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Analyzing FG shells with large deformations and finite rotations

Analyzing FG shells with large deformations and finite rotations The purpose of this study is dedicated to use an efficient mixed strain finite element approach to develop a three-node triangular shell element. Moreover, large deformation analysis of the functionally graded material shells is the main contribution of this research. These target structures include thin or moderately thick panels.Design/methodology/approachDue to reach these goals, Green–Lagrange strain formulation with respect to small strains and large deformations with finite rotations is used. First, an efficient three-node triangular degenerated shell element is formulated using tensorial components of two-dimensional shell theory. Then, the variation of Young’s modulus through the thickness of shell is formulated by using power function. Note that the change of Poisson’s ratio is ignored. Finally, the governing linearized incremental relation was iteratively solved using a high potential nonlinear solution method entitled generalized displacement control.FindingsSome well-known problems are solved to validate the proposed formulations. The suggested triangular shell element can obtain the exact responses of functionally graded (FG) shell structures, without any shear locking, instabilities and ill-conditioning, even by using fewer numbers of the elements. The obtained outcomes are compared with the other reference solutions. All findings demonstrate the accuracy and capability of authors’ element for analyzing FG shell structures.Research limitations/implicationsA mixed strain finite element approach is used for nonlinear analysis of FG shells. These structures are curved thin and moderately thick shells. Small strains and large deformations with finite rotations are assumed.Practical implicationsFG shells are mostly made curved thin or moderately thick, and these structures have a lot of applications in the civil and mechanical engineering.Social implicationsThe social implication of this study is concerned with how technology impacts the world. In short, the presented scheme can improve structural analysis ways.Originality/valueDeveloping an efficient three-node triangular element, for geometrically nonlinear analysis of FG doubly-curved thin and moderately thick shells, is the main contribution of the current research. Finite rotations are considered by using the Taylor’s expansion of the rotation matrix. Mixed interpolation of strain fields is used to alleviate the locking phenomena. Using fewer numbers of shell elements with fewer numbers of degrees of freedom can reduce the computational costs and errors significantly. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png World Journal of Engineering Emerald Publishing

Analyzing FG shells with large deformations and finite rotations

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References (52)

Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
1708-5284
DOI
10.1108/wje-10-2018-0357
Publisher site
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Abstract

The purpose of this study is dedicated to use an efficient mixed strain finite element approach to develop a three-node triangular shell element. Moreover, large deformation analysis of the functionally graded material shells is the main contribution of this research. These target structures include thin or moderately thick panels.Design/methodology/approachDue to reach these goals, Green–Lagrange strain formulation with respect to small strains and large deformations with finite rotations is used. First, an efficient three-node triangular degenerated shell element is formulated using tensorial components of two-dimensional shell theory. Then, the variation of Young’s modulus through the thickness of shell is formulated by using power function. Note that the change of Poisson’s ratio is ignored. Finally, the governing linearized incremental relation was iteratively solved using a high potential nonlinear solution method entitled generalized displacement control.FindingsSome well-known problems are solved to validate the proposed formulations. The suggested triangular shell element can obtain the exact responses of functionally graded (FG) shell structures, without any shear locking, instabilities and ill-conditioning, even by using fewer numbers of the elements. The obtained outcomes are compared with the other reference solutions. All findings demonstrate the accuracy and capability of authors’ element for analyzing FG shell structures.Research limitations/implicationsA mixed strain finite element approach is used for nonlinear analysis of FG shells. These structures are curved thin and moderately thick shells. Small strains and large deformations with finite rotations are assumed.Practical implicationsFG shells are mostly made curved thin or moderately thick, and these structures have a lot of applications in the civil and mechanical engineering.Social implicationsThe social implication of this study is concerned with how technology impacts the world. In short, the presented scheme can improve structural analysis ways.Originality/valueDeveloping an efficient three-node triangular element, for geometrically nonlinear analysis of FG doubly-curved thin and moderately thick shells, is the main contribution of the current research. Finite rotations are considered by using the Taylor’s expansion of the rotation matrix. Mixed interpolation of strain fields is used to alleviate the locking phenomena. Using fewer numbers of shell elements with fewer numbers of degrees of freedom can reduce the computational costs and errors significantly.

Journal

World Journal of Engineering – Emerald Publishing

Published: Sep 20, 2019

Keywords: Functionally graded material; Finite rotation; Geometric nonlinear analysis; Mixed strain; 3-node triangular shell element

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