Keywords: nonuniform torsion, inelastic torsion, nonlinear torsion, Wagner strain, warping, secondary torsional moment deformation effect, torsional shear correction factor, warping shear stresses, distributed plasticity, boundary element method, bar.

In this paper a boundary element method is developed for the inelastic nonuniform torsional problem of simply or multiply connected prismatic bars of arbitrarily shaped doubly symmetric cross section, taking into account the effects of geometrical nonlinearity (finite displacement - small strain theory) and secondary torsional moment deformation. The bar is subjected to arbitrarily distributed or concentrated axial and torsional loading along its length, while its edges are subjected to the most general axial and torsional boundary conditions. To the authors' knowledge, most of the relevant previous contributions are restricted to cross sections of special geometry while no research effort includes a torsional shear correction factor and a secondary warping function [1] in the modelling of the secondary torsional moment deformation effect to the problem at hand. In the method proposed in this paper a displacement based formulation is developed and inelastic redistribution is modelled through a distributed plasticity model exploiting three dimensional material constitutive laws and numerical integration over the cross sections. The transverse displacement components are expressed so as to be valid for large twisting rotations and the longitudinal normal strain includes the nonlinear "Wagner strain" term. A modified Powell hybrid algorithm which is a variation of Newton's method is adopted within an incremental formulation to resolve the elastic and plastic parts of the stress resultants along with an efficient iterative process to integrate the inelastic rate equations. The system of discretized global equilibrium equations is expressed without explicitly deriving its incremental form which is lengthier as a result of the terms associated with geometrical nonlinearity. Three boundary value problems with respect to (1) the primary warping function, (2) the secondary warping function and (3) the total angle of twist coupled with its primary part per unit length and the "average" axial displacement are formulated and numerically solved employing the boundary element method, which has not yet been employed for the numerical analysis of the problem at hand. A narrow rectangular cross section bar is worked out in order to verify the method developed at the elastic geometrically nonlinear regime and excellent agreement with existing studies has been achieved. Moreover, an I-shaped cross section bar under nonlinear inelastic nonuniform torsion, subjected to various axial boundary conditions, is analysed and very good agreement is achieved with existing numerical and experimental studies. It is observed that the secondary torsional moment deformation effect does not influence significantly nonlinear torsional analysis of open thin-walled cross section bars.

1

V.G. Mokos, E.J. Sapountzakis, "Secondary torsional moment deformation effect by BEM", International Journal of Mechanical Sciences, 53, 897-909, 2011. doi:10.1016/j.ijmecsci.2011.08.001

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £65 +P&P)