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Abstract A multiscale topology optimization framework for stress-constrained design is presented. Spatially varying microstructures are distributed in the macroscale where their material properties are estimated using a neural network surrogate model for homogenized constitutive relations. Meanwhile, the local stress state of each microstructure is evaluated with another neural network trained to emulate second-order homogenization. This combination of two surrogate models — one for effective properties, one for local stress evaluation — is shown to accurately and efficiently predict relevant stress values in structures with spatially varying microstructures. An augmented lagrangian approach to stress-constrained optimization is then implemented to minimize the volume of multiscale structures subjected to stress constraints in each microstructure. Several examples show that the approach can produce designs with varied microarchitectures that respect local stress constraints. As expected, the distributed microstructures cannot surpass density-based topology optimization designs in canonical volume minimization problems. Despite this, the stress-constrained design of hierarchical structures remains an important component in the development of multiphysics and multifunctional design. This work presents an effective approach to multiscale optimization where a machine learning approach to local analysis has increased the information exchange between micro- and macroscales.
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Linear and Nonlinear Topology Optimization using Morphing Beam Networks
Starting from a network of discrete beams, topology optimized structures are produced by simultaneously optimizing each beam’s width and the locations of each node within the network. Due to the sparse nature of a beam network and by utilizing gradient descent results in a drastic reduction in computational cost compared to existing methods. Two different optimization objectives are investigated: minimization of the strain energy occurring from loading, often referred to compliance minimization; and the design of structures with prescribed mechanical responses to an applied load.
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- Award ID(s):
- 2244342
- PAR ID:
- 10518479
- Publisher / Repository:
- ICTAM 2024
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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