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

Abstract

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): 1982), to model the inplane 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.

Nonlinear analysis of reinforced concrete structures using thin flat shell elements

“…In this paper, the Quadrilateral Thin Flat Layered Shell Element -QTFLS, proposed by Barrales [5] and Rojas et al [10], was adopted. It is a combination of the Quadrilateral Layered Membrane Element with Drilling Degrees of Freedom (DOF) -QLMD [11], and the Discrete Kirchhoff Quadrilateral Element -DKQ [12], where the Kirchhoff's assumptions for thin plates are considered.…”

“…Figure 1. Quadrilateral Thin Flat Layered Shell Element -QTFLS [10] In the QTFLS element, both the displacement and deformation fields are established through the superposition of membrane and plate behaviors. According to Barrales [5], this approach has the advantage of allowing different shape functions for each behavior.…”

An Application of the Proper Orthogonal Decomposition Method for Nonlinear Dynamic Analysis of Reinforced Concrete Structures Subjected to Earthquakes

“…The proper orthogonal decomposition POD also known as the Principal Component Analysis PCA and the Karhunen-Loève Decomposition KLD is a statistical analysis of observation data. Let's consider a data matrix containing observation vectors and each observation vector is made of m dimension (7) is row in matrix and represents all the data collected on dimension . If data set has a zero mean, the variance of becomes (8) and the covariance of and becomes .…”

“…The layered shell element consists in dividing the 2D structural element into layers along its thickness. Each layer is made up of a single material and can behave nonlinearly in 2D [5][6][7]. When dealing with nonlinearities, nonlinear solving techniques should be adopted.…”

Guest editorial: Nonlinear modelling of reinforced concrete structural walls

“…(E) The in-plane and out-of-plane behaviour of RC walls can be well documented by an adequate shell element. An efficient quadrilateral thin flat layered shell (QTFLS) element has been proposed by Rojas et al (2019) by combining the robust quadrilateral layered membrane element with drilling DOF developed by Rojas et al (2016) for the modelling of RC walls and the well-known Discrete Kirchhof Quadrilateral Element formulated by Batoz and Tahar (1982). Such element can be applied in complex 3D RC wall systems to simulate the interaction between elements at different direction of planes, such as wall and slabs, and to study the local (i.e.…”