Based On Catastrophe Theory On The Lateral Buckling Critical Load Of Combination Arch

With the development of urban transportation, more and more investment in large-spanarch bridge for it’s unparalleled advantages to the construction.However, the lateral stabilityissues become more and more prominent, and often be the controlling factors of the design.Soinstability of the arch bridge is necessary. This article is based on catastrophe theory, completeda series of studies:(1) In this paper, under uniform radial loads arc single arch and Assembling arch for thestudy, the structure of the energy expression through the to set the arch roll flexiondisplacement function, established the structure of the energy expression.Through mathematicaltransformations, the first roll flexion cusp catastrophe model, derived equation of equilibriumsurface M of the system equation and bifurcation point set B,Then, through the analysis ofsystem instability conditions,calculated the bifurcation set.Thereby get the the formula of loadbuckling of by the the system roll.Cusp catastrophe model M surface graphics, and explainedthe roll buckling conditions and system equilibrium relationship.(2) Through a series of different span，different span ratio,section of arc single arch andassembling arch’s finite element numerical solution and analyzed solution,the results show thatdeduced based on catastrophe theory the single arc arch and groups fight arch roll bucklingcritical load of the analyzed solution and finite element numerical solutions are in goodagreement.The correctness of the method of authentication of the formula is true.The results ofthis study has opened up a new way for the arch structure surface buckling research.(3) Studyed the experimental measured load, displacement and strain data,constructed thepotential energy.Data fitting by the least squares method,Will the cusp catastrophe the potentialenergy into standard type.Applied catastrophe theory to establish a system of displacement andstrain mutation mutation criterion criterion.Different mutations in different starting pointestablished criteria, the resulting structure is not necessarily the same.Consolidated resultsshows various criteria.Instability first occur plane, plane ensuing instability.Displacementsmutation discrimination more slowly, while the strain a little more sensitive mutationdiscrimination.Identification and mutation observed in experiments and the measuredload-displacement curve results to determine the same.t.The mutant discriminant method madeup the load-displacement curves can not be precisely determine yield at what occurs under loadyield defects.