Maksymiuk Y. Viscoelastoplasticity deformation and fracture processes of axisymmetrical and in-plaine deformed bodies regarding geometrical non-linearity

The solving correlations of FEM for geometrically nonlinear two-dimensional problems, which are executed on basic positions of moment finite element scheme (MFES) are worked out in thesis. The formulas for nonlinear deformations and their variations determining through movement, by changing the value of the corresponding component of the tensor transformations, form coincide with the relations for linear deformations. It allows effectively solve problems in geometrically nonlinear formulation. Solving nonlinear equations systems is performed by stepping algorithm combined with the Newton-Kantarovych's iterative procedure. The analysis of the algorithms efficiency for solving physically and geometrically problems regarding nonlinear extrapolation movement and taking into account changes in matrix stiffness by recalculation of coordinates instantaneous stiffness tensor components elastoplastic material. The match the results of reference and the calculated and experimental data displayed. The algorithm for contour J - integral determining to stress and displacement gradients is shown, a modified reactions method for J - integral determining developed for mixed and nonlinear two-dimensional fracture mechanics problems. The practical problem of life-time determining of responsible axisymmetrical and plane-deformed bodies in a continual and discrete fracture condition regarding physical and geometric nonlinearity are resolved.