A multi-layer shell element for shear walls based on OpenSEES--THUShell
Ref: Lu XZ, Xie LL, Guan H, Huang YL, Lu X, A shear wall element for nonlinear seismic analysis of super-tall buildings using OpenSees, Finite Elements in Analysis & Design, 2015, 98: 14-25.
The research group of Disaster Prevention and Mitigation in Tsinghua University has developed a multi-layer shell element for the simulation of shear wall components. The program can be downloaded at http://www.luxinzheng.net/download/OpenSEES/THUShell.zip.
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The multi-layer shell element is based on the principles of composite material mechanics. It is made up of a number of layers with different thicknesses and different material properties (i.e., concrete layers or rebar layers), as shown in Figure 1(a). The strains and curvatures of the middle-layer of the shell element are firstly obtained during the computation, and the strains in other layers can be determined based on the “plane-in-plane” assumption. Then, the stress in each layer will be calculated through the material constitutive law, and the internal force of the shear element (force and bending moment along the section) can be determined via the numerical integration of the stress in all layers. The multi-layer shell element is capable of simulating coupled in-plane/out-of-plane bending as well as in-plane direct shear and coupled bending-shear behavior of RC shear walls. The rebars are smeared into one or more layers and these rebar layers can be either isotropic or orthotropic depending on the reinforcement ratio in the longitudinal and transverse directions, as shown in Figure 2(b).
(a) Multi-layer shell element
(b) Location of the rebar layers
Figure 1. The Principal of multi-layer shell element
In this research, the corresponding multi-dimensional concrete material model, steel reinforcement model and multi-layer shell element model are developed in OpenSEES. The multi-layer shell element is based on the ShellMITC4 element that is already provided by OpenSEES. The framework of the proposed multi-layer shell element in OpenSEES is shown in Figure 2.
Figure 2 .The framework of the multi-layer shell element in OpenSEES
1 Multi-dimensional concrete model.
This command is used to create the multi-dimensional concrete material model that is based on the damage mechanism and smeared crack model.
2. Multi-dimensional Reinforcement Material
This command is used to create the multi-dimensional reinforcement material.
3. Define the Section of the Multi-layer Shell element
This command will create the section of the multi-layer shell element, including the multi-dimensional concrete, reinforcement material and the corresponding thickness.
Two solid shear wall specimens are chosen to demonstrate the feasibility of the proposed multi-layer shell element.
Table 1. Parameters of the specimen
Table 2. Parameters of the concrete
The stirrups is smeared into orthotropic rebar layers along 0º direction, whereas the longitude reinforcement is smeared into orthotropic rebar layers along 90º direction. The concentrated reinforcement in boundary zone is modeled with truss element, whose node is shared with the shell element to achieve the displacement compatibility.
The boundary zone and the other part of the wall are separately defined with two different multi-layer sections. The boundary zone is divided into 10 layers while the wall is divided into 8 layers.
Figure 3. Force-displacement of the specimens
Test date: Zhang HM, Study on the Performance-based Seismic Design Method for Shear Wall Structures, Doctoral Thesis, Tongji University, Shanghai, 2007.
By: Linlin XIE and Kaiqi LIN
Supervised by: Xinzheng LU, Yuli HUANG (ARUP) and Lieping YE
Download Address http://www.luxinzheng.net/download/OpenSEES/THUShell.zip