Constrained theories of rods

✍ Scribed by P. M. Naghdi; M. B. Rubin

• Book ID: 104631778
• Publisher: Springer Netherlands
• Year: 1984
• Tongue: English
• Weight: 854 KB
• Volume: 14
• Category: Article
• ISSN: 0374-3535
• DOI: 10.1007/bf00125605

✦ Synopsis

Utilizing a nonlinear theory of rods, which is formulated on the basis of a Cosserat curve with two directors, a number of constrained theories of various degrees of generality are developed. In addition to the nonlinear version of the Bernoulli-Euler beam theory (discussed for completeness and clarity), six other less restrictive nonlinear constrained theories are also discussed. A table is provided, which summarizes the degree of exclusion of certain modes of motion or deformation, and which indicates the system of differential equations to be used in applications. * For the special case of a straight beam, the linearized version of this theory corresponds to that of a Timoshenko beam. A discussion of the latter in the context of a special case of the linear theory of a Cosserat curve is contained in a paper of Green et al. [7].