A multilayer shell element for shear walls based on OpenSEESTHUShell Ref: Lu XZ, Xie LL, Guan H, Huang YL, Lu X, A shear wall element for nonlinear seismic analysis of supertall buildings using OpenSees, Finite Elements in Analysis & Design, 2015, 98: 1425. The research group of Disaster Prevention and Mitigation in Tsinghua University has developed a multilayer shell element for the simulation of shear wall components. The program can be downloaded at http://www.luxinzheng.net/download/OpenSEES/THUShell.zip. Related Download: OpenSees Models for a 606m Megatall Building v0.1 The multilayer 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 middlelayer of the shell element are firstly obtained during the computation, and the strains in other layers can be determined based on the “planeinplane” 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 multilayer shell element is capable of simulating coupled inplane/outofplane bending as well as inplane direct shear and coupled bendingshear 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) Multilayer shell element
(b) Location of the rebar layers Figure 1. The Principal of multilayer shell element In this research, the corresponding multidimensional concrete material model, steel reinforcement model and multilayer shell element model are developed in OpenSEES. The multilayer shell element is based on the ShellMITC4 element that is already provided by OpenSEES. The framework of the proposed multilayer shell element in OpenSEES is shown in Figure 2.
Figure 2 .The framework of the multilayer shell element in OpenSEES 1 Multidimensional concrete model. This command is used to create the multidimensional concrete material model that is based on the damage mechanism and smeared crack model.
2. Multidimensional Reinforcement Material This command is used to create the multidimensional reinforcement material.
3. Define the Section of the Multilayer Shell element This command will create the section of the multilayer shell element, including the multidimensional concrete, reinforcement material and the corresponding thickness.
4. Examples Two solid shear wall specimens are chosen to demonstrate the feasibility of the proposed multilayer 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 multilayer sections. The boundary zone is divided into 10 layers while the wall is divided into 8 layers.
Figure 3. Forcedisplacement of the specimens Test date: Zhang HM, Study on the Performancebased 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 