Office of Technology Transfer – University of Michigan

UM/VABS--University of Michigan/Variational Asymptotic Beam Section Code

Technology #2637

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Carlos E. Cesnik
Managed By
Drew Bennett
Associate Director - Software Licensing 734-615-4004


Numerical simulation of structures through 3-dimensional (3D) finite element analysis has become widely accessible to engineers using the power of modern computers. However, one should not underestimate the value of engineering understanding of physical problems to identify essential features that could simplify their mathematical models. Such approach can improve the feasibility and efficiency of the structural analysis, particularly with in the context of a multidisciplinary design environment.


Researchers at the University of Michigan developed a finite element based code, UM/VABS, for cross-sectional analysis of initially twisted and curved anisotropic beams in the presence of anisotropic piezocomposite materials. Arbitrary cross-sectional shapes and material distribution can be asymptotically analyzed for stiffness, inertia, and actuation constants. Once coupled with 1D beam solution, 3D stress, strain, and displacement fields can be recovered.

Applications and Advantages


  • Dimensional reduction of anisotropic slender-nl-structures with embedded anisotropic-nl-piezocomposite materials


  • Finite deformation mode augments the classical beam kinematics