Questions and Answers

0 Like 0 Dislike


How capable is variational asymptotic method in analysis of beams under torsion.

Hi there,


It has been a while which I am doing research on Variational Asymptotic Method (VAM) for beam analysis. I am a structural engineer and aware that this method is actually being used extensively in aerospace and specifically in rotor blade design based on the premier works by Prof. Hodges , Prof. Yu and their colleagues.

Now, my question is that to what extent this method can give accurate results in torsion. Actually, this method seems to be able to calculate the torsional properties of a beam accurately but when recovering the strain/stress field it can not give the longitudinal stress field as accurate as the exact 3D model and actually it can only consider the shear stress ( unconstrained torsion) .Now, considering the fact that rotor blades with initial twist and curves are subjected to torsion, when using this method which of the outputs are used in the design. In other words, for rotor blade design is it needed to consider the variations in longitudinal stress or the designer is only after shear stress or probably angle of twist?! Or probably the designer only uses the sectional stiffness resulted from VAM in conjunction with another method to catch torsion effects accurately? 

I am trying to find a way to make use of the VAM results in beam analysis under torsion. Torsion has been addressed in Vlasov studies for 1D analysis of open sections and  I am after to get accurate answers with this method for thin walled closed sections as well.


Any helps/hints in this regard is much appreciated in advance,


Kind regards,



Report abuse

1 Responses

  1. 0 Dislike



    Dear Kiana,

    I discussed your question with Prof. Dewey Hodges of Georgia Tech. The below is his answer. 

    The elastic constants for both Generalized Classical and Generalized Timoshenko models, as output by VABS, are well suited for 1D behavior, including torsion, for beams that do not have thin-walled, open sections. The stress recovery for such beams should be adequate. The elastic constants from the Generalized Vlasov model should work fine for 1D behavior of beams with thin-walled, open sections. Unfortunately, there is a lack of studies verifying 3D stress recovery in thin-walled, open-section beams. The Generalized Vlasov is not intended for thin-walled, closed cell beams. The reason it won’t work for this case is that the Generalized Vlasov correction is based on a warping field dominated by out-of-plane, torsional warping. The warping of thin-walled closed-cell beams is not dominated by torsion nor is it necessarily out of plane. Generalized Classical and Generalized Timoshenko theories should be adequate for this case. For certain special cases, further development of VABS may be necessary to capture the boundary-layer behavior in closed-cell beams. 

    Reply Report abuse Accept answer

    Please login to answer the question.

Do not forget to select the best answer for your question.