Calculation of an Ellipsoid-Shaped Shell Based on a Consistent Triangular Discretization Element with an Invariant Interpolation Procedure

Klochkov, Yu. V.; Gureeva, N. A.; Vakhnina, O. V.; Sobolevskaya, T A; Klochkov, Mikhail Yu.

doi:10.3103/s1052618822030074

Cited by 1 publication

(1 citation statement)

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“…28; ORCID: 0000-0001-6751-4629, Scopus ID: 57215535887, eLIBRARY SPIN-код: 2767-3955; m.klo4koff@yandex.ru layer plates and shells [3; 4], and in the calculation of three-dimensional structures and thick slabs [5; 6]. FEM was widely used in the formulation of the displacement method in the calculation of thin shells under elastic and elastoplastic deformation [7][8][9][10][11]. This method is also used in the analysis of the nonlinear deformation of plates and shells [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Quadrilateral element in mixed FEM for analysis of thin shells of revolution

Klochkov

Pshenichkina

Николаев

et al. 2023

Struct. Mech. of Eng. Const. and Build

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The purpose of study is to develop an algorithm for the analysis of thin shells of revolution based on the hybrid formulation of finite element method in two dimensions using a quadrilateral fragment of the middle surface as a discretization element. Nodal axial forces and moments, as well as components of the nodal displacement vector were selected as unknown variables. The number of unknowns in each node of the four-node discretization element reaches nine: six force variables and three kinematic variables. To obtain the flexibility matrix and the nodal forces vector, a modified Reissner functional was used, in which the total specific work of stresses is represented by the specific work of membrane forces and bending moments of the middle surface on its membrane and bending strains, and the specific additional work is determined by the specific work of membrane forces and bending moments of the middle surface. Bilinear shape functions of local coordinates were used as approximating expressions for both force and displacement unknowns. The dimensions of the flexibility matrix of the four-node discretization element were found to be 36×36. The solution of benchmark problem of analyzing a truncated ellipsoid of revolution loaded with internal pressure showed sufficient accuracy in calculating the strength parameters of the studied shell.

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