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A strain gradient quadrature element for geometrically exact beam with torsion warping
https://orcid.org/0000-0003-0278-2256
Highlights A strain gradient quadrature element for geometrically exact beam with torsion warping effects is proposed. All high order strain and strain gradient terms are retained. Fewer degrees of freedom are needed in the present approach. Influences of strain gradient effects and Wagner effects on nonlinear behaviors of beams are numerically demonstrated.
Abstract Based on the weak form quadrature element method, this paper proposes a geometrically exact strain gradient beam formulation incorporating torsion warping effects. This formulation provides a computationally efficient numerical scheme for analyzing size dependent arbitrarily cross-sectional beams undergoing large displacements and rotations. By accommodating all high order strain and strain gradient terms in the formulation, the Wagner effects that crucial to the model's accuracy are taken into account. The warping functions determined by cross-sectional governing equations involving strain gradients are obtained using a C1 quadrilateral quadrature element procedure. Five numerical tests are presented to demonstrate the validity and accuracy of the proposed formulation, while investigating the influences of size effects and Wagner effects on nonlinear behaviors of beam structures.
A strain gradient quadrature element for geometrically exact beam with torsion warping
https://orcid.org/0000-0003-0278-2256
Highlights A strain gradient quadrature element for geometrically exact beam with torsion warping effects is proposed. All high order strain and strain gradient terms are retained. Fewer degrees of freedom are needed in the present approach. Influences of strain gradient effects and Wagner effects on nonlinear behaviors of beams are numerically demonstrated.
Abstract Based on the weak form quadrature element method, this paper proposes a geometrically exact strain gradient beam formulation incorporating torsion warping effects. This formulation provides a computationally efficient numerical scheme for analyzing size dependent arbitrarily cross-sectional beams undergoing large displacements and rotations. By accommodating all high order strain and strain gradient terms in the formulation, the Wagner effects that crucial to the model's accuracy are taken into account. The warping functions determined by cross-sectional governing equations involving strain gradients are obtained using a C1 quadrilateral quadrature element procedure. Five numerical tests are presented to demonstrate the validity and accuracy of the proposed formulation, while investigating the influences of size effects and Wagner effects on nonlinear behaviors of beam structures.
A strain gradient quadrature element for geometrically exact beam with torsion warping
https://orcid.org/0000-0003-0278-2256
Highlights A strain gradient quadrature element for geometrically exact beam with torsion warping effects is proposed. All high order strain and strain gradient terms are retained. Fewer degrees of freedom are needed in the present approach. Influences of strain gradient effects and Wagner effects on nonlinear behaviors of beams are numerically demonstrated.
Abstract Based on the weak form quadrature element method, this paper proposes a geometrically exact strain gradient beam formulation incorporating torsion warping effects. This formulation provides a computationally efficient numerical scheme for analyzing size dependent arbitrarily cross-sectional beams undergoing large displacements and rotations. By accommodating all high order strain and strain gradient terms in the formulation, the Wagner effects that crucial to the model's accuracy are taken into account. The warping functions determined by cross-sectional governing equations involving strain gradients are obtained using a C1 quadrilateral quadrature element procedure. Five numerical tests are presented to demonstrate the validity and accuracy of the proposed formulation, while investigating the influences of size effects and Wagner effects on nonlinear behaviors of beam structures.
A strain gradient quadrature element for geometrically exact beam with torsion warping
Cheng, Jiahao (author) / Zhang, Run (author) / Ou, Xiang (author) / Yao, Xiaohu (author)
Thin-Walled Structures ; 197
2024-01-25
Article (Journal)
Electronic Resource
English