Rigidity matrix of a rod element with a variable cross section in problems of calculating structures using the finite element method

Abstract

Transport structures have various configurations, which makes modeling their stress state under external loads a complex task. The finite element method makes it possible to model structures of various shapes for strength calculation. This paper considers the derivation of the stiffness matrix for a rod element with a variable cross-section with finding the minimum of the functional under the corresponding boundary conditions, which gives a variational statement of the problem.