On the basis of the moment finite element scheme (MFES) the developed library of finite elements have been created^ the solvable ratios of spatial, shell, universal finite elements of general and modified variants for determination of the stress-strained state, non-stationary temperature fields, modeling of the contact interaction of the rotational bodies. The unification of step-by-step integration algorithms according to the parameters of loading, displacement, time, incremental length of the main crack for solving linear and nonlinear deformation problems, stability, overcritical behavior, essential form-modification, fracture mechanics and nonstationary thermal conductivity are presented. Based on the fundamental provisions of the nonlinear theory of elasticity, the new calculated ratios of MFES and techniques for improving the conditionality of systems of nonlinear equations, the method of numerical investigation of the evolution of the stress-strained state of blanks in the processes of metal processing by embossing for large irreversible deformations. An effective algorithm for solving of a contact problems of interaction between individual deformable bodies with one another, with rigid barriers under variable boundary conditions and taking into account friction on contact surfaces, has been developed. The main and modified version of the calculated finite-element relations of the problem of non-stationary heat conduction was obtained and an algorithm for their solution was developed taking into account the form-modification. The algorithm of numerical simulation of the distribution of initial cracks, for obtaining their trajectories on the basis of the development of the modified reaction method taking into account physical and geometric nonlinearity, calculates the parameters of the fracture mechanics along the length of the main crack to determine its critical length and estimated resource. The analysis of reliability, convergence and efficiency of settlement relationships, stepwise-iterative algorithms for modeling of evolutionary processes, methods for determining the parameters of destruction is performed on the basis of solving a large number of control examples by comparing the basic and modified variants with analytical, numerical and experimental published data. The study of the features of thermally elastic plastic deformation, stability, continual and discrete destruction and determination of the resource, crack resistance and bearing capacity of responsible structural elements, nodes and details related to the design of objects of modern technology, which are under the influence of arbitrarily distributed in space and time of force, kinematic and temperature loads.
