OPTIMIZATION OF PHYSICAL AND GEOMETRICAL PARAMETERS OF A CIRCULAR AXISYMMETRIC DIAPHRAGM WITH A RIGID CENTER

Abstract

The mathematical model of an isotropic circular plate-membrane with a non-deformable fixed central disk loaded by a uniformly distributed static load is considered in a linear formulation. On this basis, the extreme problem of determining the rational physical and geometrical characteristics of an elastic element from the condition of the maximum of the target function of the thrust (permutation) force with two coupling equations in the form of the classical Huber-Genke-Mises strength hypothesis and a geometrical relation limiting the membrane thickness in accordance with the known fundamental Kirchhoff assumptions of the technical theory of small plate bending is solved. To illustrate the proposed algorithm and calculation procedure, a numerical example of the selection of optimum parameters of a manganese steel diaphragm with given dimensions of thickness and outer radius is presented. The results of the work can be used in the process of designing high-precision membrane-type pressure gauges, widely used in mechanical engineering, aviation, instrumentation, and construction in the design of pressure tanks with controlled excess pressure of gas or liquid.