Bifurcations and Stability Analysis of Elastic Slender Structures Using Static Discrete Elastic Rods Method

Huang, Weicheng1; Zhang, Yingchao2; Yu, Tian3; Liu, Mingchao4

2023-09-01

10.1115/1.4062533

JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME   影响因子和分区

0021-8936

1528-9036

Discrete elastic rods (DER) method provides a computationally efficient means of simulating the nonlinear dynamics of one-dimensional slender structures. However, this dynamic-based framework can only provide first-order stable equilibrium configuration when combined with the dynamic relaxation method, while the unstable equilibria and potential critical points (i.e., bifurcation and fold point) cannot be obtained, which are important for understanding the bifurcation and stability landscape of slender bodies. Our approach modifies the existing DER technique from dynamic simulation to a static framework and computes eigenvalues and eigenvectors of the tangential stiffness matrix after each load incremental step for bifurcation and stability analysis. This treatment can capture both stable and unstable equilibrium modes, critical points, and trace solution curves. Three representative types of structures-beams, strips, and gridshells-are used as demonstrations to show the effectiveness of the modified numerical framework, which provides a robust tool for unveiling the bifurcation and multistable behaviors of slender structures.

computational mechanics static discrete elastic rods elastic slender structures bifurcation and stability analysis

SCI ; EI

英语

通讯

Natural Science Foundation of Jiangsu Province[BK20220794]

Mechanics

Mechanics

WOS:001043240200008

ASME

20240715557528

Bifurcation (mathematics) ; Eigenvalues and eigenfunctions ; Stability ; Stiffness matrix

Mathematics:921 ; Algebra:921.1 ; Mechanics:931.1

ENGINEERING

Web of Science

1.Southeast Univ, Sch Mech Engn, Nanjing 211189, Peoples R China
2.Nanyang Technol Univ, Sch Mat Sci & Engn, Singapore 637553, Singapore
3.Southern Univ Sci & Technol, Dept Mech & Aerosp Engn, Shenzhen 518055, Peoples R China
4.Nanyang Technol Univ, Sch Mech & Aerosp Engn, Singapore 639798, Singapore

Huang, Weicheng,Zhang, Yingchao,Yu, Tian,et al. Bifurcations and Stability Analysis of Elastic Slender Structures Using Static Discrete Elastic Rods Method[J]. JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME,2023,90(9).

Huang, Weicheng,Zhang, Yingchao,Yu, Tian,&Liu, Mingchao.(2023).Bifurcations and Stability Analysis of Elastic Slender Structures Using Static Discrete Elastic Rods Method.JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME,90(9).

Huang, Weicheng,et al."Bifurcations and Stability Analysis of Elastic Slender Structures Using Static Discrete Elastic Rods Method".JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME 90.9(2023).