Issue 49

V. Matveenko et alii, Frattura ed Integrità Strutturale, 49 (2019) 225-242; DOI: 10.3221/IGF-ESIS.49.23 233 where the coefficients (1) (2) (3) (4) (3) (4) , , , , , m m m m m m A A A A B B are determined from the recurrence relations available on E- resource (www. icmm.ru/compcoeff ) and can be calculated using the suggested options. For this purposes, it is necessary to input the number of terms of a series m , Poisson's ratio  , the number of harmonics k and the desired  , which can be either complex or real. Substituting (35) into (33), we obtain partial solutions (1) (2) (3) (4) 0 0 0 0 , , , v v v v for the function 0 v ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) (1) (1) 0 2 0 (2) (2) 0 2 0 (3) (3) (3) 0 2 0 (4) 1 (4) (4) 0 2 0 1 , 1 2 1 , 1 2 1 1 ln , 1 2 1 ln 1 2 m m m m m m m m m m m m m m x x v x P x S x x v x P x S x x S v x P D x x x S x x v x P D x x S a a a a a a a a a a a a ¥ = ¥ = ¥ = ¥ - = - é ù = ê ú ë û - - + - é ù = ê ú ë û - - + ì ü ï ï - + é ù ï ï = + + í ý ê ú ï ï ë û - - + ï ï î þ ì - é ù = + ⋅ ê ú ë û - - + å å å å , ü ï ï ï ï í ý ï ï ï ï î þ (36) where the coefficients (1) (2) (3) (4) (3) (4) , , , , , m m m m m m P P P P D D are available on E-resource (www. icmm.ru/compcoeff) and can be calculated ibidem. A general solution for 0 u and 0 v can be written as                     (1) (2) (3) (4) 0 1 0 2 0 3 0 4 0 (1) (2) (3) (4) 0 1 0 2 0 3 0 4 0 , u x C u x C u x C u x C u x v x C v x C v x C v x C v x                 (37) where 1 2 3 4 , , , C C C C are the constants defined by the prescribed combination of boundary conditions (3) - (5). C ONSTRUCTION OF PARTIAL SOLUTION FOR NONZEROTH HARMONICS OF THE FOURIER SERIES he construction of partial solutions to Eqns. (10)-(12) involves some transformations [21], which yield a system of two differential equations with respect to , k k w v                                             4 3 2 4 3 2 1 0 4 3 2 2 3 2 2 0 3 2 1 0 2 3 2 0 k k k k k k k k k k k d w x d w x d w x dw x f x f x f x f x f x w x dx dx dx dx d v x d w x d w x dw x x x v x x x x x w x dx dx dx dx                 (38) where 0 1 2 3 4 0 2 0 1 2 3 , , , , , , , , , , f f f f f       are given by              2 2 2 0 1 1 1 1 2 3 2 1 1 1 1 2 16 f x x x x x k k k                                 2 2 2 0 1 1 1 1 2 3 2 1 1 1 1 2 16 f x x x x x k k k                             2 2 1 1 1 1 2 1 4 3 1 2 2 f x x x x x x k                 T