A two‐dimensional finite element idealization for thermo‐elastic deflection in beams

Abstract

SUMMARYThis paper addresses the problem of thermo-elastic deflection in beams using a two-dimensional finite element idealization of the cross-section. Bending effects are introduced in a generalized plane strain formulation assuming that constant curvature dominates the flexural deformation. The method leads to a plane strain calculation which is very interesting from the computational point of view; thermal dependence of the physical properties can be taken into account, which would be inconceivable in a three-dimensional problem.

Prediction of the deflection and residual stress in controlled cooling of hot-rolled steel beams including load and arbitrary support

“…The generalised plane strain analysis described by Boyadjiev et al [1,2], developed from the formulation due to Abouaf et al [3], provides a good approximation to the full 3D analysis available in commercial FE packages such as LUSAS [6] and effects a substantial saving in CPU time.…”

“…The present paper gives an account of numerical and experimental validation of the computational model for predicting the deflection and residual stress in hot-rolled steel beams subjected to controlled cooling on the runout table described in Part I [1], elaborated from the earlier work of the authors [2] and the generalised plane strain formulation due to Abouaf et al [3]: it includes some examples of potential applications. Validation was constrained to some extent by the dimensions of the furnace available for heating beam specimens.…”

“…(a) Beam used for comparing the generalised plane strain analysis with the 3D finite element analysis; (b) grid points used in the FE meshes and locations(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) at which the stresses were compared.…”

Analysis of rail cooling strategies through numerical simulation with instant calculation of thermal expansion coefficient

“…Boyadjiev et al [20] used a plane-strain FE analysis for the computational prediction of deflection and residual stress in the cooling of hot-rolled beams. The analysis was based on the generalized plane-strain model of Abouaf et al [14] . They include contact with the supporting table and the effect of beam weight.…”

Column curves for elliptical hollow section members

“…Two dimensional analyses were later on conducted (e.g., [17][18][19]) and, more recently, three dimensional finite element analyses were used to predict residual stresses (e.g., [20][21][22]). Although the thermomechanical behaviour of structural steel sections under various cooling regimes was extensively studied both experimentally and analytically in the past, the modelling of this behaviour is still an interesting topic among investigators.…”