Issue 38

N. Vaysfeld et alii, Frattura ed Integrità Strutturale, 38 (2016) 1-11; DOI: 10.3221/IGF-ESIS.38.01 3 here   x u x y u x y ( , ) ,  ,   y v x y u x y ( , ) ,  are the displacements which satisfy the Lame’s equations. The Lame’s equations are written in the following form [24] u x y u x y v x y x y x y v x y v x y u x y x y x y 2 2 2 * 0 2 2 2 2 2 * 0 2 2 ( , ) ( , ) ( , ) 0 ( , ) ( , ) ( , ) 0                                (3) where   0 * 0 1 , 1 1 2         . After the expression of the constants 0 * ,   through the Muskchelishvili constant 3 4     , one obtains the system (3) in the another form u x y u x y v x y x y x y v x y v x y u x y x y x y 2 2 2 2 2 2 2 2 2 2 ( , ) ( , ) ( , ) 1 2 0 1 1 ( , ) ( , ) ( , ) 1 2 0 1 1                                        (4) The boundary conditions on the semi-strip’s edge are reformulated with the terms of the displacements         u x v x G p x x a x y 0 , 0 , 0 2 1 , 0                    (5)     u x v x x a y x , 0 , 0 0, 0         (6) One needs to solve the boundary value problem (2), (4)-(6) to estimate the stress state of the semi-strip. T HE GENERAL SOLVING SCHEME OF THE PROBLEMS ON THE SEMI - STRIP STRESS STATE ESTIMATION he Fourier’s transformation is applied to the system of Lame’s equation and to the boundary conditions by the scheme     u x y u x y dy v x y v x y 0 ( ) cos , ( ) sin ,                          (7) with the inverse formula     u x y u x y d v x y v x y 0 ( ) cos , 2 ( ) sin ,                            (8) The initial problem has the form after this T