These slides were presented at the NAFEMS World Congress 2025, held in Salzburg, Austria from May 19–22, 2025.

Abstract

This paper investigates the optimization of lightweight structures utilizing Finite Element Method (FEM) techniques, with a particular focus on incorporating constraints related to eigenfrequencies and load factors derived from a linear buckling analysis. As the engineering field moves towards more effective and sustainable design practices, the need for innovative optimization strategies becomes increasingly critical. The study presents a comprehensive approach that not only aims to enhance structural performance by optimizing geometric configurations but also ensures that the designs meet specific vibrational and stability criteria. By applying various optimization algorithms, including sizing and shape optimization, the research evaluates how constraints for natural frequencies and critical loads affect the overall design process. During the optimization of lightweight structures, eigenmodes can change significantly due to parameter variations. To track these modes, the Modal Assurance Criterion (MAC) matrix is commonly computed. This matrix helps assess the correlation between different eigenmodes, indicating how similar the modes are across iterations. When calculating the MAC matrix, one can choose to reference either the eigenmodes from the baseline model or the eigenmodes from the previous iteration. Comparing the current iteration's eigenmodes with those from the last iteration provides insights into how changes in design parameters affect the vibrational and buckling characteristics of the structure. This tracking is crucial for ensuring that the optimization process maintains or improves structural performance while adapting to new design configurations. By effectively managing eigenmode variations, engineers can enhance stability and functionality in optimized lightweight structures. Case studies involving aerospace and automotive components are utilized to highlight the practical applications and benefits of these constraints in real-world scenarios. The findings demonstrate significant improvements in the structural integrity and efficiency of lightweight designs, confirming the role of FEM in advancing modern engineering solutions. This work contributes to the development of robust lightweight structures while ensuring compliance with essential performance requirements.