Deformation behaviors of the jointed elastic filaments based on Kirchhoff rod model

2020 ◽  
Vol 2020.95 (0) ◽  
pp. 04_404
Author(s):  
Takamasa NANJO ◽  
Hiro TANAKA ◽  
Yoji SHIBUTANI
Keyword(s):  
Kirchhoff Rod ◽  
Elastic Filaments ◽  
Rod Model ◽  
Deformation Behaviors

Elastic Properties of Normal and Binormal Helical Nanowires

2006 ◽  
Vol 963 ◽  
Author(s):  
Alexandre Fontes da Fonseca ◽  
C P Malta ◽  
Douglas S Galvão
Keyword(s):  
Simple Model ◽  
Young’S Modulus ◽  
Elastic Properties ◽  
Cross Section ◽  
Young's Modulus ◽  
Helical Axis ◽  
Geometric Features ◽  
Kirchhoff Rod ◽  
Rod Model ◽  
The Cross

ABSTRACTA helical nanowire can be defined as being a nanoscopic rod whose axis follows a helical curve in space. In the case of a nanowire with asymmetric cross section, the helical nanostructure can be classified as normal or binormal helix, according to the orientation of the cross section with respect to the helical axis of the structure. In this work, we present a simple model to study the elastic properties of a helical nanowire with asymmetric cross section. We use the framework of the Kirchhoff rod model to obtain an expression relating the Hooke's constant, h, of normal and binormal nanohelices to their geometric features. We also obtain the Young's modulus values. These relations can be used by experimentalists to evaluate the elastic properties of helical nanostructures. We showed that the Hooke's constant of a normal nanohelix is higher than that of a binormal one. We illustrate our results using experimentally obtained nanohelices reported in the literature.

Twist and Stretch of Helices Explained via the Kirchhoff-Love Rod Model of Elastic Filaments

2013 ◽  
Vol 111 (10) ◽  
Author(s):  
Bojan Đuričković ◽  
Alain Goriely ◽  
John H. Maddocks
Keyword(s):  
Elastic Filaments ◽  
Rod Model

scholarly journals Path Analysis for Hybrid Rigid–Flexible Mechanisms

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1869
Author(s):  
Oscar Altuzarra ◽  
David Manuel Solanillas ◽  
Enrique Amezua ◽  
Victor Petuya
Keyword(s):  
Path Analysis ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Buckling Mode ◽  
Boundary Constraints ◽  
Kirchhoff Rod ◽  
Flexible Rods ◽  
Rod Model ◽  
Body Joints ◽  
Flexible Mechanisms

Hybrid rigid–flexible mechanisms are a type of compliant mechanism that combines rigid and flexible elements, being that their mobility is due to rigid-body joints and the relative flexibility of bendable rods. Two of the modeling methods of flexible rods are the Cosserat rod model and its simplification, the Kirchhoff rod model. Both of them present a system of differential equations that must be solved in conjunction with the boundary constraints of the rod, leading to a boundary value problem (BVP). In this work, two methods to solve this BVP are applied to analyze the influence of external loads in the movement of hybrid compliant mechanisms. First, a shooting method (SM) is used to integrate directly the shape of the flexible rod and the forces that appear in it. Then, an integration with elliptic integrals (EI) is carried out to solve the workspace of the compliant element, considering its buckling mode. Applying both methods, an algorithm that obtains the locus of all possible trajectories of the mechanism’s coupler point, and detects the buckling mode change, is developed. This algorithm also allows calculating all possible circuits of the mechanism. Thus, the performance of this method within the path analysis of mechanisms is demonstrated.

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