Open AccessShells analysis in orthogonal curvilinear coordinate system with variation-difference method
Author(s) -
В. Н. Иванов,
Alisa A Shmeleva
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/675/1/012066
Subject(s) - curvilinear coordinates , coordinate system , principal curvature , orthogonal coordinates , elliptic coordinate system , curvature , coordinate space , mathematics , orthogonal basis , ellipsoidal coordinates , principal axis theorem , torsion (gastropod) , principal component analysis , orthogonal functions , mathematical analysis , shell (structure) , geometry , physics , mean curvature , engineering , mechanical engineering , medicine , surgery , statistics , quantum mechanics
The variation-difference method is a convenient numerical method for shells of complex forms. It is enough when only cinematic boundary conditions are satisfied because the method is based on the principle of Lagrange. Another advantage of the variation-difference method is the better opportunity to create computer programs based on it. For shell analysis in orthogonal coordinate system as well as for shell analysis in principal curvatures the system of equations describing stress-strain state can be simplified. In this paper the difference between analysis in orthogonal coordinate system and analysis in principal curvatures of the surface is considered. The main distinction of the analysis of shells in orthogonal curvilinear coordinate system is the necessity of determination of components which include curvature of torsion of coordinate lines. The addition of these components in the equations of the theory of shells for the coordinate system in principal curvatures gives possibility to analyze shells in common orthogonal coordinate system. In this article shell analysis in orthogonal coordinate system is applied to shells based on normal cyclic surfaces.