Reinforcement layout design for concrete structures based on continuum damage and truss topology optimization
This article presents a new procedure for the layout design of reinforcement in concrete structures. Concrete is represented by a gradient-enhanced continuum damage model with strain-softening and reinforcement is modeled as elastic bars that are embedded into the concrete domain. Adjoint sensitivity analysis is derived in complete consistency with respect to path-dependency and the nonlocal model. Classical truss topology optimization based on the ground structure approach is applied to determine the optimal topology and cross-sections of the reinforcement bars. This approach facilitates a fully digital work flow that can be highly effective, especially for the design of complex structures. Several test cases involving two- and three-dimensional concrete structures illustrate the capabilities of the proposed procedure.
KeywordsReinforced concrete Topology optimization Continuum damage Truss optimization
The work of the first author was funded by the Danish Council for Independent Research | Technology and Production Sciences. The work of the second author was funded by Villum Fonden via the NextTop project. These supports are gratefully acknowledged. We wish to thank Claus B.W. Pedersen for several fruitful discussions and for his important comments. We also thank Krister Svanberg for the FORTRAN MMA code.
- Bendsøe MP, Sigmund O (2003) Topology optimization—theory, methods and applications. Springer, BerlinGoogle Scholar
- Dombernowsky P, Søndergaard A (2009) Three-dimensional topology optimisation in architectural and structural design of concrete structures. In: Proceedings of the International Association for Shell and Spatial Structures (IASS) symposium, Valencia, SpainGoogle Scholar
- fib Task Group 44 (2008) Practitioners’ guide to finite element modelling of reinforced concrete structures. International Federation for Structural Concrete (fib), Lausanne, SwitzerlandGoogle Scholar
- Lemaître J, Desmorat R (2005) Engineering damage mechanics. Springer, BerlinGoogle Scholar
- Liang Q, Xie Y, Steven G (2000) Topology optimization of strut-and-tie models in reinforced concrete structures using an evolutionary procedure. ACI Struct J 97(2):322–330Google Scholar
- Marti P (1985) Truss models in detailing. Concr Int 7:66–73Google Scholar
- Moen CD, Guest JK (2010) Reinforced concrete analysis and design with truss topology optimization. In: Proceedings of the 3rd fib international congress, Washington DC, USAGoogle Scholar
- Schlaich J, Schafer K, Jennewein M (1987) Toward a consistent design of structural concrete. PCI J 32(3):74–150Google Scholar
- Sigmund O, Bendsøe MP (2004) Topology optimization: from airplanes to nano-optics. In: Stubkjær K, Kortenbach T (eds) Bridging from technology to society. Technical University of Denmark, Lyngby, DenmarkGoogle Scholar