Abstract:
For the conformal mapping of an $L$ – shaped domain with an arbitrary length $A$ and width $h$ of its shelves and an entering corner of $\pi\beta$, explicit analytical formulas are found for the coefficients $c_n$ of the mapping function expansion near the vertex $w_1$ of the entering corner. The formulas for the quantities $c_n$, called the Stress Intensity Factors (SIF), are obtained as a series in the powers of the small parameter $\delta :=\exp(-\pi A/h)$ with coefficients determined only by the exponent of the angle $\beta$ using explicit formulas. A brief bibliographic review on the problem of calculating stress intensity factors is also included.
Key words:$L$-shaped domain, conformal mapping, Schwarz–Christoffel integral, analytical solution of theparameter problem, expansion of the conformal mapping at the entering corner, explicit type of stressintensity factors (SIF).
