Topology optimization with natural frequency and structural stability criteria using eigenvector aggregates
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Li, Bao
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Abstract
Topology optimization is a powerful tool for designing lightweight, high-performance structures by optimizing material distribution to meet specific performance objectives. One of the most challenging applications of topology optimization involves ensuring structural stability and achieving the desired natural frequencies of the design by formulating problems as generalized eigenvalue problems. Eigenvectors provide essential information on the mode shapes for a structure, offering insights into tailoring its behavior to specific requirements. However, imposing eigenvector constraints in topology optimization is challenging due to the non-differentiability of repeated eigenvalues, the complexity of balancing competing objectives, and the high computational cost of calculating eigenvector derivatives. This thesis addresses these challenges by introducing an innovative eigenvector aggregation approach to handle eigenvector constraints in topology optimization. It presents a comprehensive study of the eigenvector aggregate, including its applications in natural frequency and buckling optimization, as well as the ability to hand the repeated eigenvalues. Additionally, this work presents efficient methods for computing eigenvector-based derivatives and validates these methods in the thermal, natural frequency, and buckling optimization problems. Furthermore, this thesis investigates nonlinear initial post-buckling problems and introduces efficient optimization criteria based on Koiter asymptotic theory for post-buckling performance optimization. It presents a novel two-layer adjoint-based sensitivity analysis for Koiter-based optimization, significantly reducing the computational cost.
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Date
2024-11-25
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Dissertation