Derivation of linear beam equations using nonlinear continuum mechanics

Abstract

Familiar linear elastic and viscoelastic beam equations (Euler-Bernoulli, Rayleigh, Kelvin-Voigt, Timoshenko, and Shear Diffusion) and boundary conditions are derived from a nonlinear theory of large motions rather than the usual variational techniques. Also included is a fairly detailed derivation of the nonlinear theory and a careful discussion of the hypotheses.