Inelastic nonuniform torsion of bars of doubly symmetric cross section by BEM

In this paper a boundary element method is developed for the inelastic nonuniform torsional problem of simply or multiply connected cylindrical bars of arbitrarily shaped doubly symmetric cross section taking into account the effect of warping shear stresses. The bar is subjected to arbitrarily distributed or concentrated torsional loading along its length, while its edges are subjected to the most general torsional boundary conditions. A displacement based formulation is developed and inelastic redistribution is modeled through a distributed plasticity model exploiting three dimensional material constitutive laws and numerical integration over the cross sections. An incremental – iterative solution strategy is adopted to restore global equilibrium along with an efficient iterative process to integrate the inelastic rate equations. Three boundary value problems with respect to the variable along the bar axis angle of twist, to the primary and to the secondary warping functions are formulated and solved employing the boundary element method. Numerical results are worked out to illustrate the method, demonstrate its efficiency and wherever possible its accuracy.