A Critical Study of Howell et al.'s Nonlinear Beam Theory

Abstract: In our analysis, we show that Howell et al.'s nonlinear beam theory does not depict a representation of the Euler-Bernoulli beam equation, nonlinear or otherwise. The authors' nonlinear beam theory implies that one can bend a beam in to a constant radius of deformation and maintain that constant radius of deformation with zero force. Thus, the model is disproven by showing that it is invalid when the curvature of deformation is constant, while even the linear Euler-Bernoulli beam equation stays perfectly valid under such deformations. To conclude, we derive a nonlinear beam equation by using Ciarlet's nonlinear plate equations and show that our model is valid for constant radius of deformations.