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Node-dependent kinematic models applied to reinforced concrete structures

Riccardo Augello, Erasmo Carrera, Alfonso Pagani, Mário R. T. Arruda and Jiahui Shen

Vol. 11 (2023), No. 1, 19–43
Abstract

This paper proposes a node-dependent kinematics technique for the development of efficient mathematical modelling of reinforced concrete structures. The present approach allows for building models optimized in terms of accuracy and computational resource utilization. Some areas of the structures are approximated using refined models with enhanced three-dimensional capabilities, whereas one-dimensional uniaxial models are employed in the remaining domain. In this way, the three-dimensional accuracy is limited only in the area of interest. This approach is possible thanks to the Carrera unified formulation, which can generate from low- to high-order models in a unified manner. The three-dimensional displacement field is approximated by using Lagrange polynomials in the portion of the structure where the three-dimensional accuracy needs to be achieved, modelling the steel and the concrete domains as two independent entities. On the other hand, low-order Taylor expansion-based models are used to model zones far from the critical ones with classical theories, such as Euler–Bernoulli and Timoshenko beams. The continuity between the two different domains is guaranteed by employing the node-dependent kinematic approach, in which the kinematics of the structure can vary. The finite element method is adopted, so that no other mathematical artifices are needed to join different theories. Several examples are considered to highlight the potential of the node-dependent kinematics approach when applied to reinforced concrete structures.

Keywords
componentwise, reinforced concrete, one-dimensional model, finite element model, Carrera unified formulation
Mathematical Subject Classification
Primary: 74G70, 74S05
Milestones
Received: 21 June 2022
Revised: 26 September 2022
Accepted: 7 November 2022
Published: 23 October 2023

Communicated by Francesco dell'Isola
Authors
Riccardo Augello
Department of Mechanical and Aerospace Engineering
Politecnico di Torino
Torino
Italy
Erasmo Carrera
Department of Aeronautics and Aerospace Engineering
Politecnico di Torino
Torino
Italy
Alfonso Pagani
Department of Mechanical and Aerospace Engineering
Politecnico di Torino
Torino
Italy
Mário R. T. Arruda
Instituto Superior Técnico
Universidade de Lisboa
Lisboa
Portugal
Jiahui Shen
Department of Mechanical and Aerospace Engineering
Politecnico di Torino
Torino
Italy