Mathematical Modelling of Circular Corrugated Membranes

The paper presents a technique for determining bifurcation points for circular corrugated membranes. The applied Kirchhoff-Love theory for non-shallow shells was used as a base for deriving nonlinear as well as linearized boundary value problems of equilibrium. Two areas of applications considered: the targeted introduction of small technological changes in the shape of the cup for the elimination of unwanted bifurcation points to provide the work of the shell in an axisymmetric mode and shape optimization problems related with obtaining linear loading diagram for a sufficiently large values of the shell strains. It was shown that the experimentally manifested sensitivity of a spherical dome to imperfections is associated with a large number of closely located bifurcation points along non-axisymmetric modes. The considered example of the genetic algorithm usage to the problem of the shell shape optimization demonstrated its efficiency and reliability.