A shell element for design-oriented elasto-plastic analysis of reinforced concrete wall structures using convex optimization

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 elasto-plastic analysis of fully cracked reinforced concrete wall structures subjected to monotonic loading. Using nonlinear-elastic constitutive models to imitate elasto-plasticity, 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.