Solutions of the torsion problem for some kinds of bars with multiply connected section

Abstract This paper is a continuation of the senior author's previous papers[1, 2]. In the paper the multiply connected region dealt with is a rectangular section containing several rectangular holes (Figs. 2–4). The boundary value problem of such a multiply connected region in the case of torsion problem can be divided into two similar problems. Each one of these problems belongs to a Dirichlet problem of Laplace equation [3]. There is only one undetermined constant K , which is determined from the single value condition of the displacement [3]. When solving these boundary value problems, the original section is divided into several rectangular subregions (Figs. 2–4), and then the Duhem theorem (see Appendix I) is used. After two boundary value problems are solved, the undetermined constant K can be found by using the above mentioned condition. Finally, the torsional rigidity can be easily deduced. Three sets of numerical results are shown in Tables 1–3.