Computational Notebooks in a Finite Element Analysis Course: Engineering Students' Reflections on the Value and Challenges of Computational Approaches

This work-in-progress paper introduces an innovative approach that uses computational notebooks to teach Finite Element Analysis (FEA) in a Mechanical Engineering undergraduate course to aid the understanding of complex phenomena in Mechanics of Materials, and enhance students' computational thinking skills. Research indicates that students, irrespective of their educational level, face difficulties in grasping fundamental concepts in mechanics of materials. These challenges arise from the inherent complexity of concepts like stress, strain, torsion, and buckling, which are difficult to observe, hindering comprehension. Therefore, this work aims to leverage the synergy between mechanics of materials and computational principles to actively engage students in advanced topics such as structural strength, failure of structures, and sensitivity analysis, through the use of computational notebooks. To evaluate the effectiveness of this approach, we first asked students to analyze truss structures using hand calculations following the discrete stiffness method within a Finite Element Analysis framework. Subsequently, we implemented the same method as a simulation tool in a MATLAB Computational Notebook. Finally, we asked the students to reflect on: (1) the value of using computational methods to approach Finite Element Analysis when compared to hand calculations; (2) the difficulties they faced when implementing the activities in the MATLAB Computational Notebook; (3) the support they required to successfully complete these activities; and (4) the effectiveness of the simulation tool in understanding the effect of forces and stress distributions in structures. We anticipate that computational notebooks will provide an ideal platform for sharing lessons and tutorials, enhancing student engagement, and promoting active learning. Students have access to the complete source code, allowing them to develop computational skills. Early exposure to coding, modeling, and simulation techniques is crucial in preparing students for the computational demands of modern engineering workplaces.

I. Background

Computational tools and methods have emerged as essential elements in scientific exploration and engineering design. Virtually every field encompasses a “computational” subdiscipline, where practitioners and researchers harness the power of computation to unravel phenomena and devise innovative solutions. Consequently, undergraduate curricula in various disciplines are increasingly integrating computational concepts and skills into core courses. Some of these integrations approach computational problem-solving as a means to foster computational thinking [1]; while others recognize it as an essential component of applied computational science that is embedded within other science and engineering disciplines [2].