Аndriyevskiy V. Termoviscoelastoplasticity deformation and continual fracture of prismatic bodies

In this dissertational work on the basis of a semi-analytic finite element method (SFEM) the effective numerical approach to the decision of spatial problems of stationary heat conductivity, termoviscoelastoplasticity and modeling of continual failure zones propagation in prismatic spatial bodies of the complex shape with arbitrary boundary conditions which are under the long term power and temperature loading conditions is developed. Object of research are processes of temperatures redistribution, physically-nonlinear deformation process and continual failure of prismatic bodies under the influence of power loading and temperature. The purpose of work consists in creation of the effective numerical approach to the decision of spatial problems of stationary heat conductivity, termoviscoelastoplasticity and continual failure, and also research on this basis of change of stress-strained state parameters, damage accumulation process and continual failure zones propagation process in prismatic spatial bodies of the complex shape. Research methods. Approximation spatial prismatic bodies is carried out with SFEM, the mixed Mihlin's and Lagranzhe's polynoms are applied to modeling of arbitrary kinds of boundary conditions at butt ends of body. The moment scheme of finite elements is used for obtain of SFEM resolving parities; the execution of the rigidity matrix and a nodes reactions vector obtaining is conducted in terms of physical components of stress and deformations tensors. The decision of physically nonlinear problems of plasticity and creep is carried out on the basis of step-by-step algorithm with use of Newton-Kantorovich's iterative procedure. The decision of the SFEM system equations on everyone step is carried out on the basis of a method of block iterations with the top relaxation. The account of the physical nonlinearity connected with presence of deformations of plasticity and creep of a material, it is carried out in the right part of the equations system. Thus, for reduction of computing expenses, extrapolation of displacements' increments has been realized. Reliability and convergence of received results are investigated by the decision of test problems. Scientific novelty of the received results consists in the following: for the first time resolving parities for new non-uniform prismatic finite element taking into account change of a metric tensor component in a plane of finite element cross-section section are received; resolving parities are received and the algorithm of the decision of a problem of stationary heat conductivity for prismatic bodies is developed; on the basis of extrapolation of displacements' for the first time the effective step-by-step algorithm of the SFEM system of nonlinear equations for termoviscoelastoplasticity problems taking into account damage accumulation process are developed; the algorithm of continual failure zones propagation in prismatic bodies on the basis of SFEM is developed; new decisions of termoviscoelastoplasticity problems are received, modeling of occurrence and continual failure zones propagation process and influence of non-uniform temperature distribution on stress-strained state parameters and lifetime value of real spatial structure parts is investigated. Practical value of the received results consists in creation of a technique and software for definition of the stress-strained state and a lifetime of responsible spatial structure parts which are under the arbitrary distributed in space power loadings in a stationary temperature field. The received results are used in Institute of Structural Mechanics of Kiev National University of Construction and Architecture at performance of state budgetary research work № 1DB-2005 and at performance of research works behind project №F25.1/105 of the State fund of basic researches of the Ministry of Education and Science of Ukraine. Results of dissertational work can be applied in power, mechanical engineering and other areas of technique to definition of bearing ability of details and designs which represent prismatic bodies.