M.Sc Thesis
M.Sc Student Ofir Yoav Analysis of Stresses and Wrinkles in a Parachute Canopy Model Using "Wrinkle Fields" Department of Aerospace Engineering Professor Dan Givoli Professor Emeritus Avinoam Libai (Deceased)

Abstract

We have analyzed the deformation and stresses in a parachute canopy model. The parachute is assumed to be in a steady state, and wrinkles which form over parts of the surface are taken under consideration. The parachute is presented as an axisymmetric hyperelastic shell membrane. The shape of the undeformed canopy is given. In addition, the canopy may have a small hole at its apex. The canopy is loaded by the air pressure, assumed to be uniform distributed, and the circumferential forces applied by the strings. The problem is strongly nonlinear, since the deformation of the canopy is very large. There is a coupling between the force loading and the deformation, where the loading direction is dependent on the deformation. The basic case were investigated is of a canopy made of a Hookean material, and considered as an isotropic ideal membrane that cannot carry compressive stress resultants. After that we have considered a non-ideal (but still isotropic) membrane, which is slightly stiffened.
Three extensions were made to the above: A canopy loaded by non-uniform distributed (but known) air pressure; An orthotropic canopy; A canopy made of a Neo-Hookean material.

Since the canopy cannot carry compressive stress resultants, wrinkles form over specific regions of the surface. Those wrinkles have to be taken under consideration while solving the parachute problem, since they affect the stresses distribution and the deformation of the canopy. Here we consider this affection by using "wrinkle fields", which is an effective formulation of the wrinkles through the material law.

The problem was attacked by using a numerical iterative procedure: On every iteration, the governing equations of the stresses and the deformation were solved by using a shooting method.  It turned out that the numerical process is fast and efficient, also due to the fact that all the calculations were explicit.

After solving the desired cases we saw wrinkled regions on the surfaces of the canopies. The results of all the examined cases indicate a clear correlation between the magnitude of the loading forces and the relative size of the wrinkled region on the surface of the canopy.

In non-ideal canopies we could see wrinkles only when the applied forces were large enough to overcome the stiffness of the membrane.

The behavior of  canopies with a hole at the apex and without a hole turned out to be quite similar.