Generalized Timoshenko Theory of the Variational Asymptotic Beam Sectional Analysis

Abstract

The generalized Timoshenko theory for composite beams embedded in the computer program VABS has the same structure as Timoshenko’s original theory for isotropic beams without the restrictive assumptions of the original theory. An overview of this theory is presented to show its general and rigorous framework. Certain theoretical details missing from previous developments are supplied, such as the proof of a kinematical identity and the expression of the recovery theory in terms of sectional stress resultants. It has been demonstrated that the VABS generalized Timoshenko theory reproduces the elasticity solution for the flexure problem of isotropic prisms. Numerical results are presented in support of the long-term validation effort, focusing especially on calculation of sectional stiffnesses (including shear correction factors) and shear center location, making use of the VABS model for composite beam analysis (including buckling and vibration), and recovering three-dimensional field variables over the section. The accuracy of the VABS generalized Timoshenko theory is demonstrated, and some of its practical advantages over three-dimensional finite element analysis are exhibited. Presented at the 44th Structures, Structural Dynamics and Materials Conference, Norfolk, Virginia, April 7 – 10, 2003 Assistant Professor, Department of Mechanical and Aerospace Engineering, Utah State University, Logan, Utah 84322-4130. Formerly, Post Doctoral Fellow, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia. Email: wenbin.yu@usu.edu. Professor, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia, 303320150. Email: dewey.hodges@ae.gatech.edu. Fellow, AHS.