Abstract
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 varios 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.
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Naghdi, P.M., Rubin, M.B. Constrained theories of rods. J Elasticity 14, 343–361 (1984). https://doi.org/10.1007/BF00125605
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DOI: https://doi.org/10.1007/BF00125605