On one hand, the integral of the membrane theory occurs in the formula for boundary effects and on the other hand, the oscillating part of the solution occurs in the formula for the membrane state.
The question whether a membrane theory can determine tangential characteristics of shell deformation in a transient process was also of Alumae's interest.
In this study, the existing equations of an orthotropic shell were obtained, by using the hypothesis of membrane theory
. Then, the equations were solved for a sphere shell as a parachute and it appears that the values of force in main axels are always positive and we can conclude that all of the forces into the parachute are tension force.
The Lagrangian equation together with an assumption of the membrane theory
is used in the finite element implementation.
It is reasonable to apply the membrane theory
to study the deformation of PET during this process.
In this work, a Galerkin based finite element method is implemented for the solution of the set of PDEs resulting from membrane theory
(3), and examples of free and confined inflation are given.