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Geometrically exact beam element with rational shear stress distribution for nonlinear analysis of FG curved beams
https://orcid.org/0000-0002-0165-8969
Abstract Based on the geometrically exact beam theory, a first-order shear deformable curved beam element is developed for geometrically nonlinear analysis of functionally graded (FG) curved beams. In order to accurately predict the distribution of transverse shear stress, the stress equilibrium condition is introduced into the element formulation by using the mixed finite element method with displacements and internal forces as independent fields. The element nodal force vector and consistent tangent stiffness matrix for nonlinear iterative solution are obtained by going through a consistent linearization procedure. Numerical examples are presented to validate the present formulation. As indicated by the numerical results, the proposed element demonstrates a high level of solution accuracy and good applicability. Furthermore, using the proposed element, an investigation is conducted into the nonlinear stability of FG structures with different material distribution parameters, and the accuracy loss caused by unreasonable distribution of shear stress is discussed.
Highlights A geometrically exact beam element is proposed for nonlinear analysis of FG beams. The rational shear stress distribution is derived from stress equilibrium condition. Numerical examples are conducted to investigate the performance of the beam element. The accuracy loss caused by unreasonable distribution of shear stress is discussed.
Geometrically exact beam element with rational shear stress distribution for nonlinear analysis of FG curved beams
https://orcid.org/0000-0002-0165-8969
Abstract Based on the geometrically exact beam theory, a first-order shear deformable curved beam element is developed for geometrically nonlinear analysis of functionally graded (FG) curved beams. In order to accurately predict the distribution of transverse shear stress, the stress equilibrium condition is introduced into the element formulation by using the mixed finite element method with displacements and internal forces as independent fields. The element nodal force vector and consistent tangent stiffness matrix for nonlinear iterative solution are obtained by going through a consistent linearization procedure. Numerical examples are presented to validate the present formulation. As indicated by the numerical results, the proposed element demonstrates a high level of solution accuracy and good applicability. Furthermore, using the proposed element, an investigation is conducted into the nonlinear stability of FG structures with different material distribution parameters, and the accuracy loss caused by unreasonable distribution of shear stress is discussed.
Highlights A geometrically exact beam element is proposed for nonlinear analysis of FG beams. The rational shear stress distribution is derived from stress equilibrium condition. Numerical examples are conducted to investigate the performance of the beam element. The accuracy loss caused by unreasonable distribution of shear stress is discussed.
Geometrically exact beam element with rational shear stress distribution for nonlinear analysis of FG curved beams
https://orcid.org/0000-0002-0165-8969
Abstract Based on the geometrically exact beam theory, a first-order shear deformable curved beam element is developed for geometrically nonlinear analysis of functionally graded (FG) curved beams. In order to accurately predict the distribution of transverse shear stress, the stress equilibrium condition is introduced into the element formulation by using the mixed finite element method with displacements and internal forces as independent fields. The element nodal force vector and consistent tangent stiffness matrix for nonlinear iterative solution are obtained by going through a consistent linearization procedure. Numerical examples are presented to validate the present formulation. As indicated by the numerical results, the proposed element demonstrates a high level of solution accuracy and good applicability. Furthermore, using the proposed element, an investigation is conducted into the nonlinear stability of FG structures with different material distribution parameters, and the accuracy loss caused by unreasonable distribution of shear stress is discussed.
Highlights A geometrically exact beam element is proposed for nonlinear analysis of FG beams. The rational shear stress distribution is derived from stress equilibrium condition. Numerical examples are conducted to investigate the performance of the beam element. The accuracy loss caused by unreasonable distribution of shear stress is discussed.
Geometrically exact beam element with rational shear stress distribution for nonlinear analysis of FG curved beams
Li, Wenxiong (author) / Ma, Haitao (author) / Gao, Wei (author)
Thin-Walled Structures ; 164
2021-04-11
Article (Journal)
Electronic Resource
English
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Constrained dynamics of geometrically exact beams
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