DOI: https://doi.org/10.32347/2410-2547.2019.103.71-81

### Semiаnalytical finite elements method efficiency in the geometrically nonlinear elastic-plastic problems

#### Abstract

Particular interest, among the variety of objects considered using analytical and numerical methods, are bodies of revolution with complex shape and cross-sectional structure. The selected geometric class is used as natural structure components in the construction and various fields of mechanical engineering. The sufficiently high prevalence of these forms in the construction and machine-building sectors on the one hand, and the possibility of a significant simplification math equestions by taking into account their geometric features on the other, is attracting increasing attention of researchers.

It is known that today the finite element method (FEM) is the most powerful tool for analyzing the problems of building mechanics and deformable solid mechanics. Over the past few years, the dimension of FEM models has grown dramatically, driven by increased demands for accuracy and reliability of results. In addition, the difficulties of studying the behavior of structures in the presence of dynamic loads are many times increased in comparison with static analysis. To overcome these problems, in many cases, it introduce additional hypotheses, which, as a rule, narrow the class of objects and processes under study, but can significantly improve efficiency and significantly reduce the duration of the calculation. Semi-analytical finite element method (SAFEM) is one of such approaches that is widely used for solving problems whose objects are prismatic and rotational bodies. High efficiency of SAFEM for a certain range of objects was demonstrated in the field of static analysis, continuous mechanics of fracture under creep conditions, processes of nonlinear deformation of reinforced concrete structures. The analysis of the results obtained by domestic and foreign scientists on this issue shows that most analytical and numerical methods of scientific research are usually oriented to geometrically nonlinear problems at static load. The veracity and effectiveness of the semi-analytical finite element method in the problems of geometrically nonlinear elastoplastic deformation of axisymmetric structures under dynamic loads is considered. The capabilities of methodology are demonstrated by examples of numerical modeling of the stress-strain state of building structures with large linear strains and analysis of technological processes of pulsed metal processing.

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