Application of Genetic Algorithms to the Shape Optimization of the Nonlinearly Elastic Corrugated Membranes

Abstract

Corrugated membranes are extremely important structural parts of a great number of devices, highly sensitive pressure sensors in particular. In engineering of corrugated shapes different factors could be taken into account as crucial. Among them – membrane’s work without buckling, buckling for the prescribed load, flatness of the membrane characteristic – dependence of the applied pressure on the liquid or gas volume, a lack of the plastic deformation and so on. In this paper an approach to different problems of optimization and design using genetic algorithm is proposed. To model elastic behavior of the membrane the non-linear equations based on the Kirchhoff-Love hypothesis and not imposed constrains on the shallowness of the membrane’s shape are used. Several multi-parameter families of the axially symmetric “design”, i.e. functions of the shape that describe the dependence of the middle surface prominence on the membrane radius, are considered. These designs were obtained due to special modifications of spherical dome, conical membrane and their integration. The value of the linear section length of the membrane characteristic served as an optimality criterion. The paper presents modified genetic algorithm, describes refinement mechanism of its settings and observes examples of the designs, which are optimal in the specified shape classes.