Construction of elastoplastic shallow panels manufactured by stretching from sheet metal

Abstract

In the article, in a geometrically and physically nonlinear formulation, the problem of the stress-strain state of shallow shells on a rectangular plane under pressure loading is solved. The solving equations of the theory of flexible shallow shells are obtained on the basis of the Henki-Ilyushin deformation theory of plasticity and the equations of the geometrically non-linear theory of shells, which contain quadratic terms with respect to the angles of rotation of the normals to the median surface. The geometrical parameters of the median surface are taken in the initial undeformed state. The equations are written in a form that makes it possible to carry out numerical calculations of problems with allowance for geometric and physical nonlinearities or only with geometric nonlinearity, to take into account unloading, compressibility of the material and secondary plastic deformations. The results of numerical calculations of critical loads, unloading zones and secondary plastic deformations are presented. Recommendations are given on the choice of geometrical parameters when designing shallow shells.