Snap-through of the system of open shallow axi-symmetric bimetallic shell by non-linear theory

The paper deals with stresses, strains and buckling conditions in the thin axi-symmetric shallow bimetallic shells with circular opening at the top of the shell. According to the third order theory by the Czech researcher E. Chawalla, which takes into account the equilibrium state of forces and moments acting on the deformed system, the paper presents a model for mathematical description of the system's geometry, stresses, thermo-elastic strains and displacements. The mathematical formulation is based on the theory of large displacements. As an example, the results for spherical shallow shells are shown, approximated by a parabolic function. The shells are loaded with temperature and/or with load acting at the top of the shell or at the shell's inner edge. The displacement state and the snap-through temperature are calculated numerically by the Runge Kutta algorithm of the fourth order, by non-linear shooting method.