Elasto-plastic behaviour of double-curved shells under a concentrated load

The paper presents the application of the so-called geometrical elements method to the solution of the elasto-plastic behaviour of spherical shells subjected to an axisymmetrical concentrated load. The approach is based on the observation that during large deformations, the shell structure deforms in a nearly isometrical manner. The shell is sub-divided into elements of two kinds: purely-isometrically deformed elements and quasi-isometrically deformed elements. Equilibrium of the structure is defined by the stationariness of the total potential energy. The total energy is compared with Pogorelov's result for the same strain energy. The solution obtained defines the large deformation behaviour and motion of the plastic zones on the surface of the shell.A simplified solution for similar problems of the shells with double positive Gaussian curvature is also presented.