Application of computer-generated finite-difference equations to decision and inverse problems in elasticity

摘要

The use of appropriate finite-difference equations in static isotropic elasticity problems, based on experimental measurements of an elastic quantity at a small number of equidistant points and computer algebra elimination techniques such as the famous Buchberger algorithm for Grobner bases, is proposed for the inverse elasticity problem concerning the decision about the existence of a singularity (concentrated force, hole, inclusion, crack, etc.) and, further, the determination of the related characteristic loading and geometrical quantities. Both elementary problems and non-trivial problems concerning a concentrated force, a crack, a circular hole and the torsion of an elliptical bar illustrate the present computational approach. Further possibilities are also suggested in brief. (C) 1998 Elsevier Science Ltd. All rights reserved. References: 50