Developments of the mixed grid isogeometric Reissner–Mindlin shell: Serendipity basis and modified reduced quadrature

Lei, Zhenya; Gillot, F; Jézéquel, L.

doi:10.1016/j.euromechsol.2015.06.010

Cited by 16 publications

(5 citation statements)

References 49 publications

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“…Компоненты вектора перемещения точки внутренней области конечного элемента выражаются через их узловые значения с помощью интерполяционных зависимостей вида [7][8][9][10][11][12][13][14][15][16][17][18]…”

Section:  unclassified

“…ленные методы анализа их напряженно-деформированного состояния (НДС) с применением высокопроизводительной вычислительной техники [3][4][5][6][7]. Одним из наиболее распространенных численных методов анализа НДС тонкостенных конструкций является метод конечных элементов (МКЭ) в различных формулировках [8][9][10][11][12][13][14][15][16][17][18]. Несмотря на значительное количество публикаций, посвященных данной проблематике, по-прежнему актуальной является задача совершенствования конечно элементных алгоритмов в плане решения проблем совместности используемых конечных элементов, повышения точности численных решений и других важных аспектов по данному направлению.…”

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Numerical analysis of the stress-strain state of thin shells based on a joint triangular finite element

Klochkov

Николаев

Vakhnina

2019

Struct. Mech. of Eng. Const. and Build

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Relevance. The use of the finite element method for determining the stressstrain state of thin-walled elements of engineering structures predetermines their discretization into separate finite elements. Splitting irregular parts of the structure is impossible without the use of triangular areas. The triangular elements of shell structures are joint in displacements and in their derivatives only at the nodal points. Therefore, ways to improve the compatibility conditions at the boundaries of triangular elements are relevant. Aims of research. The aim of the work is to improve the compatibility conditions at the boundaries of adjacent triangular elements based on equating the derivatives of normal displacements in the middle of the boundary sides. Methods. In order to improve the compatibility conditions at the boundaries of triangular elements in this work, the Lagrange functional is used with the condition of ensuring equality in the middle of the sides of adjacent elements derived from normal displacements in the directions of perpendiculars tangent to the middle surface of the shell. Results. Using the example of analysing an elliptical shell, the efficiency of using a joint triangular finite element is shown, whose stiffness matrix is formed in accordance with the algorithm outlined in this article.

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Numerical analysis of the stress-strain state of thin shells based on a joint triangular finite element

Klochkov

Николаев

Vakhnina

2019

Struct. Mech. of Eng. Const. and Build

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“…Дальнейшая процедура формирования матрицы жесткости четырехугольного конечного элемента и столбца узловых усилий на (j+1)-м шаге нагружения осуществляется стандартным для МКЭ образом [14][15][16][17][18][19].…”

Section: конечный элемент тонкой оболочкиunclassified

Variants of determining correlations of deformation theory of plasticity in the calculation of shell of rotation on the basis of finite element method

Klochkov

Николаев

Vakhnina

et al. 2019

Struct. Mech. of Eng. Const. and Build

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Relevance. The problems of decline of resource-demanding of objects of building and engineer dictate the necessity of consideration of processes of deformation of constructions at the resiliently-plastic state. The widely in-use theory of account of practical properties of material is a deformation theory of plasticity. The aim of the research is development of variants of receipt of determining correlations on the step of ladening at deformation of material outside a resiliency. Methods. Algorithms over of receipt of determining correlations of theory of small resiliently-plastic deformations are brought on the step of ladening in two variants. In the first they turn out differentiation of expressions of tensions as functions of deformations on the basis of deformation theory of plasticity; in the second determining correlations turn out on the basis of hypothesis about the proportion of components of deviators increases of tensions to components of deviators increases of deformations. Results. On the test example of calculation of the jammed cylindrical shell realization of the got determining correlations is presented.

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“…Common shell elements include bivariate elements and solid elements. The former ones are mainly based on Kirchhoff-Love shell theory [1][2][3][4][5] or Reissner-Mindlin shell theory, [6][7][8][9][10][11][12] while the latter ones are developed according to 3D continuum theory. The solid-shell element has attracted the interest of many researchers [13][14][15][16][17] since it has several obvious advantages.…”

Section: Introductionmentioning

confidence: 99%

High‐fidelity tensor‐decomposition based matrix formation for isogeometric buckling analysis of laminated shells with solid‐shell formulation

Fan

Huang

Zeng

et al. 2022

Numerical Meth Engineering

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The computation cost of matrix formation in isogeometric analysis can be drastically reduced by employing tensor decomposition, but the performance like accuracy and robustness still depends on the approach used to realize the low‐rank approximation for the nonpolynomial integral kernels. In the buckling analysis of laminated shells with solid‐shell model, the integral kernels are not smooth in the thickness direction due to their material and stress distribution and have a high complexity because the curvilinear coordinate systems are involved in the representation of anisotropic constitutive relations, which makes it more difficult to guarantee the decomposition accuracy. This paper proposes a robust high‐fidelity tensor‐decomposition based matrix formation method for stiffness matrix and geometric stiffness matrix of the isogeometric buckling analysis problem. The proposed method avoids using a spline approximation and employs the hierarchical block‐wise decomposition approach (HBD) to obtain a determinate decomposition result, which saves more time without loss of accuracy and produces less canonical ranks with a reliable procedure. Besides, the matrix calculation is partly independent of the number of layers, showing a higher efficiency when the number of layers is larger. Finally, several experiments with various Gaussian curvatures are implemented to validate the proposed method.

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Developments of the mixed grid isogeometric Reissner–Mindlin shell: Serendipity basis and modified reduced quadrature

Cited by 16 publications

References 49 publications

Numerical analysis of the stress-strain state of thin shells based on a joint triangular finite element

Numerical analysis of the stress-strain state of thin shells based on a joint triangular finite element

Variants of determining correlations of deformation theory of plasticity in the calculation of shell of rotation on the basis of finite element method

High‐fidelity tensor‐decomposition based matrix formation for isogeometric buckling analysis of laminated shells with solid‐shell formulation

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