The Consistent Mass Matrix of Euler Beam Element including Shear Deformation
[1]ZHANG Junfeng,HU Lianchao,WU Jingjiang,et al.The Consistent Mass Matrix of Euler Beam Element including Shear Deformation[J].Journal of Zhengzhou University (Engineering Science),2024,45(pre):2-.[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 pre
Page number:
2-
Column:
Public date:
2024-12-31
- Title:
- The 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:
- -
- 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. It was shown that the inertia force along the axial direction is always ignored in the mass matrix derivation for the bending condition if the shear deformation in not included, so only the shape functions for vertical deformation are needed for the bending condition. When the shear deformation is included, the inertia force along the axial direction must be considered and the shape functions for the section rotation angle due to bending are also required besides the complete shape functions for vertical deformation due to the bending and shear forces. For tapered Euler element, 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 moments with the elements in the mass matrix according to their positions. Additionally, the stiffness matrix could also be deduced on the foundation of the complete shape functions for vertical deformation and the shape functions for the section rotation angle. This derivation procedure is different with the traditional manner superficially but they share thesame principle essentially.
- References:
- -
- Similar References:
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Last Update:
2024-05-23