BE analysis of composite bars having generic cross sections and variable rigidity subjected a nonuniform torsion

Resumo

In this paper, a robust and efficient algorithm is presented to solve composite bars with variable cross-
section and subjected to nonuniform torsion. The bar may be subjected to concentrated or distributed twist loads

and is under general boundary (end) conditions. Torsion problems are often encountered in engineering practice
as in members of spatial frames, in curved bridges, in rigid building cores, etc.. In this class of problem, the
warping of a given cross section is described by the known Laplace/Poisson equation, while the angle of twist
along the beam is described by a fourth-order differential equation with variable coefficients. In the present
strategy, the boundary-element subregion-by-subregion (BE SBS) technique, developed in previous works, is
employed to solve the coupled boundary-value problems (BVPs) related to the cross section. An important detail
of the BE SBS technique is the use of Krylov iterative solvers, which allows the elimination of operations with
the large blocks of zeroes existing in the coupled system of equations. For the solution of the global differential
equation of equilibrium in the beam, which describes the angle of twist along the beam, a strategy based on the
weighted residual method is developed. Complex composite cross sections under torsion are analyzed to show
the performance of the whole solution process.