Theoretical Analysis on Postbuckled Large Deformation and Subsequent Contact in a Spring-hinged Beam with Changing Length

Large deformations with contact area occurring in flexible beams such as bellows used for zigzag springs and flexible vessels, pipes etc., have a structure that absorbs large relative displacements. Large deformations with contact area occurs in folding process of paper and woven fabric, and are investigated both theoretically and experimentally. The analysis is based on an assumption that geometrical nonlinearity arises as the result of large deformations, while the material remains in linearly elastic status. In this paper, a slender beam is subjected to compressive forces at spring-hinged ends. Several theoretical solutions are obtained in terms of elliptic integrals. Representative parameters such as the arc length, deflection, curvature, bending moment and bending stress are presented in terms of these integrals. The predicted results are compared with the experimental data and both are found to be in fairly good agreement with each other.