VABS Homepage

Target Applications

• Helicopter rotor blades
• Wind turbine blades
• Gas turbine blades
• High aspect ratio wings
• Wing section design
• Other general composite/smart beams, shafts, rods, columns, or bars.

Introduction

• VABS adopts the variational asymptotic method (VAM) as its mathematical foundation. The original 3D analysis is rigorously split into a 2D cross-sectional analysis for beam properties and a 1D geometrically-exact beam analysis for the global behavior.
• VABS has the unique capability to reproduce 3D Elasticity theory for prismatic beams made of isotropic materials, which could not be achieved by any other beam theory.
• VABS uses 3D material constants as input. They are not laminate stiffnesses or plane-stress-reduced stiffness as used in many other models
• VABS is a general-purpose 2D Finite Element code with a rich element library and it is fully modularized and can be easily integrated into any CAD/CAM software
• VABS can produce an asymptotically correct Euler-Bernoulli beam model (represented by a 4 X 4 stiffness matrix) for prismatic or initially curved/ twisted composite beam with arbitrary reference cross section and reference line
• VABS can construct a generalized Timoshenko beam model (represented by a 5 X 5 stiffness matrix) being as asymptotically correct as possible for prismatic or initially curved/ twisted composite beam.
• VABS can capture trapeze effect which is a nonlinear effect in 1D constitutive law due to moderate-to-large local rotations
• VABS can capture Vlasov effect which is significant for thin-walled open section when torsional stiffness is much smaller compared to other stiffnesses. It can give a stiffness model based arbitrary reference, particularly, VABS can calculate the Vlasov beam model (represented by a 5X5 stiffness matrix) based on choosing the shear center (which is also calculated by VABS) as the beam axis
• VABS can find shear center location for arbitrary cross section made with arbitrary material
• VABS can recover 3D fields using results from 1D solver with almost the same accuracy but with 2 or 3 orders less computational effort. And multiple 3D results can be recovered without resolving the warping problem for multiple 1D results.
• VABS can obtain the generalized mass matrix and corresponding center of mass/gravity for the cross section
• VABS can handle highly curved plies. The ply orientation can vary through the local area of one element. The 3D material properties are calculated point-wisely
• VABS uses skyline storage mode in the most recent released version to reduce memory requirement and speed up the calculation (for large problems, it is around many times faster than banded storage)

VABS Documentation

• What is VABS?
• VABS tutorial
• VABS procedures

Typical Examples

1. Analyze realistic rotor blades (VABS with ANSYS)
2. Recovering 3D stresses (I) (VABS vs elasticity)
3. Recovering 3D stresses (II) (VABS vs ABAQUS)
4. Recovering 3D stresses (II) (VABS vs ANSYS)
5. Vlasov beam theory (VABS vs analytical models)
6. Shear center and shear correction factors (VABS, ANSYS, and a simplified model)
7. Effect of stiffness on 1D results (VABS, NABSA vs ABAQUS)

VABS on Internet

• Internet Finite Element Resources

VABS Frequently Asked Questions

VABS Technical Support

Want to Try?

Main Contributors

• Dewey H. Hodges: Initiated the project to use the variational asymptotic method to perform the cross-sectional analysis for a general composite beam. Supervised all the processes of developing the theory and the codes.
• Carlos E. S. Cesnik : Author of the original version of VABS (this version has been virtually disappeared since year 2000); his classical theory for initially curved and twisted composite beams are implemented in the current code; his "alternative" and generalized theories are not implemented in the current code.
• Bogdan Popescu: Trapeze effect (important for rotor blades); Timoshenko modeling and Vlasov effect for prismatic composite beams and oblique cross sectional analysis for classical theory (these latter analyses have been altered and/or generalized by Wenbin Yu and implemented in the current code).
• Vitali Volovoi: Extensive consultation on theory all along the way; many analytical solutions used in validation; a Tc/Tcl mesh generator for VABS, not included in the standard distribution.
• Wenbin Yu: Updated version of Timoshenko modelling for prismatic beams; Timoshenko modeling for initially curved/twisted composite beams; removed certain restrictions (reference line is now arbitrary, obliqueness not a small angle with initial curvature/twist, and generalized material specification to triangular elements could be used); optimized node numbering to reduce the size of the problem; handle highly curved layers; special techniques to reduce the memory use and speed the calculation for large problems; the recovery theory (partially contributed by Xianyu Hong); author and Tech support for the current version of VABS.

Main References

• Danielson, D. A.; and Hodges, D. H.: "Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor," J. Applied Mechanics, vol. 54, no. 2, 1987, pp. 258 - 262.
• Hodges, D. H.: "A Mixed Variational Formulation Based on Exact Intrinsic Equations for Dynamics of Moving Beams," International Journal of Solids and Structures, vol. 26, no. 11, 1990, pp. 1253 - 1273.
• Cesnik, C. E. S.; and Hodges, D. H.: "Variational-Asymptotical Analysis of Initially Curved and Twisted Composite Beams," Applied Mechanics Reviews, vol. 46, no. 11, part 2, Nov. 1993, pp. S211 - S220.
• Cesnik, C. E. S.; and Hodges, D. H.: "VABS: A New Concept for Composite Rotor Blade Cross-Sectional Modeling," Journal of the American Helicopter Society, vol. 42, no. 1, Jan. 1997, pp. 27 -38.
• Popescu, B.; and Hodges, D. H.: "Asymptotic Treatment of the Trapeze Effect in Finite Element Cross-Sectional Analysis of Composite Beams," International Journal of Non-Linear Mechanics, vol. 34, no. 4, 1999, pp. 709 - 721.
• Popescu, B.; Hodges, D. H.; and Cesnik, C. E. S.: "Obliqueness Effects in Asymptotic Cross-Sectional Analysis of Composite Beams," Computers and Structures, vol. 76, no. 4, 2000, pp. 533 - 543.
• Yu, W.; Hodges, D. H.; Volovoi, V. V. and Cesnik, C. E. S.: "On Timoshenko-Like Modeling of Initially Curved and Twisted Composite Beams," International Journal of Solids and Structures, Vol. 39, no. 19, 2002, pp. 5101-5121.
• Yu, W.; Volovoi, V. V.; Hodges, D. H. and Hong, X.: "Validation of the Variational Asymptotic Beam Sectional Analysis," AIAA Journal, vol. 40, no. 10, Oct. 2002, pp. 2105 - 2112.
• Yu, W.; and Hodges, D. H.: "Elasticity Solutions versus Asymptotic Sectional Analysis of Homogeneous, Isotropic, Prismatic Beams," Journal of Applied Mechanics, vol. 71, no. 1, 2004, pp. 15-23.

• Yu, W.; and Hodges, D. H.: "Generalized Timoshenko Theory of the Variational Asymptotic Beam Sectional Analysis, " Journal of the American Helicopter Society, vol. 50, no. 1, 2005 pp. 46-55.

• Yu, W.; Hodges, D. H.; Volovoi, V. V.; and Eduardo, D. F.: "A Generalized Vlasov Theory of Composite Beams," Thin-Walled Structures, vol. 43, no. 9, 2005, pp. 1493-1511.

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