Optimization of a second-order multiply-connected inhomogeneous boundary-value problem was considered in terms of elastic torsion. External boundary and material proportions are the applied constraints in finding optimal internal configurations of the cross section. The optimization procedure is based on the numerical simulation of the membrane analogy and the results obtained indicate that the procedure is usable as an engineering tool. Optimal solutions are obtained for some representative cases of the torsion problem and they are presented in the form of tables and figures.
The twisting stiffness of a rectangular cross section consisting of a single row of solid circular cross-section fibers embedded in a matrix is analyzed. The problem is formulated as a Dirichlet torsion problem of a multielement region and solved by the boundary-point least-squares method. Numerical results for a single-fiber square cross section compare favorably with previous relaxation-method results. New numerical results for three and five-fiber composites suggest that the torsional rigidity of a multifiber composite can be approximated from the torsional rigidities of single and three-fiber models.
Abstract
The object of this paper is to find a solution for the torsion problem of a circular shaft with a number of longitudinal semicircular notches. By using elementary functions the author has been able to simplify the numerical calculations in contrast to previous work in similar cases by other writers.
One Theoretical Method for Solving the Elasto-Plastic Torsion Problem
