Adaptive F.E. method for the shakedown and limit analysis of pressure vessels

• Published in: European journal of mechanics, A, Solids A, Solids, 2003-07, Vol.22 (4), p.525-533
• Main Authors: Franco, José Ricardo Queiroz, Ponter, Alan R.S., Barros, Felı&#x0301, cio Bruzzi
• Format: Article
• Language: English
• Subjects: Applied sciences; Error indicator; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Mechanical engineering. Machine design; Physics; Pressure vessels; Shakedown and limit analysis; Solid mechanics; Steel design; Steel tanks and pressure vessels; boiler manufacturing; Structural and continuum mechanics; Viscoelasticity, plasticity, viscoplasticity
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/S0997-7538(03)00065-2

Upper bound estimates of limit and shakedown loads for pressure vessels are calculated by using the technique described in this paper. These have been achieved by applying Koiter's theorem and by discretizing the shell into finite elements. The flow law associated with an hexagonal prism yield surface, relates the plastic strain increments and curvatures to plastic multipliers. A suitable matrix also relates such a plastic strain field to a displacement field through a classical relation. A novel method enforces a consistent relationship between nodal displacements and nodal plastic multipliers by minimizing the residual between the two independent descriptions of the plastic increments, measured with respect to the energy norm. The discretized problem is then reduced to a minimization problem and solved by linear programming. An a posteriori error indicator in the energy norm is derived with and adaptive mesh refinement scheme.