Abstract
The paper discusses some questions of equilibrium, stability and shape optimization of circular membranes with arbitrary profile along the meridian. Such membranes can be used as a flexible barrier to isolate the media on one side of a diaphragm from media on the other side, whilst allowing the transmission of pressure with minimal loss. The main goal of the analysis is to propose techniques for designing such shape of corrugated membranes that satisfy the requirements of so call “slow growing linear or almost linear” behavior of the pressure-volume diagram. 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. A genetic algorithm was used to evaluate and optimize the characteristics of corrugated membranes. The presented analysis of the membrane with the maximum linear stroke showed its efficiency and reliability. At the same time, special attention should be paid to the basic parametrization used in modelling, since the mathematically optimal solution is not always suitable from the point of view of membrane production technology.
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