The Deformation And Stress Analysis On The Post-buckling Of Cold Rolled Strip

In recent decades, China has showed a strong demand for the cold-rolled stripproducts. The production of the strip with mid-to-lower quality is relatively large while thehigh-end products are in short supply. The flatness quality can not reach the advancedinternational level. Therefore, the future development of the iron and steel industry shouldbe devoted to improving the technology of strip flatness control. As an important part ofthe shape control model, studying on the buckling model to predict the flatness is ofimportant significance for improving the quality and productivity of strip products.After thingking about the buckling process in depth, this paper points out the flaw inthe past research on the post-buckling deformation and puts forward that the criticalbuckling length differs from the buckling length. According to the actual situation, thebuckling model has been built and solved by the Ritz method, which is based on thetheory of large deflection and the minimum potential energy principle. The bucklinglength is defined as the length corresponding to the minimum strain energy of the rolledplate per length. The basic shape pattern described by the Legendre polynomial is adoptedas the residual stress and the corresponding displacement functions for the bucklingpattern in three directions are assumed. A Newton-Raphson method combined with theNewton downhill method is used to program the equation solution. Calculations for edgeand center wave defect forms have been accomplished as an example. The criticalbuckling length, buckling length, buckling amplitude and flatness have all been obtainedfor the given load profile, and the post-buckled stress has also been analyzed.As the buckling problem of the rolled strip is related with many factors, the effects ofthe residual stress, strip thickness and width on the buckling length, buckling amplitudeand flatness have been studied and discussed for edge and center wave. The critical loadthat makes the plate buckle has also been obtained in the calculation, which is usuallyobtained by a pre-buckling analysis before. Considering that the tension in the rollingprocess makes an important role in the buckling deformation, the buckling deformationand buckled stress analysis under the with-tension condition have also been studied in this paper.