A numerical method to generate optimal load paths in plain and reinforced concrete structures

• Topology optimization is used to find optimal truss-like load paths in r.c. members.
• Concrete is modeled as a hyper-elastic material that carries only compression.
• Strut-only models are generated for structures made of plain concrete.
• Strut-and-tie models are generated for concrete structures with prescribed rebar cages.
• Stress diffusion problems can be dealt with in case of point forces.

A numerical method based on topology optimization is proposed to generate optimal strut-only models for structures made of plain concrete and optimal strut-and-tie models for concrete structures where fixed regions of reinforcement are prescribed. Assuming concrete as a hyper-elastic material carrying only compression, both the inherently nonlinear equilibrium equation and the energy-based topology optimization problem are solved within the same minimization procedure. Numerical simulations investigate load paths within the two-dimensional domain in case of conventional rebar cages. A stress diffusion problem is considered as well.