Numerical method of construction of eigen value spectrum of a non linear problem arising from one problem of mixed deformation of plate with crack

In the work a method of numerical finding of eigen values of class of non linear problems on eigen values arising from the problem of defining stressedly-deformed state near the apex of crack in the materials with exponential determining equations in conditions of compound deforming in full range of mixed forms of deformation from normal fracture up to simple shear is suggested. With the help of suggested approach new eigen values of the problem, different from the known eigen value, that corresponds to the classical solution of Hutchison–Rice–Rosengren are obtained.