Research of evolution of the stress strain and definition of the estimated life-time of massive structure elements using of the universal finite element

Abstract

Mathematical modeling of the continual fracture processes under long creep conditions on the basis of FEM is a rather complex problem. The efficiency of solving of this problem depends on the completeness of the finite element library and the algorithms for solving systems of nonlinear equations, as well as on the software organization. The main principles of the moment sheme of finite elements (MSFE) is the base for procedure of obtaining of finite-element solving relationships. In contrast to the generally accepted approaches the use of MSFE provides an independent representation of deformations in the form of Maclaurin series in addition to the choose of the law of displacements distribution. At the base of the algorithm for solving a system of nonlinear equations, the method of integration over the load parameter is adopted. It is assumed to reduce an integration step consecutively to obtain reliable results. To optimize discrete FEM models, an approach based on the initial fragmentation of the computational model was used. The accuracy of solving of a system of nonlinear equations at each step of the load parameter is determined by comparing the sum of the squares of the nodal reactions and the sum of the squares of the nodal values of the external loads. The equations of termoviscolastoplastic deformation taking into account the damage of materials are taken as initial relations. The principle of using of quasiregular fragmentation which involves constructing a general irregular finite element model based on regular finite element fragments is basis of the procedure of constructing the finite element model of objects under consideration. This make it possible to optimize substantially the total number of unknowns. When calculating of a new objects, the convergence of the results is justified by a sequential increase of the parameters of the mesh model, a decrease of integration step value due to an increase of their number within a given range of loads, and an increase of the accuracy of solving of nonlinear equations system at each step. In order to justify the reliability of the results, obtained on the basis of the universal finite element, the parameters of the stress-strain state and the damage parameter ω were compared with data calculated on the basis of finite elements of a general type with numerical integration and elements with integration in a closed form.