Consistent Mass Matrix of Euler Beam Element including Shear Deformation
[1]ZHANG Junfeng,HU Lianchao,WU Jingjiang,et al.Consistent Mass Matrix of Euler Beam Element including Shear Deformation[J].Journal of Zhengzhou University (Engineering Science),2024,45(05):128-134.[doi:10.13705/j.issn.1671-6833.2024.05.009]
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Journal of Zhengzhou University (Engineering Science)[ISSN
1671-6833/CN
41-1339/T] Volume:
45
Number of periods:
2024 05
Page number:
128-134
Column:
Public date:
2024-08-08
- Title:
- Consistent Mass Matrix of Euler Beam Element including Shear Deformation
- Keywords:
- the consistent mass matrix; Euler beam element; shape functions; shear deformation; tapered elements
- CLC:
- TU973
- DOI:
- 10.13705/j.issn.1671-6833.2024.05.009
- Abstract:
- The study was initiated for the consistent mass matrix of Euler beam element including shear deformation. The consistent mass matrix of uniform element was got separately for the uncoupled tension, torsion, and bending conditions, with the shear deformation included or not, based on the shape functions and the virtual work. Itwas shown that the inertia force along the axial direction was always ignored in the mass matrix derivation for thebending condition if the shear deformation was not included, so only the shape functions for vertical deformationwere needed for the bending condition. When the shear deformation was included, the inertia force along the axialdirection must be considered and the shape functions for the section rotation angle due to bending were also requiredbesides the complete shape functions for vertical deformation due to the bending and shear forces. For tapered Eulerelement, the theoretical expression for the consistent mass matrix would be quite complicated and a simple expression was proposed following an approximate strategy, matching the ending or average section areas or polar momentswith the elements in the mass matrix according to their positions. Additionally, the stiffness matrix could also bededuced on the foundation of the complete shape functions for vertical deformation and the shape functions for thesection rotation angle. This derivation procedure was different with the traditional manner superficially but theyshared the same principle essentially.
- References:
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Last Update:
2024-09-02