An assessment and extension of geometrically nonlinear beam theories. (1st December 2019) - Culver, Dean; McHugh, Kevin; Dowell, Earl
Highlights: Derived equations of motion for a fully extensible beam without truncating nonlinear terms. Quantified the error in assuming negligible longitudinal displacement for nonlinear beam dynamics when ends are fixed. Found equation for the constraint force in inextensible beams without truncating nonlinear terms. Abstract: 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.