Analysis of Systems with Unilateral Constraints through the Finite Element Method in the Form of a Classical Mixed Method

Ignatyev, Alexander V.; Ignatyev, V.A.; Onischenko, E V

doi:10.1016/j.proeng.2016.07.166

Cited by 5 publications

(2 citation statements)

References 1 publication

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“…Основными недостатками данной формулировки МКЭ можно назвать отсутствие непрерывности производных от перемещений на ребрах и боковых поверхностях конечных элементов. Разработка конечных элементов в смешанной формулировке [16][17][18][19][20][21][22][23][24][25] позволяет понизить степень аппроксимирующих функций для выражения искомых величин через узловые неизвестные, дает возможность выполнить условия непрерывности напряжений и перемещений не только в узловых точках, но и на ребрах и боковых поверхностях элементов дискретизации.…”

Section: Rus 1 введениеunclassified

“…It can be stated that the main disadvantages of this FEM formulation are the lack of continuity of the displacement derivatives on the edges and side surfaces of finite elements. The development of finite elements in the mixed formulation [16][17][18][19][20][21][22][23][24][25] allows to reduce the degree of approximating functions for expressing the desired quantities through nodal unknowns, makes it possible to fulfill the conditions for the continuity of stresses and displacements not only at the nodal points, but also on the edges and lateral surfaces of the discretization elements.…”

Section: Introductionmentioning

confidence: 99%

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

Gureeva

Анатольевна²,

Klochkov

et al. 2020

Struct. Mech. of Eng. Const. and Build

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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.

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Section: Rus 1 введениеunclassified

Section: Introductionmentioning

confidence: 99%

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

Gureeva

Анатольевна²,

Klochkov

et al. 2020

Struct. Mech. of Eng. Const. and Build

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Analysis of Flexible Bars and Frames with Large Displacements of Nodes By Finite Element Method in the Form of Classical Mixed Method

Ignatyev

Onischenko

2017

IOP Conf. Ser.: Mater. Sci. Eng.

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

Klochkov

Николаев

Vakhnina

et al. 2019

IOP Conf. Ser.: Mater. Sci. Eng.

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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.

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Analysis of Systems with Unilateral Constraints through the Finite Element Method in the Form of a Classical Mixed Method

Cited by 5 publications

References 1 publication

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

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

Analysis of Flexible Bars and Frames with Large Displacements of Nodes By Finite Element Method in the Form of Classical Mixed Method

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

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