Algorithm for calculating flat-loaded shells of environmental structures

• Published in: IOP conference series. Earth and environmental science 2022-01, Vol.965 (1), p.12051
• Main Authors: Nikolaev, A P, Kiselev, A P, Yushkin, V N, Marchenko, S S
• Format: Article
• Language: English
• Subjects: Algorithms; Deformation; Displacement; Environmental protection; Hermite polynomials; Mathematical analysis; Parameters; Shells; System effectiveness; Thin walled shells
• ISSN: 1755-1307; 1755-1315
• DOI: 10.1088/1755-1315/965/1/012051

Structures made of thin-walled shells are widely distributed elements in the environmental protection systems. In this connection, it is necessary to develop their effective and refined calculation. The point of the shell of the environmental protection structures is considered with a plane load in the initial position, deformed after j loading steps (displacement vector) and adjacent after (j + 1) loading step. The displacement increments and their derivatives are taken as nodal unknowns. The displacement vectors of the inner point of a finite element are represented in the initial basis, and their components are approximated through nodal unknowns using Hermite polynomials of the 3rd degree. To determine the deformed state of the shell, the algorithm of the method of discrete continuation with respect to the parameter in the vicinity of a singular point is used, in which the increment of loading at the step is the desired parameter. Based on the obtained dependencies, a step-by-step calculation procedure is organized, which allows you to get correct results if there is a special point.