A nonlinear quadrilateral thin flat layered shell element for the modeling of reinforced concrete wall structures

  • F. RojasEmail author
  • J. C. Anderson
  • L. M. Massone
S.I. : Nonlinear Modelling of Reinforced Concrete Structural Walls


In this article, a simple and accurate quadrilateral thin flat layered shell element formulation for the nonlinear analysis of reinforced concrete (RC) wall systems under static and cycling loads is presented. The 4 node shell element, with 6 degree of freedom (DOF) per node (3 displacements and 3 rotations) is created by superposing the quadrilateral layered membrane element with drilling degrees of freedom (12 DOF, 2 displacement and 1 rotation per node) developed by Rojas et al. (Eng Struct 124:521–538, 2016), and the Discrete Kirchhoff Quadrilateral Element (12 DOF, 1 displacement and 2 rotations) formulated by Batoz and Tahar (Int J Numer Methods Eng 18(11):1655–1677, 1982), to model the in-plane and the out of plane bending behavior of the shell element, respectively. In addition, to model the complex behavior and coupling of the axial, flexural and shear behavior, observed in complex RC wall structures, the transversal section of the shell element consists of a layered system of fully bonded, smeared steel reinforcement and smeared orthotropic concrete material with the rotating angle formulation. The formulation used a tangent stiffness matrix approach, which include the coupling of membrane and bending effects. For verification, the shell element formulation is used to model a set of experimental results for T-shaped RC walls that are available in the literature. The proposed element is robust, simple to implement, and it can predict the global results (load vs. displacement and maximum capacity) and also the local behavior (vertical strain at the base level along the web and the flange) observed in RC wall structures.


Reinforced concrete wall T-shaped walls Nonlinear layered shell element FEM model 



This study was financially supported by Chile’s National Commission on Scientific and Technological Research (CONICYT) for the Fondecyt Initiation into Research 2014—Project No. 11140429. Also, the help with some figures by Mr. Fernando Muñoz is thanked.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of ChileSantiagoChile
  2. 2.Department of Civil and Environmental EngineeringUniversity of Southern CaliforniaLos AngelesUSA

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