Modelling stability of reinforced concrete walls applying convex optimization

Poulsen

et al. 2023

The structural response of slender reinforced concrete (RC) structures may be highly nonlinear due to cracking, reinforcement yielding, and geometrically nonlinear effects. While advanced models can simulate the detailed response of such structures, they are generally ill‐suited for limit state verification in practical design scenarios due to a high computational and modeling effort. A design‐oriented method for evaluating the geometrically linear response of cracked RC wall structures was recently presented and demonstrated to allow the analysis of large‐scale models with more than 2400 finite shell elements within minutes on a standard personal computer. This paper proposes a design‐oriented numerical method for efficient instability analysis of slender RC wall structures, also enabling the inclusion of thermal effects. Based on a two‐step linearized buckling analysis, the method first determines the geometrically linear structural response by solving the complementary energy minimization problem, including, if relevant, thermal strains and reduced material stiffness. This solution is used to derive the sectional stiffness upon which a linearized buckling problem is formulated and subsequently solved as a linear eigenvalue problem. The model is validated using examples with exact solutions, and its applicability to large‐scale models is demonstrated through an example with a four‐story stairwell modeled using more than 3200 finite elements.

“…The concept, which is similar to what was proposed by Ref. [15], is illustrated in Figure 1 for the one‐dimensional case. As illustrated, the method estimates the critical buckling load

P_{cr}

based on the response to the applied load

P_{0}

.…”

Section: Analysis Proceduresmentioning

confidence: 73%

Design‐oriented nonlinear‐elastic buckling analysis of reinforced concrete wall structures using convex optimization

Poulsen

et al. 2023

“…The effect of the layer discretization on the solution accuracy was investigated for stress‐based finite beam elements in reference [20], where as few as five layers were found to give reasonably accurate results. This example investigates the effect of the number of layers on the solution accuracy for the shell element.…”

Section: Verification Examplesmentioning

confidence: 99%

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

Poulsen

et al. 2022

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.

“…The method proposed in this paper uses an approach similar to the one introduced in Reference 12 where the complementary elastic energy was minimized subject to equilibrium conditions. This approach enables efficient evaluation of the stresses, the displacements, and the strains, which further allows for a straightforward analytical assessment of the crack widths in a postprocess.…”

Section: Introductionmentioning

confidence: 99%

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

Larsen

et al. 2021

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.