Algebraic reduction of beams for CAD-integrated analysis

Beams are high-aspect-ratio structural members that are used extensively in civil, automotive, aerospace, and MEMS applications. In all such applications, one must typically analyze and optimize the beams through computer simulations. Standard 3-D finite element analysis (FEA) of beams can be used in such simulations; it is however prone to errors, and is computationally expensive for thin structures. Therefore, a common strategy is to carry out a dimensionally reduced 1-D beam analysis. Unfortunately, 1-D beam analysis is hard to automate and integrate with 3-D CAD. In this paper, we propose an alternate “algebraic reduction” method that combines the generality of 3-D FEA, and the computational efficiency of 1-D beam analysis. This is achieved via a dual-representation framework where the geometry of the beam is captured via a 3-D finite element mesh, while the physics is captured via a 1-D beam model. The proposed method is formally established, and supported through numerical experiments.