Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)


Mechanical Engineering


A new approach in the application of 'the Finite Element Method to determine the stress distribution in stress concentration zones has been proposed and investigated. This approach uses the forces on the elements relatively far removed from the concentration zone to obtain the stresses near the zone by an iterative procedure, "Iterative Shrink1ng." For certain geometries applicable to high concentration zones, i.e. singularities in the stress field, it was shown that the basic equation of "Iterative Shrinking" reduces to simply the remultiplying of the starting matrices. In this case, termed "Conformal Shrinking," the computational effort reduces considerably. The problem of a finite line crack in an infinite plate, which has a theoretical solution, was solved by "Conformal Shrinking" to test the accuracy of this approach. The variation of the "Conformal Shrinking" solutions with the structural geometry of the finite element divisions was investigated. It was found that the "Iterative Shrinking" solutions vary with the geometry parameters; however, the variation was around the theoretical solution. The structural geometries leading to the optimal solution was pointed out. Although the basic geometry was relatively crude as dictated by the computer time available, the solution contains a 10% error in the criteria parameters chosen.

Library of Congress Subject Headings

Strains and stresses



Number of Pages



South Dakota State University