Determination of parameters of plastic deformation of elliptic membranes

Abstract

Introduction. Thin-walled structural elements, combining lightness with high strength, are widely used in all industries. Widespread round design elements. However, based on the functional purpose, thin-walled structural elements of various shapes in plan are becoming more and more common. Methods. A technique has been developed for the study of thin elliptic membranes for the case of plastic deformation under the action of uniform pressure. The deflections of the membranes in the experiment are more than ten thicknesses. In this regard, to solve the problem, the following are used: geometric nonlinear relations for the deformations of the middle surface (according to Kh.M. Mushtari and K. Z. Galimov), relations for finite displacements and deformations for curvature expressions (according to K.Z. Galimov), physical relations (according to the theory of plasticity A.A. Ilyushin). Due to the smallness of the membrane thickness, only tensile membrane strains and forces are taken into account. The problem is solved by the Bubnov - Galerkin method and reduced to solving a nonlinear system of three algebraic equations. The “shooting” algorithm for solving the resulting system of equations is described. Results. The work on the assessment of the reliability of the results. To estimate the error, the comparison of the calculation results with the experimental results of G.D. Golovlev was also performed. An example of the calculation of an elliptical membrane is considered.