Analytical solution of Hill's nonlinear partial differential equation for plastically deforming beams subjected to bending and torsion together and stress fields


Proceedings of the 2nd Biennial European Joint Conference on Engineering Systems Design and Analysis. Part 1 (of 8), London, Canada, 4 - 07 July 1994, vol.64, pp.351-360 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 64
  • City: London
  • Country: Canada
  • Page Numbers: pp.351-360
  • Bursa Uludag University Affiliated: Yes


In this paper, Hill's non-linear partial differential equation firstly derived by Handelman is analytically solved for a plastically deforming bar, whose cross-section is surrounded by a continuous but not continuously derivable curve, subjected to bending and twisting moments together at its free end, and interaction curves for equilateral triangle and square cross-section are given. Interaction curves obtained show that the interaction curves are nearly independent of the shape of cross-section. By the method developed, Stresses σxz, σyz and σzz forming stress field can analytically be expressed.