In the analysis of isotropic and prismatic beams, the usual approach is to assume that the stress field is uni-axial (Bernoulli hypothesis). Such an assumption is not valid in the case of composite beams and if applied, results in large errors. The analysis becomes even further complex if the beam performs large deflections (even though at small strain) and the equations become geometrically nonlinear. One successful solution method in such cases is the so-called Variational-Asymptotic Method (VAM). This method starts from the elastic energy functional and has the common advantage of asymptotic methods of being mathematically well-grounded with no ad hoc assumptions. This method splits the three dimensional (3-D) geometrically nonlinear elasticity analysis for beam problems into a nonlinear 1-D analysis along the beam that utilizes the results of a linear 2-D analysis used to determine the cross-sectional stiffness matrices. The linear 2-D cross-sectional analysis is performed by the Variational Asymptotic Beam Sectional Analysis program (VABS). At present, there are two versions of VABS: the Georgia Tech version (GT/VABS release 2.1), released and maintained by Professors Yu and Hodges, and the UM/VABS release 1.30, released and maintained by Professor Cesnik at the University of Michigan. Both of these codes are widely used. The main aim of this paper is to provide a comparative study of the capabilities and the results obtainable by using the two existing VABS programs. The programs are used to solve a series of problems including solid section, open, and multi-cell thin-walled structures made of isotropic or composite materials and in search of classic, Timoshenko and Vlasov stiffness matrices (as well as mass matrices). The results obtained for a few cases reveal that these two programs provide about identical mass matrices and identical diagonal elements of stiffness matrices. However, the off-diagonal (coupling) elements in the stiffness matrices are not, in general, close enough to each other. Therefore, one may conclude that even though the outcomes are about identical in the mass matrix calculation, these two VABS programs do not, in general, provide close enough stiffness matrices.

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Conference 18th International Conference on Adaptive Structures and Technologies, ICAST 2007
Citation
Ghorashi, M. (Mehrdaad), & Nitzsche, F. (2007). Comparison of the variational asymptotic beam sectional analysis methods applied to composite beams. In Carleton University - 18th International Conference on Adaptive Structures and Technologies, ICAST 2007 (pp. 153–165).