Equilibrium-based reconstruction of three-dimensional stresses in GBT

In this paper, a procedure for a posteriori reconstruction of three-dimensional stresses in the finite element analysis of beams modelled within the framework of the Generalized Beam Theory is presented. The reconstruction is based on the enforcement of the pointwise three-dimensional equilibrium equations over the beam, interpreted as an assembly of thick plates, and on the use of the Recovery by Compatibility in Patches procedure. No corrections to meet the equilibrium boundary conditions on bottom/top wall faces are needed. Numerical results show that the proposed approach allows to effectively recover local stress profiles which match those of three-dimensional solid finite element models.