The Elastic–Plastic Torsion Problem: A Posteriori Error Estimates for Approximate Solutions

Abstract

We consider the variational inequality that describes the torsion problem for a long elasto-plastic bar. Using duality methods of the variational calculus, we derive a posteriori estimates of functional type that provide computable and guaranteed upper bounds of the energy norm of the difference between the exact solution and any function from the corresponding energy space that satisfies the Dirichlet boundary condition.

Keywords:

• A posteriori error estimates
• Deformation of bars
• Elastic-plastic torsion
• Variational inequalities

AMS Subject Classification:

• 74G65
• 74C05
• 65N15
• 65K10