Stress analysis in sharp angular notches using auxiliary fields

On the computation of stress fields on polygonal domains with V‐notches

“…Carpenter [15,16,17] used the finite element method with up to 6000 degrees of freedom in combination with such an integral for the extraction of Q I . The same combination of methods was used by Atkinson et al [18], see Table 1, and in a refined way by Sinclair et al [19]. With 850 degrees of freedom, the latter authors report values of Q I with a relative error of 10 −3 for a setup with an analytic solution.…”

“…We denote this mapping A. Once the mapping A is known it is possible to perform product integration for the convolution of the kernel M 3 with the function Φ(τ ), expressed of the form of (18), when source points of Φ(τ ) are on a corner panel.…”

“…To overcome both these problems we add to the sequence of exponents λ n and µ n given by (3) and (4) a sequence of positive integers. We adopt the rule of including, in the series in (18), values of λ n and µ n up to a magnitude of ten. Then we complete this series with the integers 1, 2, 3, .…”

Stress computations on perforated polygonal domains

“…The situation is similar for the piecewise constant property of the applied traction, which is used for analytic evaluation of the right-hand sides of Eqs. (1) and (2). In Ref.…”

“…(13) as a path-independent integral which encloses the notch [2,50]. An advantage with this post-processor is that it is less sensitive to the quality of the solution VðzÞ close to the notch than the formula (17).…”