Large deflection of 3D curved rods: An objective formulation with principal axes transformations. (15th January 2016)

• Record Type: Journal Article
• Authors: Yilmaz, M.; Omurtag, M.H.
• Is Part Of: Computers & structures. Volume 163(2016)
• Page Start: 71
• Page End: 82
• Publication Date: 2016-01-15
• Subjects: Large deflection -- Finite rotation -- 3D curved rod -- Principal axes transformation; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2015.10.010
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: Definition of the finite rotational transformation between configurations is novel. A general section triad and its relation with the Frenet–Serret frame is presented. Objectivity of stain measures is sustained throughout the element. Equilibrium equations are obtained with a fixed-point approach. Extraction of rotational parameters from a rotation matrix is avoided. Abstract: This study shows that the deformed configuration space of 3D rods can be spanned in an objective manner by means of a semi-configuration-dependent approach. We employ a partially dependent default rotational triad defined using the spatial reference curve, a custom director-unit-vector, and a twisting-like-angle interpolation to obtain the true orientations of the cross-sections. Numerical verification shows that, rotating the custom director-unit-vector in conjunction with the element's first node, strain measure objectivity is ensured throughout the element domain. Employing the fundamental theorem of calculus, this simple but accurate finite-element implementation need not invoke the virtual work principle in the classical sense.