Open AccessCONSTRUCTION OF SOLVING EQUATIONS OF SEMI-ANALYTICAL METHOD OF FINISHED ELEMENTS FOR PRISMATIC BODIES OF COMPLEX SHAPE
Author(s) -
Г. М. Иванченко,
Yurii Maksymiuk,
Андрій Козак,
Ivan Martyniuk
Publication year - 2021
Publication title -
upravlìnnâ rozvitkom skladnih sistem
Language(s) - English
Resource type - Journals
eISSN - 2412-9933
pISSN - 2219-5300
DOI - 10.32347/2412-9933.2021.46.55-62
Subject(s) - curvilinear coordinates , finite element method , coordinate system , elasticity (physics) , mathematics , stiffness matrix , stiffness , mathematical analysis , von mises yield criterion , fourier transform , fourier series , geometry , structural engineering , materials science , engineering , composite material
The article presents an effective numerical approach to the study of arbitrarily loaded massive and thin-walled prismatic bodies of complex shape, the deformation of which can take place beyond the elasticity of the material. The equations of the semi-analytical finite element method (SAFEM) when used to decompose the displacements of Fourier series. The main relations between the spatial problem of the theory of elasticity in a curvilinear coordinate system and the theory of plastic flow for an isotropically reinforcing material under the Mises fluidity condition are presented. In accordance with the method of the moment scheme of finite elements (MSFE), the expressions of deformations of the prismatic finite element due to the nodal values of amplitude displacements are obtained. Formulas for calculating the stiffness matrix coefficients of a finite element (FE) with variable and averaged in the cross-sectional plane mechanical and geometric parameters are derived.