Application of a triangular finite element with Lagrange correction factors in calculations of thin shells of ellipsoidal type

Abstract

The study of the stress-strain state of a thin shell of an ellipsoidal type was carried out. The finite element method was used as a research tool using the triangular fragment of the middle surface as the discretization element. The nodal variable parameters of the triangular element of discretization selected the components of the displacement vector, their first and second derivatives with respect to global curvilinear coordinates. Fifth-degree polynomials were used as polynomial functions. To improve the consistency of the triangular element of discretization on the boundaries of adjacent elements, the Lagrange correction factors in the nodes entered in the midpoints of the sides of the triangular element were additionally used as unknowns. The analysis of the results of the calculation of the thin shell of the ellipsoidal type showed high efficiency of using the modified triangular finite element.