Dynamic and buckling analysis of a thin elastic-plastic square plate inca uniform temperature field

The nonlinear models of the elastic and elastic-linear strain-hardening square plates with four immovablysimply-supported edges are established by employing Hamil-ton’s Variational Principle in a uniform temperature field.Theunilateral equilibrium equations satisfied by the plasticallybuckled equilibria are also established.Dynamics and stabil-ity of the elastic and plastic plates are investigated analyti-cally and the buckled equilibria are investigated by employingGalerkin-Ritz’s method.The vibration frequencies,the firstcritical temperature differences of instability or buckling,theelastically buckled equilibria and the extremes dependingon the final loading temperature difference of the plasticallybuckled equillibria of the plate are obtained.The results indi-cate that the critical buckling value of the plastic plate is lowerthan its critical instability value and the critical value of itsbuckled equilibria turning back to the trivial equilibrium arehigher than the value.However,three critical values of theelastic plate are equal.The unidirectional snap-through mayoccur both at the stress-strain boundary of elasticity and plas-ticity and at the initial stage of unloading of the plastic plate.