A refined element-based Lagrangian shell element for geometrically nonlinear analysis of shell structures

For the solution of geometrically nonlinear analysis of plates and shells, the formulation of a nonlinear nine-node refined first-order shear deformable element-based Lagrangian shell element is presented. Natural co-ordinate-based higher order transverse shear strains are used in present shell elem...

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Main Authors: Woo-Young Jung, Sung-Cheon Han
Format: Article
Language:English
Published: SAGE Publishing 2015-04-01
Series:Advances in Mechanical Engineering
Online Access:https://doi.org/10.1177/1687814015581272
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spelling doaj-453c227ec18048329d2b9d8b32c7c8b72020-11-25T03:32:32ZengSAGE PublishingAdvances in Mechanical Engineering1687-81402015-04-01710.1177/168781401558127210.1177_1687814015581272A refined element-based Lagrangian shell element for geometrically nonlinear analysis of shell structuresWoo-Young Jung0Sung-Cheon Han1Department of Civil Engineering, Gangneung-Wonju National University, Gangneung, Republic of KoreaDepartment of Civil & Railroad Engineering, Daewon University College, Jecheon, Republic of KoreaFor the solution of geometrically nonlinear analysis of plates and shells, the formulation of a nonlinear nine-node refined first-order shear deformable element-based Lagrangian shell element is presented. Natural co-ordinate-based higher order transverse shear strains are used in present shell element. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Furthermore, a refined first-order shear deformation theory for thin and thick shells, which results in parabolic through-thickness distribution of the transverse shear strains from the formulation based on the third-order shear deformation theory, is proposed. This formulation eliminates the need for shear correction factors in the first-order theory. To avoid difficulties resulting from large increments of the rotations, a scheme of attached reference system is used for the expression of rotations of shell normal. Numerical examples demonstrate that the present element behaves reasonably satisfactorily either for the linear or for geometrically nonlinear analysis of thin and thick plates and shells with large displacement but small strain. Especially, the nonlinear results of slit annular plates with various loads provided the benchmark to test the accuracy of related numerical solutions.https://doi.org/10.1177/1687814015581272
collection DOAJ
language English
format Article
sources DOAJ
author Woo-Young Jung
Sung-Cheon Han
spellingShingle Woo-Young Jung
Sung-Cheon Han
A refined element-based Lagrangian shell element for geometrically nonlinear analysis of shell structures
Advances in Mechanical Engineering
author_facet Woo-Young Jung
Sung-Cheon Han
author_sort Woo-Young Jung
title A refined element-based Lagrangian shell element for geometrically nonlinear analysis of shell structures
title_short A refined element-based Lagrangian shell element for geometrically nonlinear analysis of shell structures
title_full A refined element-based Lagrangian shell element for geometrically nonlinear analysis of shell structures
title_fullStr A refined element-based Lagrangian shell element for geometrically nonlinear analysis of shell structures
title_full_unstemmed A refined element-based Lagrangian shell element for geometrically nonlinear analysis of shell structures
title_sort refined element-based lagrangian shell element for geometrically nonlinear analysis of shell structures
publisher SAGE Publishing
series Advances in Mechanical Engineering
issn 1687-8140
publishDate 2015-04-01
description For the solution of geometrically nonlinear analysis of plates and shells, the formulation of a nonlinear nine-node refined first-order shear deformable element-based Lagrangian shell element is presented. Natural co-ordinate-based higher order transverse shear strains are used in present shell element. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Furthermore, a refined first-order shear deformation theory for thin and thick shells, which results in parabolic through-thickness distribution of the transverse shear strains from the formulation based on the third-order shear deformation theory, is proposed. This formulation eliminates the need for shear correction factors in the first-order theory. To avoid difficulties resulting from large increments of the rotations, a scheme of attached reference system is used for the expression of rotations of shell normal. Numerical examples demonstrate that the present element behaves reasonably satisfactorily either for the linear or for geometrically nonlinear analysis of thin and thick plates and shells with large displacement but small strain. Especially, the nonlinear results of slit annular plates with various loads provided the benchmark to test the accuracy of related numerical solutions.
url https://doi.org/10.1177/1687814015581272
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