Investigation of equilibrium states of viscoelastic circular plates by the deformation map technique

The geometrically non‐linear response of a circular plate is investigated by means of a ‘deformation map’. The plate is subjected to static radial forces and bending moments, both uniformly distributed along the supported edges, in addition to a transverse load. The deformation map gives the complete picture for the investigated structure. The classical formulation of large deformation for the above‐mentioned problem goes back to Timoshenko (1940). To create a deformation map, it is necessary to convert the boundary value problem into an initial value problem (Cauchy's problem). The Runge‐Kutta (RK) method can then be used to solve numerically the equilibrium equations for the above‐mentioned circular plate. In the paper several kinds of transverse loading are considered and their influence on the plate response is examined. It is shown that in some cases the plate's behaviour is chaotic‐like (unpredictable), in the sense that various equilibrium states are possible for a certain given set of loads. Yet, it is shown that the viscoelasticity reduces the range of the possible equilibrium states, and thus stabilizes the system.