Design-oriented elasto-plastic analysis of reinforced concrete structures with in-plane forces applying convex optimization

Assessment of the cracked behavior at service load and verification of sufficient deformation capacity in the ultimate state are often required when designing reinforced concrete structures. Most existing methods dedicated to nonlinear analysis of reinforced concrete, however, are not well-suited in practice for use in design processes involving large-scale structural problems due to an enormous modeling effort and lack of numerical stability. This paper presents a new finite element framework for efficient elasto-plastic analysis of two-dimensional reinforced concrete structures subjected to in-plane forces. The basic concept is to adopt a stress-based finite element formulation and cast the problem as a convex optimization problem where energy principles are invoked through a formalistic application of nonlinear-elastic material models. The method accounts for reinforcement yielding and concrete crushing, including the strength reduction due to cracking, and can be used to imitate the elasto-plastic response of fully-cracked structures subjected to monotonic loading. The efficiency of the method is demonstrated, inter alia, by an analysis of a complex structure, where the discretized problem has more than 1 million variables and is solved within a few minutes on a standard personal computer.