Dissertations and Theses

Date of Award


Document Type



Mechanical Engineering

First Advisor

Honghui Yu


membrane, wrinkling, thin film, post-buckling, finite element method


Membranes and thin film structures are widely used in modern technologies. Applications include solar sails and sunshields in space missions, biological membranes and flexible circuit boards. Wrinkling of membrane or a stiff film on a soft substrate may occur in either desired or unwanted patterns. This work tries to obtain some understanding on the wrinkling phenomenon and provide guidance in avoiding wrinkling or effectively controlling the wrinkle patterns.

Many works have been published about wrinkling in the thin sheets since the 20th century. However, there is no simple analytical way to systematically characterize the wrinkling in these studies. In this work, a simple energy method is proposed to calculate the critical strain for the wrinkle onset, the number of wrinkles, the wrinkle amplitude and the radius of the wrinkled region on a pre-tensioned circular membrane under torsional load at the inner hole of the membrane. The results are compared with those from the commercial finite element analysis software ABAQUS.

In the eigenvalue and eigenmode buckling analysis with finite element method, the number of wrinkles is relatively sensitive to the pre tensile stretching, the mesh size and the element types, especially for the thin membrane cases. The reason for the sensitivity is explained by the analytical solution proposed. The final converged results from FEM on the critical buckling load and the number of wrinkles agree well with those from the analytical method. The post-buckling analysis indicates the existence of the energy barriers among different eigenmodes and the uncertainty of the final post-buckling shape.

Compared with the membrane case, a stiff thin film on a compliant substrate exhibits similar features when it is twisted at the center of the top surface. Same as in the membrane case, the critical strain for wrinkling and the wrinkle patterns are sensitive to the ratio of inner radius and thickness, but are insensitive to the size of the outer radius as long as it is above several times of the inner radius. The effect of stiffness ratio of the film and the substrate is similar to that of pre-tension in the membrane case. When the relative stiffness of the compliant substrate increases, the number of wrinkles also increases same as the effect of pretension in the membrane case.

Available for download on Monday, May 24, 2021