The nonlinear models of the elastic and elastic-linear strain-hardening square plates with four immovably simply-supported edges are established by employing Hamiltons Variational Principle in a uniform temperature fi...The nonlinear models of the elastic and elastic-linear strain-hardening square plates with four immovably simply-supported edges are established by employing Hamiltons Variational Principle in a uniform temperature field. The unilateral equilibrium equations satisfied by the plastically buckled equilibria are also established. Dynamics and stability of the elastic and plastic plates are investigated analytically and the buckled equilibria are investigated by employing Galerkin-Ritzs method. The vibration frequencies, the first critical temperature differences of instability or buckling, the elastically buckled equilibria and the extremes depending on the final loading temperature difference of the plastically buckled equillibria of the plate are obtained. The results indicate that the critical buckling value of the plastic plate is lower than its critical instability value and the critical value of its buckled equilibria turning back to the trivial equilibrium are higher than the value. However, three critical values of the elastic plate are equal. The unidirectional snap-through may occur both at the stress-strain boundary of elasticity and plasticity and at the initial stage of unloading of the plastic plate.展开更多
基金The project supported by the National Natural Science Foundation of China(10272002)the Doctoral Program from the Ministry of Education of China(20020001032)
文摘The nonlinear models of the elastic and elastic-linear strain-hardening square plates with four immovably simply-supported edges are established by employing Hamiltons Variational Principle in a uniform temperature field. The unilateral equilibrium equations satisfied by the plastically buckled equilibria are also established. Dynamics and stability of the elastic and plastic plates are investigated analytically and the buckled equilibria are investigated by employing Galerkin-Ritzs method. The vibration frequencies, the first critical temperature differences of instability or buckling, the elastically buckled equilibria and the extremes depending on the final loading temperature difference of the plastically buckled equillibria of the plate are obtained. The results indicate that the critical buckling value of the plastic plate is lower than its critical instability value and the critical value of its buckled equilibria turning back to the trivial equilibrium are higher than the value. However, three critical values of the elastic plate are equal. The unidirectional snap-through may occur both at the stress-strain boundary of elasticity and plasticity and at the initial stage of unloading of the plastic plate.
