Real-time, high-fidelity linear elastostatic beam models for engineering education

Euler-Bernoulli beam theory is a fundamental subject in structural engineering education, as it characterizes the quintessence of a bending phenomenon. Since this theory relies on assumptions, we generally use finite element analysis when it comes to predicting the physical behavior of a real beam. However, finite element analysis is cumbersome for engineering education because it is not conducive to real-time or repetitive analyses during a lecture. To address this difficulty, we propose to exploit a certified reduced basis analysis to produce a real-time, high-fidelity beam model for engineering education. For demonstration, we construct two three-dimensional, square cross-sectional beam models with certified reduced basis analysis and compare them to the corresponding finite element beam models in terms of accuracy and efficiency. A comparative study shows that the certified reduced basis beam models permit actual errors and runtimes less than 0.1 % and 0.003 seconds, respectively, on average. As a result, we believe that the certified reduced basis beam models are compelling alternatives to their finite element counterparts and would greatly enhance engineering education.