Solution of Plane Problems of Elasticity Utilizing Partitioning Concepts

Abstract

A partitioning plan combined with the modified mapping-collocation method is presented for the solution of awkward configurations in two-dimensional problems of elasticity. It is shown that continuation arguments taken from analytic function theory can be applied in the discrete to “stitch” several power series expansions of the stress function in appropriate subregions of the geometry. The effectiveness of such a plan is illustrated by several numerical examples.

Stress intensity factors for multiple edge cracks in rotating hollow discs

“…Without the partitioning capability in some configurations the difference in the maximum and minimum values of Iffl cause round off errors in the computer in computing with ~ raised to various powers. Similar observations for other problems are made in [4]. This is in fact also the reason some gaps exist in the data presented herein, indicating the need for a yet another partitioning plan.…”

“…1. To avoid convergence difficulties as noted in [4] for certain geometries the partitioning plans in Figs. 2, 3, and 4 are introduced.…”

“…The analytical technique used is the modified mapping-collocation method [3] combined with partitioning [4,5]. This method is a combination of the complex variable and conformal mapping formulation of two dimensional elasticity and boundary collocation techniques.…”

Weight function for a single edge cracked geometry with clamped ends

“…Several investigators [5][6][7][8][9] have proposed linear elastic fracture mechanics solutions of the stress intensity factor for the MSE(T) geometry. Recently, Blatt, John and Coker [3] developed the stress intensity factor and compliance solutions for the MSE(T) geometry using a finite element analysis.…”

Fracture Mechanics Analysis of an Attachment Lug

“…Extensive contributions have been made by Bowie and his colleagues [4,5,6] Work on finite-element fracture mechanics analysis at MIT has followed the path of assumed-stress hybrid elements, first proposed by Pian [8] for ordinary continuum elements. The hybrid method was subsequently extended by Tong, Pian, Luk, and Lasry [9,10,11,12] to formulation of rectangular elements which incorporate an elastic crack-tip singularity, but which also have an assumed linear or quadratic variation of displacements along the element edges and are thus compatible with ordinary elements (Figure 1).…”