Fracture of Materials Under Compression Along Cracks by Aleksander N. Guz & Viacheslav L. Bogdanov & Vladimir M. Nazarenko

Author:Aleksander N. Guz & Viacheslav L. Bogdanov & Vladimir M. Nazarenko
Language: eng
Format: epub
ISBN: 9783030518141
Publisher: Springer International Publishing

(b)for non-equal roots—it is necessary to determine harmonic functions , () that satisfy Laplace Eq. (3.28) and conditions (3.173), (3.180), (3.185)–(3.188), as well as conditions (3.169) of the continuity of the components of stress tensor , on the entire plane , provided they are expressed via functions .

3.4.2 Dual Integral Equations

Let the required potential harmonic functions be presented as Fourier integral transforms in terms of coordinate —integral expansion in terms of partial solutions of Eq. (3.19) (for equal roots) or (3.28) (for non-equal roots). Without loss of the approach generality, owing to the symmetry of configuration relative to the axis, we will confine ourselves to the representation of potential functions as Fourier cosine expansions in terms of coordinate (as is customary—e.g., in [47] etc.), viz.:

for equal roots

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