Displacement estimates of pipe elbows prior to plastic collapse loads Original Research Article

The non-differentiability of the plastic dissipation calculated through the Von-Mises yield function leads to convergence difficulties when using mathematical programming to solve Köiterʹs kinematical formulation of the classical limit analysis. This problem is avoided replacing the plastic dissipation by the strain energy of a fictitious viscoelastoplastic material with a nearly infinite Young modulus. Classical limit analysis can only give information about the limit load multiplier and the plastic collapse mechanism. Based on Zarkaʹs method and using the finite element method and mathematical programming, it is possible to obtain not only the limit load but also an estimate of the elastoplastic displacements. This is very useful because construction codes usually impose limits on the electroplastic displacements. Some pipeline systems are examined using a 1-dimensional shell type finite element to illustrate the procedure. The results obtained are compared with simplified analytical solutions and with alternative numerical results using 2-dimensional shell elements and realistic materials.