Asymptotic models for optimizing the contour of multiply-connected cross-section of an elastic bar in torsion

Abstract

a b s t r a c tAn asymptotic solution is obtained for the problem of maximizing the torsional rigidity of elastic, multiply-connected cylindrical bars for a given area of cross-section. The shapes of the inner contours of the multiply-connected cross-section are specified while the outer contour is determined as a result of the shape optimization. We apply the method of matched asymptotic expansions to construct a first-order asymptotic model. The conditions for unique solvability of the asymptotic model have been established under some restrictions imposed on the location of the inner contours and their polarization matrices. The economy achieved by optimization is estimated.

A scalar prototype problem of deep abrasive drilling with an infinite free boundary: an asymptotic modeling study

“…Free and moving boundary problems [1,2], where the problem domain is a priori unknown are encountered in different areas of science and engineering [3], including laser drilling of metals [4,5], crack propagation and delamination in composite materials [6,7], in Hele-Shaw flow [8,9], and elastic and plastic torsion [10,11].…”