An assessment and extension of geometrically nonlinear beam theories

Equations of motion for beams assuming only longitudinal, normal stress are derived for large-amplitude beam deflection. The formulation includes various physical extensibility conditions without expansion or truncation of their nonlinear nature. The Lagrange multiplier for an inextensible beam model is explicitly written. The limits of the applicability of various beams models with purely longitudinal, normal stress are explored, and the validity of a pure transverse displacement for a beam with fixed ends is quantified.

Duke Scholars

Author Earl H. Dowell Thomas Lord Department of Mechanical Engineering and Materia ...