Reliability-Based Topology Optimization Using the Virtual Element Method: An Integrated Framework
Publication: Journal of Structural Engineering
Volume 150, Issue 7
Abstract
This paper introduces a topology optimization approach based on the virtual element method (VEM), incorporating uncertainties. The objective of this optimization process is to design an optimal material layout for problems governed by linear elasticity equations to minimize the volume while satisfying probabilistic compliance constraints. The VEM is used to solve the boundary value problem in reliability-based topology optimization (RBTO). In the comparison between the VEM and the standard finite element method (FEM), a key difference emerges in the absence of explicitly defined shape functions tied to discrete degrees of freedom in VEM. Unlike FEM, VEM directly constructs the discrete bilinear form and load linear form without the need for computing shape function derivatives within the elements. This flexibility accommodates meshes with intricate geometries and arbitrarily shaped elements. The paper discusses the computational efficiency of VEM RBTO and explores the geometric impact of tessellations on converged topologies, demonstrating reduced susceptibility to checkerboard patterns compared to conventional quadrilateral elements. Additionally, the single-loop approach is examined, showcasing comparable accuracy to the first-order/second-order reliability methods (FORM/SORM) of RBTO using VEM. Numerical results for several problems that demonstrate the feasibility of the proposed method are presented.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The author acknowledges the support by the Innovative and Interdisciplinary Research Program of Syracuse University (Grant No. II-50-2021).
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Published In
Journal of Structural Engineering
Volume 150 • Issue 7 • July 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Aug 4, 2023
Accepted: Jan 22, 2024
Published online: May 15, 2024
Published in print: Jul 1, 2024
Discussion open until: Oct 15, 2024
ASCE Technical Topics:
- Continuum mechanics
- Design (by type)
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Finite element method
- Geometrics
- Highway and road design
- Linear functions
- Materials engineering
- Materials processing
- Mathematical functions
- Mathematics
- Methodology (by type)
- Models (by type)
- Motion (dynamics)
- Numerical methods
- Optimization models
- Solid mechanics
- Uncertainty principles
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