The Stability Research On Critical Load Of A Class Of Frame With Variable Cross-section

With the bigger and higher of construction machinery equipment,the frame which was an superior engineering structure had become an important research in the stability field of structural mechanics.Until now,there were too many researches about dynamic stability and static stability for uniform cross-section frame.It’s hard to calculate the critical load for variable cross-section frame because of the varying section.And it’s impossible to calculate the critical load by Euler method.Hence,it was of theoretical and practical significance to build an effective algorithm for stability critical load and avoid overload to destroy structure.This thesis mainly studied the dynamic and static stability of variable cross-section fame under difficult vertical loadings and it is calculation of critical load.The main research contents are stated as follows:First of all,aiming at the stability problem of large thin-walled structures with variable cross-section,the optimization algorithm for the critical load of a kind of single-bay frame with symmetrical structure under symmetric loadings was studied,and the numerical method for the critical load of the thin-walled frame with variable cross-section was discussed.In the Eclipse environment,unconstrained gradient optimization program was compiled and the specific example of frame with constant section and variable cross-section were solved.With great practicability,algorithm could provide new thread for the solution of critical load in the engineering structure.Secondly,a kind of single-bay frame with symmetrical structure on arbitrary restrained under the asymmetric loading has been built.The Timoshenko beams had been separated.The deflection of each discrete point,critical load,axial force,shear force and bending moment were used as the design variables.The model of nonlinear differential equations on boundary conditions had been built.The finite difference method with optimization method and the optimization algorithm of critical load based on improved particle swarm were combined.ABAQUS had been used to check the simulation results of the example of frame with variable cross-section under the asymmetric loading.The reasonable structural resolution and design variables were used to get effective position and critical load with high precision.A mechanical relation of position and loading on frame could be better described to give a further support for engineering design and analysis.Finally,the dynamic stability of frame with variable cross-section under the asymmetric periodic loading had been analyzed.Based on the standard of Budiansky-Roth,the displacement response relates the amplitude of periodic load was got by ABAQUS.Amplitude-Response curve of frame with variable cross-section had been drew.The amplitude node of periodic loading had been find and the critical load dynamic stability had been calculated.Based on governing equation of frame bucking,The model of dynamic stability of frame had been built to calculate critical load.The error was contrasted to prove the precision of IPSO under dynamic stability.The research of this thesis will provide a feasible computing method of variable cross-section’s stability critical load for mechanical engineering.