On the asymmetric line-contact deformation between two planar elasticae
Journal
International Journal of Solids and Structures
Journal Volume
256
Date Issued
2022-12-01
Author(s)
Yang, Zhi Han
Abstract
Two identical elastic beams capable of large deformation may contact each other in a line segment, which can be of various shapes. In previous studies, the special cases of the symmetric and antisymmetric line-contact deformations are treated as two-point contact deformations because there is no distributed force between the two beams. In the general asymmetric case, however, there exists distributed force between them. The existence of the distributed force makes the solution of the line-contact deformation a challenge. In the beginning of this paper, an experimental set-up including two beams and one slider is introduced to demonstrate the line-contact deformations when the slider is pushed inward. The deformation of interest consists of three segments. In the first and the third segments the two beams are separated. In the second segment of asymmetric line contact, we replace the two beams with one whose bending stiffness is twice as much as a single beam. This implies that the two beams are allowed to slide over each other without friction during deformation. By doing so, the distributed force will not appear in the equilibrium equations. At the two edges of the line-contact segment, the geometric continuity and the force and moment balances must be ensured. After solving the shape of the combined beam, the distributed and point contact forces can be calculated from the free body diagram of one of the two beams. In the end we measure the relation between the pushing force and the slider movement of the double-elastica slider assembly. The measured data is close to the theoretical predictions. The bifurcation and the jump phenomena predicted in the theory are also confirmed in the experiment.
Subjects
Asymmetric line-contact | Combined beam | Elastica
Publisher
PERGAMON-ELSEVIER SCIENCE LTD
Type
journal article