Stress-strain state of shell of revolution analysis by using various formulations of three-dimensional finite elements

Abstract

The aim of the work is to perform a comparative analysis of the results of analyzing arbitrarily loaded shells of revolution using finite element method in various formulations, namely, in the formulation of the displacement method and in the mixed formulation. Methods. To obtain the stiffness matrix of a finite element a functional based on the equality of the actual work of external and internal forces was applied. To obtain the deformation matrix in the mixed formulation the functional obtained from the previous one by replacing the actual work of internal forces in it with the difference of the total and additional work was used. Results. In the formulation of the displacement method for an eight-node hexahedral solid finite element, displacements and their first derivatives are taken as the nodal unknowns. Approximation of the displacements of the inner point of the finite element was carried out through the nodal unknowns on the basis of the Hermite polynomials of the third degree. For a finite element in the mixed formulation, displacements and stresses were taken as nodal unknowns. Approximation of the target finite element values through their nodal values in the mixed formulation was carried out on the basis of trilinear functions. It is shown on a test example that a finite element in the mixed formulation improves the accuracy of the strength parameters of the shell of revolution stress-strain state.

Comparative Analysis of Nonlinear Deformation and Buckling of Thin Elastic Shells of Step-Variable Thickness

“…Therefore, the problems of analyzing the behavior of thin elastic shells have a long history and currently continue to arouse great and constant interest. In recent decades, the number of works on the subject has increased significantly [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Much attention is paid to the study of elastic shells of stepwise-variable thickness, in particular, thin shells reinforced with ribs [1-6, 8-9, 12, 15, 16].…”

Stress state of hydrotechnical facilities resistant to natural disasters

“…Significant disadvantages of this method include the lack of continuity of the derived displacements on the contours and faces of finite elements while maintaining continuity at the nodal points. The use of finite elements in the mixed formulation [13,14,15,16] leads to the fulfillment of the conditions for continuity of stresses and deformations not only at the nodal points, but also on the contours and faces of finite elements.…”

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“…Most of the methods for studying thin-walled structures are focused on a relatively limited class of shells, predominantly of canonical form, and simple loading processes, mainly mechanical. Therefore, methods of numerical analysis, primarily the finite element method, are widely used to solve various problems in the study of shell structures [1][2][3][4][5][6]. The complication of the geometric shape, which actually occurs in every real shell structure, requires the use of refined approaches from the standpoint of the three-dimensional theory of thermoelasticity and the development of 3-d finite elements on this basis.…”