Development of a nonlinear quadrilateral layered membrane element with drilling degrees of freedom and a nonlinear quadrilateral thin flat layered shell element for the modeling of reinforced concrete walls

The primary thrusts of this dissertation are to develop and test a new quadrilateral layered membrane element with drilling degrees of freedom (DOF) and a quadrilateral thin flat layered shell element for the nonlinear analysis of reinforced concrete walls. The drilling degrees of freedom refers to the incorporation of the in-plane rotation as a degree of freedom at each node of the element. The membrane element consists of a quadrilateral element with a total of 12 DOF, 3 per node, 2 displacements and 1 in-plane rotation, and uses a blended field interpolation for the displacements over the element. This formulation is an extension of the one developed by Xia et al. in 2009. The shell element is created by the combination of the membrane element developed in this dissertation and a Discrete Kirchhoff Quadrilateral Element (DKQ, 12 DOF), formulated by Batoz and Tahar in 1982, to model the out of plane bending behavior of the element. The modeling of the section of the membrane and 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 layered section for the shell includes the coupling membrane and bending effects. These elements are implemented on a finite element framework using the object oriented programing language under MATLAB. The framework or MATLAB toolbox for Finite Elements developed for this dissertation allows to incorporate, develop and test new elements, materials, sections and analysis algorithms in a easy and quick manner. The proposed elements are evaluated using experimental results that are available in the literature. It is shown that the new elements are in excellent agreement with the experimental results for the different load configuration, monotonic and cyclic loading, and they are able to predict the failure modes for the different wall configurations analyzed in this dissertation.