Elastic-plastic secondary indeterminate problem for thin-walled pipe through the inner-wall loading by three-point bending

References

• Chudasama, M. K., Raval, H. K. (2014). Bending force prediction for dynamic roll-bending during 3-roller conical bending process. Journal of Manufacturing Processes 16:284–95. doi:10.1016/j.jmapro.2013.09.008
   Web of Science ®Google Scholar
• Fan, S. (1989). A new extracting formula and a new distinguishing means on the one variable cubic equation. Nature Science Journal of Hainan Teachers College 2(2):91–98.
   Google Scholar
• Feng, Z., Champliaud, H. (2012). Investigation of non-kinematic conical roll bending process with conical rolls. Simulation Modelling Practice and Theory 27:65–75. doi:10.1016/j.simpat.2012.05.007
   Web of Science ®Google Scholar
• Feng, Z., Champliaud, H., Dao, T. M. (2009). Numerical study of non-kinematical conical bending with cylindrical rolls. Simulation Modelling Practice and Theory 17:1710–22. doi:10.1016/j.simpat.2009.08.004
   Web of Science ®Google Scholar
• Gandhi, A. H., Gajjar, H. V., Raval, H. K. (2008). Mathematical modelling and finite element simulation of pre-bending stage of three-roller plate bending process. ASME 2008 International Manufacturing Science and Engineering Conference collocated with the 3rd JSME/ASME International Conference on Materials and Processing 1(2008): 617–625. doi:10.1115/MSECICMP2008-72454
   Google Scholar
• Gandhi, A. H., Raval, H. K. (2008). Analytical and empirical modeling of top roller position for three-roller cylindrical bending of plates and its experimental verification. Journal of Materials Processing Technology 197:268–78. doi:10.1016/j.jmatprotec.2007.06.033
   Web of Science ®Google Scholar
• Gerstmayr, J., Matikainen, M. K. (2006). Analysis of stress and strain in the absolute nodal coordinate formulation. Mechanics Based Design of Structures and Machines 34(4):409–30. doi:10.1080/15397730601044895
   Web of Science ®Google Scholar
• Khan, D., Biswas, K. (2010). On the evaluation of path independent integral JF∗ for circular arc crack. Mechanics Based Design of Structures & Machines 38(3):300–27. doi:10.1080/15397731003727103
   Web of Science ®Google Scholar
• Li, H. Z., Liu, M. S., Chen, H. (2006). Elastic-plastic analysis of a beam with one degree of indeterminacy under an even load. Engineering Mechanics 10:86–90.
   Google Scholar
• Li, Y. S., Li, T., Guo, X. H., Li, X. Y. (2014). A fast analytical method for statically indeterminate problems of cable-beam coupled structures. Engineering Mechanics S1:11–16. doi:10.6052/j.issn.1000-4750.2013.03.S018
   Google Scholar
• Liu, S. P. (2010). Remaining life assessment and optimal design of statically indeterminate pipe system with circumferential crack. International Communications in Heat and Mass Transfer 37(3):266–73. doi:10.1016/j.icheatmasstransfer. 2009.09.003
   Web of Science ®Google Scholar
• Liu, S. P., Ando, K. (2000). Leak-before-break and plastic collapse behavior of statically indeterminate pipe system with circumferential crack. Nuclear Engineering and Design 195(3):261–70. doi:10.1016/s0029-5493(99)00211-3
   Web of Science ®Google Scholar
• Lógó, J. (2005). New type of optimal topologies by iterative method. Mechanics Based Design of Structures and Machines 33(2):149–71. doi:10.1081/sme-200067035
   Web of Science ®Google Scholar
• Williams, H. E., Dym, C. L. (2005). Using rotations to obtain compatibility equations for statically indeterminate trusses. Journal of Structural Engineering 131(2):353–58. doi:10.1061/(asce)0733-9445(2005)131:2(353)
   Web of Science ®Google Scholar
• Xia, Y., Chen, B., Zhou, X. Q., Xu, Y. L. (2013). Field monitoring and numerical analysis of Tsing ma suspension bridge temperature behavior. Structural Control & Health Monitoring 20(4):560–75. doi:10.1002/stc.515
   Web of Science ®Google Scholar
• Ye, J. (2007). The finite difference method used for the calculation of statically indeterminate beams. Mechanics in Engineering 29(2):67–68.
   Google Scholar
• Yohchia, C., Krauthammer, T. (1989). A combined ADINA finite difference approach with sub-structuring for solving seismically induced nonlinear soil-structure interaction problems. Computers and Structures 32 (3–4):779–85. doi:10.1016/0045-7949(89)90363-5
   Google Scholar
• Yoo, Y. S., Ando, K. (2001). Plastic collapse and LBB behavior of statically indeterminate piping system subjected to a static load. Nuclear Engineering and Design 207(3):341–50. doi:10.1016/s0029-5493(01)00342-9
   Web of Science ®Google Scholar
• Yoo, Y. S., Ando, K. (2003). Leak-before-break behavior of statically indeterminate piping system. Nuclear Engineering and Design 224(3):253–63. doi:10.1016/s0029-5493(03)00113-4
   Web of Science ®Google Scholar
• Zhang, Z. Q., Song, J. L., Fu, J. H., Li, Y. T., Guo, Y. N. (2014). A refined model of three-roller elastoplastic asymmetrical pre-bending of plate. Journal of Iron and Steel Research International 21:328–34. doi:10.1016/s1006-706x(14)60050-9
   Web of Science ®Google Scholar
• Zhao, J., Yin, J., Ma, R., Ma, L. (2011). Spring back equation of small curvature plane bending. Science China-Technological Sciences 54(9):2386–96. doi:10.1007/s11431-011-4447-4
   Web of Science ®Google Scholar
• Zhao, J., Zhan, P., Ma, R., Zhai, R. (2014). Prediction and control of springback in setting round process for pipe-end of large pipe. International Journal of Pressure Vessels and Piping 116:56–64. doi:10.1016/j.ijpvp.2014.01.006
   Web of Science ®Google Scholar