The Ritz-De Moivre Method Research And Computer Simulation On Dynamic Buckling Of Bars Induced By Axial Stress Wave

Bars are the basic structural units in engineering, the application of themcan be seen everywhere. Buckling problems, especially the dynamic bucklingproblems draw most attentions of the global scholars. The methods of solvingthe problems are different, the final results are also different. In this paper,several aspects are studied in the following:1. The significance and background of research was briefly described inthis paper. The research situation of the buckling of bar and the compositematerial bar, the ritz method and computer simulation in buckling problemswere explained.2. Considering the effect of stress wave, the dynamic buckling problem ofmetal bar under axial step load was analyzed. The Boundary conditions: one endsimply supported, one end fixed supported and one end clamp, one end clamped.The nonlinear control equations of rod, wave-front constraints and theexpression of dynamic buckling critical load was deduced by considering theshear deformation, rotation effect. The influence of shear deformation on thecritical buckling load was briefly described. 3. The control equations and wave-front constraints of the compositematerial rod were deduced by considering the shear deformation and rotationeffect based on the Hamilton principle. The expression of the critical dynamicbuckling load was obtained by considering the effect of stress wave based on DeMoivre. The accurate modal function was acquired by using the Ritz method.The Boundary conditions: one end simply supported, one end fixed supportedand one end clamp, one end clamped.4. The ABAQUS finite element analysis software was used to carry out thesimulation for the dynamic buckling of metal bar under axial step load. Thebifurcation of strain time-history curve of the symmetric elements on the top andbottom surface of a metal bar were used to verify the critical buckling time, weobtained the simulation value of critical load and the buckling modal graphs.This paper also uses the difference of critical buckling times to discuss theinfluence of bar buckling by stress wave reflected. The critical buckling loadafter stress wave reflected is much smaller than before. In bar’s buckling: thelonger the critical buckling time, the smaller the critical buckling load.