University of Twente Student Theses
Design Optimization Strategies for Geometrically Nonlinearly Deforming Structures using Analytical Gradients
Posthumus, Tobias (2024) Design Optimization Strategies for Geometrically Nonlinearly Deforming Structures using Analytical Gradients.
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| Abstract: | Optimization of nonlinearly deforming structures requires solving the system state variables while searching for the optimal design variables. For large structures with numerous state variables or a high number of design variables, using computationally efficient strategies in the optimization process becomes crucial. Efficient gradient-based optimization can be achieved by using analytical gradients. Creating an algorithm to systematically compute analytical gradients can be cumbersome and time-consuming, but significantly increases optimization speed. In this work, two optimization strategies are investigated: nested and SAND (simultaneous analysis and design) optimization. In the nested approach, the state variables are solved in a nested function for each optimization iteration. In the SAND approach, the state variables are solved along with the design variables. The nested approach involves an implicit relationship between state and design variables. Here, the direct and adjoint methods are used. The research shows that analytical gradient computation is several orders of magnitude faster than the numerical approach using finite differences, with increasing effect for optimization problems with more design variables. Additionally, the work shows that using analytical gradients for both the nested and SAND approaches yields feasible and efficient optimization results for complex structures with up to hundreds of design variables and more than a thousand state variables. Obtaining analytical gradients systematically proves to be a worthwhile investment, as it enables the optimization of far more complex systems than current gradient-based optimization using finite differences can achieve within a reasonable time. |
| Item Type: | Essay (Master) |
| Faculty: | ET: Engineering Technology |
| Subject: | 52 mechanical engineering |
| Programme: | Mechanical Engineering MSc (60439) |
| Link to this item: | https://purl.utwente.nl/essays/101575 |
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