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A comparison of two procedures for computation of the thermal Stresses in not rolled beams
Author(s) -
Boyadjiev Ilia,
Lam YeeCheong,
Thomson Peter
Publication year - 1997
Publication title -
steel research
Language(s) - English
Resource type - Journals
eISSN - 1869-344X
pISSN - 0177-4832
DOI - 10.1002/srin.199700566
Subject(s) - finite element method , beam (structure) , curvature , transverse plane , computation , structural engineering , stress (linguistics) , stiffness matrix , plane stress , thermal , stiffness , coordinate system , mechanics , materials science , mathematics , engineering , geometry , physics , thermodynamics , algorithm , linguistics , philosophy
The thermal stresses and deflections in not rolled steel beams can be modelled by using a finite element approximation to the three‐dimensional case based on two dimensional analysis. This is significant because a finite element model of thermal stress in a long beam would require very long computational times in the general case. An iterative method is employed in early analyses [1…5]. The problem is considered one‐dimenssional – the transverse stresses are neglected and the longitudinal stress only is computed. This approximation can result in significant errors when the magnitude of the transverse stresses is comparable with that of the longitudinal stress. Such is the case in industrial practice for instance in accelerated water cooling of Channels or air cooling of rails after hot rolling. One of the most comprehensive simplified finite element thermal stress analyses of hot rolled beams of complex cross sectional geometry is that offered by Abouaf, Marcelin and Chenot [6; 7]. Initially, generalised plane strain was assumed and two additional parameters, namely the curvature and a unit deformation of the fibre at the origin of the coordinate System, were included directly in the Solution. The above method requires Solution of a System of equations in which the stiffness matrix has to be utilised on three occasions. This is computationally expensive, because usually 80% or more of the total Solution time is used for solving the system of equations in which the stiffness matrix participates. In this paper the iterative method described in [1…5] is extended to include the transverse stresses in the analysis. In addition material nonlinearity is taken into account by using the von Mises’ plasticity theory. The system of equations is solved only once for an increment of stress in the elastic range. The present paper offers a comparison between the two procedures.