A generalized Vlasov theory for composite beams

A generalized Vlasov theory for composite beams with arbitrary geometric and material sectional properties is developed based on the variational asymptotic beam sectional analysis. Instead of invoking ad hoc kinematic assumptions, the variational-asymptotic method is used to rigorously split the geometrically-nonlinear, three-dimensional elasticity problem into a linear, two-dimensional, cross-sectional analysis and a nonlinear, one-dimensional, beam analysis. The developed theory is implemented into VABS, a general-purpose, finite-element based beam cross-sectional analysis code. Several problems are studied to compare the present theory with published results and a commercial three-dimensional finite element code. The present work focuses on the issues concerning the use of the Vlasov correction in the context of the accuracy of the resulting beam theory. The systematic comparison with three-dimensional finite element analysis results helps to quantitatively demonstrate both the advantages and limitations of the Vlasov theory.