Application of finite elements of various dimensions in strength calculations of thin-wall constructions of agro-industrial complex

Abstract

The article presents a comparative analysis of the effectiveness of the use of finite elements of various dimensions in the study of the stress-strain state (SSS) of objects of the agro-industrial complex (AIC). To determine the strength parameters of the AIC objects, which can be attributed to the class of thinwalled, it is proposed to use a two-dimensional finite element in the form of a fragment of the middle surface of a triangular shape with nodes at its vertices. To improve the compatibility of a two-dimensional finite element at the boundaries of adjacent elements, it is proposed to use the Lagrange multipliers introduced in additional nodes located in the middle of the sides of the triangular fragment as additional unknowns. It is proposed to use a three-dimensional finite element in the form of a prism with triangular bases to study the SSS of agricultural objects of medium thickness and thick-walled. To improve the compatibility of the prismatic element, Lagrange multipliers in the middle of the sides of the upper and lower bases are also used. On the example of calculating a fragment of a cylindrical pipeline rigidly clamped at the ends loaded with internal pressure, the effectiveness of the developed two-dimensional and three-dimensional finite elements with Lagrange multipliers was proved. The validity of the use of a twodimensional element for researching the SSS of agricultural objects belonging to the class of thin-walled was proved.