A transfer matrix model of large deformations of curved rods

Abstract

Transfer matrix models have been frequently used to analyze the structural behavior of rods, including curved and pretwisted ones. The advantages of these models include their relative simplicity, numerical efficiency and ease of implementation. Previous investigations did not include nonlinear analyses of curved rods that undergo large deformations. The present paper describes a nonlinear transfer matrix model of curved and pretwisted rods, which is capable of analyzing very large spatial deformations. The rod is divided into segments. A body system of coordinates is attached to each segment. This system translates and rotates with the segment during the deformation. If the segments are kept small enough, the local deformations of each segment, relative to its body system of coordinates, are small. The segments’ systems of coordinates rotate relative to their neighbors and if this rotation is dealt with properly, large rotations and displacement of the curved rod can be analyzed. In spite of its nonlinear nature, the model remains relatively simple and efficient. The new model is used to solve a few problems and the results show very good agreement with other analytical, finite-element, and experimental results.