Probabilistic Topology Optimization Framework for Geometrically Nonlinear Structures Considering Load Position Uncertainty and Imperfections

Muayad Habashneh, Oveys Ghodousian, Hamed Fathnejat and Majid Movahedi Rad ()
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Muayad Habashneh: Department of Structural and Geotechnical Engineering, Széchenyi István University, 9026 Győr, Hungary
Oveys Ghodousian: Department of Civil Engineering, Takestan Branch, Islamic Azad University, Takestan 3481949479, Iran
Hamed Fathnejat: Basque Center for Applied Mathematics, 48001 Bilbao, Spain
Majid Movahedi Rad: Department of Structural and Geotechnical Engineering, Széchenyi István University, 9026 Győr, Hungary

Mathematics, 2024, vol. 12, issue 23, 1-16

Abstract: In this manuscript, a novel approach to topology optimization is proposed which integrates considerations of uncertain load positions, thereby enhancing the reliability-based design within the context of structural engineering. Extending the conventional framework to encompass imperfect geometrically nonlinear analyses, this research discovers the intricate interplay between nonlinearity and uncertainty, shedding light on their combined effects on probabilistic analysis. A key innovation lies in treating load position as a stochastic variable, augmenting the existing parameters, such as volume fraction, material properties, and geometric imperfections, to capture the full spectrum of variability inherent in real-world conditions. To address these uncertainties, normal distributions are adopted for all relevant parameters, leveraging their computational efficacy, simplicity, and ease of implementation, which are particularly crucial in the context of complex optimization algorithms and extensive analyses. The proposed methodology undergoes rigorous validation against benchmark problems, ensuring its efficacy and reliability. Through a series of structural examples, including U-shaped plates, 3D L-shaped beams, and steel I-beams, the implications of considering imperfect geometrically nonlinear analyses within the framework of reliability-based topology optimization are explored, with a specific focus on the probabilistic aspect of load position uncertainty. The findings highlight the significant influence of probabilistic design methodologies on topology optimization, with the defined constraints serving as crucial conditions that govern the optimal topologies and their corresponding stress distributions.

Keywords: topology optimization; geometric imperfection; elastoplastic model; probabilistic design (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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