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Corotational isogeometric shear deformable geometrically exact spatial form beam element for general large deformation analysis of flexible thin-walled beam structures
Highlights A new 3D corotational isogeometric shear deformable geometrically exact beam element undergoing arbitrarily large deformation is presented. By constructing a co-rotated frame, the pure deformations are extracted to derive the spatial exact invariant strain measure with lie derivative formalism. The consistent tangent stiffness matrix belonging to proposed element are derived in closed form of the discrete variables for deformation field of arbitrary order.
Abstract In this paper, a new 3D generic order corotational geometrically exact beam element undergoing arbitrarily large deformations is presented. The novelty of the formulation lies in the use of the standard corotational framework, that is the decomposition into rigid body motion and pure deformation, to derive not only the objective, path-independent and singularity-free spatial exact strain measure but also the internal force and the consistent tangent stiffness matrix. The new formulation is derived by firstly conducting the consistent linearization of the weak formulation for the equilibrium equations of Reissner–Simo theory in the spatial form. By constructing a co-rotated frame that continuously rotates and translates with the element, the nodal strain-producing deformations can be extracted with the rigid-body translations and rotations removed from the element total motion. Subsequently, the corotational deformation variables are exploited to establish the distribution of deformation field within the beam element through B-spline basis functions, and derive the invariant and path independent exact strain measure in the spatial form by Lie derivative formalism. Through performing the variational operations of the compact transformation between corotational and global variables, the consistent tangent stiffness matrix are derived in closed form of the discrete variables for deformation field of any order. The proposed formulation is applicable to not only low-order two-node geometrically exact elements but also high-order multi-node straight or curved ones. The accuracy and robustness of the new formulation are demonstrated through the solutions of various benchmark problems.
Corotational isogeometric shear deformable geometrically exact spatial form beam element for general large deformation analysis of flexible thin-walled beam structures
Highlights A new 3D corotational isogeometric shear deformable geometrically exact beam element undergoing arbitrarily large deformation is presented. By constructing a co-rotated frame, the pure deformations are extracted to derive the spatial exact invariant strain measure with lie derivative formalism. The consistent tangent stiffness matrix belonging to proposed element are derived in closed form of the discrete variables for deformation field of arbitrary order.
Abstract In this paper, a new 3D generic order corotational geometrically exact beam element undergoing arbitrarily large deformations is presented. The novelty of the formulation lies in the use of the standard corotational framework, that is the decomposition into rigid body motion and pure deformation, to derive not only the objective, path-independent and singularity-free spatial exact strain measure but also the internal force and the consistent tangent stiffness matrix. The new formulation is derived by firstly conducting the consistent linearization of the weak formulation for the equilibrium equations of Reissner–Simo theory in the spatial form. By constructing a co-rotated frame that continuously rotates and translates with the element, the nodal strain-producing deformations can be extracted with the rigid-body translations and rotations removed from the element total motion. Subsequently, the corotational deformation variables are exploited to establish the distribution of deformation field within the beam element through B-spline basis functions, and derive the invariant and path independent exact strain measure in the spatial form by Lie derivative formalism. Through performing the variational operations of the compact transformation between corotational and global variables, the consistent tangent stiffness matrix are derived in closed form of the discrete variables for deformation field of any order. The proposed formulation is applicable to not only low-order two-node geometrically exact elements but also high-order multi-node straight or curved ones. The accuracy and robustness of the new formulation are demonstrated through the solutions of various benchmark problems.
Corotational isogeometric shear deformable geometrically exact spatial form beam element for general large deformation analysis of flexible thin-walled beam structures
Han, Qinghua (author) / Wu, Chao (author) / Liu, Mingjie (author) / Wu, Hao (author)
Thin-Walled Structures ; 198
2024-02-06
Article (Journal)
Electronic Resource
English
Exact element static stiffness matrices of shear deformable thin-walled beam-columns
| Online Contents | 2004