The Ritz Research And Computer Simulation On Dynamic Buckling Of Plates Under In-plane Step Loading

The plate as a basic element of the common structure is widely applied to thefields of machinery, architecture, aviation, spaceflight, etc. The dynamicbuckling of plates has been received widespread attention by researchers.Because the researchers’ viewpoints and the operating methods are different, thefinal results of dynamic buckling are inconsistent. In this paper, based on theVariable Separation method, a new method of Ritz method combined withAbraham de Moivre’s formula is used for the dynamic buckling analysis ofplates subjected to in-plane step loading.The main work is as follows:1. Using the Reissner plate assumption, the rotational kinetic energy andshear deformation effect is considered in the theory and the governing equationsof dynamic buckling on the plates under the step load are deduced by Hamiltonprinciple.2. Taking into account the effect of stress wave, a new method of Ritz method combined with Abraham de Moivre’s formula is proposed for thedynamic buckling analysis of plates subjected to in-plane step loading. Thetrigonometric function including time items is used as the trial function.According to the parity of function, the effective dynamic buckling solution isdeduced, which satisfies the boundary conditions and constraint conditions ofthe wave front. In addition, based on Abraham de Moivre’s formula, thegoverning equation has been simplified, and then the critical buckling load ofplates has been obtained when the reflection of the stress wave does not occur.At the same time, the critical buckling load of plates has been obtained bythe Variable Separation method. The critical buckling load curve is obtained byRitz Method using MATLAB software, and this curve is compared with thecurve of the Variable Separation method. The results show Ritz methodcombined with Abraham de Moivre’s formula can be effectively applied in thestudy of dynamic buckling.3. Comparing the critical buckling load curves, the influence of sheardeformation on the critical buckling load with different thickness is discussedand the changing trends can be obtained. The influences of plies angle, widthand orders of buckling mode on the dynamic buckling load are studied, and theinfluence of buckling mode orders on amplitude of the buckling mode isanalyzed.4. The dynamic buckling studying of plates with different thicknesses andwidths are simulated by ABAQUS. Time-history curves of strain on the key elements and the dynamic buckling mode in the direction of propagating waveare obtained by ABAQUS. The simulating results agree well with the theoreticalresults. The maximum error is less than5percent within a limit of allowableerror. Observing the local modes of dynamic buckling on plates from thepostprocessing of ABAQUS, the buckling is growing with time, and thebuckling mode is also added.