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.

The iterative nature of the design processes for building structures requires computational models to be robust, efficient, and accessible while reflecting the actual structural behavior with sufficient accuracy. For limit state analysis of reinforced concrete structures, efficient linear-elastic models are generally inaccurate, while the modeling and computational complexity of most high-accuracy nonlinear models inhibit their use in design processes for large-scale structures. A recently proposed framework for elasto-plastic analysis of cracked reinforced concrete panels was demonstrated to be capable of analyzing models with more than 10,000 finite elements within minutes on a standard personal computer. This paper proposes an extension of this work in terms of a finite shell element for elastoplastic analysis of fully cracked reinforced concrete wall structures subjected to monotonic loading. Using nonlinear-elastic constitutive models to imitate elastoplasticity, the proposed shell element couples the in-plane section force variation to the nonlinear through-thickness stress variation in a stress-based formulation using a layer-based submodel. The method is validated with exact solutions, and its applicability in design processes involving large-scale structures is demonstrated using a finite element model of a four-story stairwell with more than three million variables, which is solved within minutes on a personal computer.

No abstract