural rigidity of membrane material. Based on the tension tensor theory, we get two kinds of wrinkling model, the tension force state model and the energy function model. Both of the wrinkling models classify the tension force state of any point of a membrane into three states-tension, wrinkling and relaxation. Also, the commonly used criteria for wrinkling are that the main stresses of any point of a membrane are nonnegative. In this thesis, we give another equal form which uses the Cartesian(X, Y, Z components) coordinate system to describe the relationships and also we prove that the two forms have the same essence.In the second category, the model considers the flexural rigidity of membrane material. Based on the large deformation and small strain hypothesis, this thesis gives another wrinkling model using the Von Karman shell theory. First, this wrinkling model describes the displacements, stresses and strains using the slow varying Fourier series and then solves the unknowns in the displacements Fourier series. Applying this model, we give the analytical solution of the wrinkling of uniform tensioned membrane and also give the numerical solution of the wrinkling of non uniform tensioned membrane and the condition where and when the wrinkling starts. Second, we write a program to study the generation and development of wrinkling using the finite software Ansys. For a rectangular membrane standing shear force on one of its edges, the results indicate that the amplitude and number of wrinkling become larger with the larger shear displacement and the distances between any nearby wrinkling get shorter. What’s more, the new wrinkling generates from the middle place of the rectangular membrane and gets uniform and the wrinkling located on the edges hardly changes its location.For a kind of space pre-tensioned membrane structures, a non-dimensional dynamic influence function method is proposed by S.W.Kang, which can efficiently figure out the frequencies of arbitrarily shaped, homogeneous membranes with the fixed boundary. Firstly, a model using the Bessel function as the solution to the partial differential equation for transverse vibration of thin membrane is established which can be used to calculate the natural frequencies of membrane with different radius of curvature and chord length. Secondly, for planar pre-tensioned membrane, we calculate the natural frequencies of circular, L-shape and subdivide arc boundary of membranes. Finally, on the condition that stresses are unchanged, this paper analyzes the relationship between the natural frequencies and boundary geometrical parameters of membrane, and indicates that the boundary which makes the area of membrane larger matches higher frequencies, vice versa. After all, we build the optimization model which optimizes the boundary geometrical parameters. Last we build the finite element model containing the membrane and slopes and the model indicates the method availability.