A shear deformable corotational beam element for large displacement analysis of microbeams and microframes

10 pages•Published: July 19, 2023

Cong Ich Le, Thanh Tien Pham and Dinh Kien Nguyen

Abstract

The large displacement analysis of microbeams and microframes is presented in this paper via a shear deformable corotational beam element. In order to account for the small size effect, the modified couple stress theory (MCST) is employed in conjunction with Timoshenko beam theory in deriving the internal force vector and tangent stiffness matrix of the beam element. Hierarchical functions are used to interpolate the local displacements and rotation. Newton-Raphson iterative procedure is adopted in combination with the arc-length method to solve the nonlinear equilibrium equation and to trace the equilibrium paths. Various microbeams and microframes are analyzed to show the influence of the size effect on the behavior of the microstructure. The obtained result reveals that the size effect plays an important role on the large deflection response, and the displacements of the structure are overestimated by ignoring the size effect. A parametric study is carried out to highlight the influence of the material length scale parameter on the large displacement behavior of the microbeams and microframes.

Keyphrases: corotational formulation, hierarchical interpolation, large displacement analysis, microbeam

In: Trung Nghia Tran, Quoc Khai Le, Tich Thien Truong, Thanh Nha Nguyen and Hoang Nhut Huynh (editors). Proceedings of International Symposium on Applied Science 2022, vol 5, pages 61-70.

Links:	https://easychair.org/publications/paper/3z79
	https://doi.org/10.29007/bn24

BibTeX entry

@inproceedings{ISAS2022:shear_deformable_corotational_beam,
  author    = {Cong Ich Le and Thanh Tien Pham and Dinh Kien Nguyen},
  title     = {A shear deformable corotational beam element for large displacement analysis of microbeams and microframes},
  booktitle = {Proceedings of International Symposium on Applied Science 2022},
  editor    = {Trung Nghia Tran and Quoc Khai Le and Tich Thien Truong and Thanh Nha Nguyen and Hoang Nhut Huynh},
  series    = {EPiC Series in Engineering},
  volume    = {5},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2516-2330},
  url       = {/publications/paper/3z79},
  doi       = {10.29007/bn24},
  pages     = {61-70},
  year      = {2023}}

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