# Modeling 3D Slender Solids (Beams) with Complex Microstructures: VABS™

Variational Asymptotic Beam Sectional Analysis (VABS) is considered to be the only tool that has the potential to rigorously model three-dimensional (3D) slender solids (commonly known as beams) with complex microstructures. After 20 years of development, VABS is now becoming the most preferable tool for the helicopter and wind turbine industries. Engineers and researchers from all over the world are actively using VABS, which is the standard tool for analysis and design of composite slender structures such as helicopter rotor blades, wind turbine blades, composite bridges, high aspect ratio wings, and other slender structural components. The unique technology underlying VABS enables it to become the first truly efficient high-fidelity modeling tool for composite beams, saving users many orders of magnitude in computing time relative to 3D finite element analyzes (FEA), without accuracy loss. The advantages of VABS over other technologies have been noticeably demonstrated by virtue of its generality, efficiency, and accuracy.

### Unique Technology

Unique Technology VABS employs the different beam theories based on the concept of simplifying the original nonlinear 3D analysis of slender structures into a one-dimensional (1D) nonlinear beam analysis using the variational asymptotic method, which is a powerful mathematical method. VABS is designed to model structures for which one dimension is much bigger than the other two (i.e., a beam-like body), even if the structures are developed from composite materials and comprise of a complex internal structure. VABS takes a finite element mesh of the cross section including all the details of material and geometry as inputs to calculate the sectional properties including inertial properties and structural properties. These properties are required for the 1D beam analysis to predict the slender structure’s global behavior. It is also possible to recover the 3D pointwise displacement/stress/strain distribution within the structure based on the global behavior of the 1D beam analysis.

### Key Benefits

The key benefits of the VABS are as follows:

• Drastically reduced design cycle and time to market by helping users save many orders of magnitude in engineering design and analysis time
• Extraordinary competitiveness as the only available technology to meticulously model real structures such as composite blades
• An enabling technology for nonlinear aeroelastic analysis of highly flexible structures
• The best compromise between efficiency and accuracy, an effective alternative for computation-intensive 3D FEA

### Applications

The key applications of the VABS are as follows:

• Helicopter rotor blades
• Gas turbine blades
• Wind turbine blades
• Wing section design
• Composite bridges
• High aspect ratio wings
• Other general smart/composite structures:
• Shafts
• Rods
• Beams
• Bars
• Columns

### Materials

VABS is not restricted by materials. The structure can be developed from an arbitrary number of general materials including:

• Braided composites
• Woven composites
• Conventional materials
• Fiber reinforced composites
• Foam materials and others

### Efficient High-Fidelity

Enabled by VABS, analysis can be performed in an effortless and efficient manner like conventional beam analysis, without losing accuracy compared to more complicated and time-consuming 3D FEA. With VABS, it is presently possible to confidently design and analyze real structures with complicated microstructures because of this unique efficient high-fidelity feature of VABS. For instance, structures that are as complicated as real composite rotor blades with hundreds of layers can be effortlessly handled by a laptop computer.

### Versatile

VABS is implemented using the finite element techniques with a general element library that comprises of all the typical 2D elements such as 3, 4, 5, 6-noded triangular elements and 4, 5, 6, 7, 8, 9-noded quadrilateral elements. Users are given the freedom to choose the type of elements, and it is possible to mix different types of elements within one mesh, if needed. This flexibility permits VABS to model beams of different shapes.

VABS can handle arbitrary layups. Users can provide one parameter for the ply orientation and one parameter for the layup orientation to uniquely specify the material system in the global coordinate system. It is possible to use nine parameters for the ply orientation if the ply angle is not uniform within an element and a ply is highly curved.

VABS does not need the beam reference line to be the locus of cross-sectional area centroids. VABS is capable of calculating the centroid for any arbitrary cross section, and users can select their own reference line for the convenience of the 1D global beam analysis.

VABS can deal with orthotropic materials, general anisotropic materials, and isotropic materials.

VABS can be conveniently and quickly integrated with other environments such as multidisciplinary optimization environments, commercial finite element packages, or computer-aided design environments.

### Additional Features and Benefits

• Material properties: VABS has no restrictions on material properties and can deal with any material including orthotropic, isotropic, or general anisotropic materials.
• Multiphysical capability: VABS can examine structures under the coupled effects of mechanical, thermal, and electromagnetic fields.
• Shape of the cross-section: Truly arbitrary geometries accommodated. Modeling of realistic rotor blades is only possible via VABS. Oversimplified approximation for real structures is not needed.
• Various engineering beam models: Generalized EulerBernoulli model, generalized Timoshenko model to account for transverse shear, generalized Vlasov model for composite beams with vital restrained warping effects. No ad-hoc assumptions such as plane sections remaining plane and normal to the beam axis are invoked.
• Modeling of Initially twisted/curved/oblique beams: The structure can be initially curved or twisted and/or have a naturally oblique cross-section.
• Recovery of field variables: Possible to accurately recover 3D strains, stresses, and displacements from 1D displacements and sectional resultants.
• Trapeze effect: performs a nonlinear sectional analysis to integrate the trapeze effect for beams under large centrifugal forces which impacts the torsional rigidity.
• Free companion 1D beam analysis: GEBT, also produced by Prof. Yu as a companion code for VABS, is a general-purpose 1D nonlinear beam analysis code. It is based on the geometrically exact beam theory and can be used for dynamic, static, eigenvalue analysis.
• Overall benefits: Extremely high levels of accuracy—comparable to 3D nonlinear FEA yet with the efficiency of simple 1D beam analysis. Possible to analyze/design complex structures which is not possible using 3D FEA within the existing computing resources.