Reinforcement layout design for concrete structures based on continuum damage and truss topology optimization

Oded Amir, Ole Sigmund

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)157-174
Number of pages18
JournalStructural and Multidisciplinary Optimization
Issue number2
StatePublished - Feb 2013
Externally publishedYes


  • Continuum damage
  • Reinforced concrete
  • Topology optimization
  • Truss optimization

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization


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