“…For determining the load carrying capacities of structures; the stability criterion, as well as the strength and stiffness criteria, must be considered especially for the structures having thin-walled members. There are, mainly, two types instability: namely, bifurcation of equilibrium [1][2][3][4][5][6][7][8][9][10][11], and snap-buckling. Snap-through behaviour of structural elements (especially; shallow spherical shells, shallow arches and initially imperfect rods which have been used in many engineering, biological, industrial and scientific systems and have been subjected to severe external effects) is a very important physical phenomenon, not only for engineers but also for the scientists dealing with various structural systems.…”