Analysis on the uniformly loaded rectangular cross-section cantilever by a modified load–deflection model

• Published in: Journal of physics. D, Applied physics Applied physics, 2009-02, Vol.42 (4), p.045505-045505 (8)
• Main Authors: Tsai, Shang-Hsi, Wang, Yeng-Tseng, Kan, Heng-Chuan
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Structural mechanics (beam, string...); Theory and numerical methods
• ISSN: 0022-3727; 1361-6463
• DOI: 10.1088/0022-3727/42/4/045505

The load-deflection relationship of the uniformly loaded rectangular cross-section cantilever is analysed by a modified mechanical model, which exhibits its conformity to the physical situation by considering both the tangential and normal surface stresses. The analytical solution of the modelling equation is solved and presented in terms of the first and the second kinds of the Airy functions in association with Scorer's function. The resultant deflection profile contains an inflection point due to the restoring bending moment contributed by the critical surface loadings. The relationships of the tip deflection and the loading scenario are investigated, which reveal the fact that various loading scenarios can result in different deflection profiles, albeit with the same tip deflection. A numerical algorithm is given in the appendix to solve the loading scenario, by which the surface loadings can formally be determined for the designated applications for the devices utilizing the cantilever structure.