Issue 38

N. Vaysfeld et alii, Frattura ed Integrità Strutturale, 38 (2016) 1-11; DOI: 10.3221/IGF-ESIS.38.01 7                    G zi i p G i A z z i z i p p G zi i G z i i p p z i i z i p p 1 4 1 2 2 2 1 1 sinh 2 1 sinh 2 1 1 1 1 4 2 1 2 cosh 1 3 1 1 sinh 2 1 1 sinh                                                                                                                             G zi zi i p p z i i p 1 1 16 1 1 2 1 1 sinh 1                                                      here p 2  , 0.31    is found from the known solution of the analogical problem for an edge with the angle of openness pi/2 [25]. According to [21] one needs to find the roots of the equation   A z 0   . The found roots of the kernel’s symbol (14) have the next form: 1,2 0.5562 0.3690,     3,4 1.2792 0.2380,    5,6 3.2089 0.7127,    7,8 5.2170 1.0251,...    , where k k    because of the problem’s statement. The generalized method of SIE solving [22, 23] was applied for the solving of the Eq. (13). According to it the unknown function      is expanded by the series in each interval           N k k k N k k k N s s 1 0 2 1 , 1; 0 , 0;1                            (15) where                 k k k k k k N k Re 2 Re 2 1 1 cos Im ln 1 , 0, 1 2 1 sin Im ln 1 ,                          ,                 k N k k N k N k k N N k N Re 2 Re 2 1 1 cos Im ln 1 , , 1 2 1 sin Im ln 1 ,                              . The segment   1;1  is divided on N 2 equal segments with the length h N 1  . The Eq. (13) is considered when i h x ih i N 1 , 0, 2 1 2       . After the substitution of the unknown function (15) into the singular integral Eq. (13) one obtains system of the linear algebraic equations relatively to the unknown constants k s k N , 0, 2 1   of the expansion (15). N k ki i k s d f i N 2 1 0 , 0, 2 1       (16) where ki i d f i k N , , , 0, 2 1   are shown in the Application C. The expression (16) presents the system of N 2 equations with regard of N 2 unknown constants k s . The substitution of the founded constants in the formula (15) and following using of the formulae (12) completes the construction of the problem’s solution.