March 3, 2026

Explicit Form of Asymptotic Coefficients in a Reentrant Corner for Conformal Mapping of an L-Shaped Domain

Key Points

Explicit formulas for asymptotic coefficients were derived, focusing on the reentrant corner of the L-shaped domain.
The expansion coefficients, known as stress intensity factors, are represented as a series based on a small parameter.
Analysis of the coefficients depends solely on the reentrant corner's size, determined by beta.
Finding explicit formulas advances the understanding of conferring mapping in complex geometries.

Abstract

For the conformal mapping of an L-shaped domain with ledges of arbitrary length A and width h and a reentrant corner of size, we find explicit analytical formulas for the expansion coefficients {c₍} of the mapping function near the vertex {w₁} of the reentrant corner. The formulas for {c₍}, which are known as stress intensity factors (SIFs), are derived in the form of series in powers of the small parameter: = (- A/h) with coefficients determined only by using explicit formulas. A brief bibliographic survey concerning the problem of calculating SIFs is given.

Bookmark

Explicit Form of Asymptotic Coefficients in a Reentrant Corner for Conformal Mapping of an L-Shaped Domain

Key Points

Abstract

Cite This Study