Development of Isoparametric Shell Elements with Variable Edge Order and Movable Nodes in the Nonlinear Hybrid Simulation of Reinforced Concrete Structures

Abstract

In this study, nonlinear isoparametric shell elements with variable edge order and moving nodes from CBAL4M to CBAL12M were developed and integrated into FINITE. Specific mapping and surfaces for two-dimensional isoparametric shell elements, shape functions, and their derivatives are presented. The advantage of the developed shell element is that it can represent not only the smeared reinforcement on the wall and slab but also the discrete special reinforcement that is important for crack propagation in the nonlinear simulation of RC structures. With the advantage of movable nodes, the discrete reinforcement can be effectively covered and the position of the discrete reinforcement can be determined. When modelling reinforced concrete structures dominated by shear walls, the use of variable edge orders at the slab-wall interfaces where high stresses or forces are expected reduces the calculation time and capacity by using an optimal number of nodes for hybrid modelling. Nonlinearity is considered only in the form of material nonlinearity with a stress-strain curve, tension stiffening, and cracking including crack rotation. The analytical model is validated by comparing the results at the element level of the Vecchio and Collins test panels at the University of Toronto and at the structural level of the five-story shear wall building with staggered openings at the University of Michigan. Nonlinear hybrid simulations of 2D and 3D models of 2-story and 5-story shear wall-dominated RC buildings are investigated with the developed element considering ultimate load curves, deflection shapes, crack patterns, stress distributions, and 3D effects and force mechanisms. For this purpose, a three-story scaled test model was constructed and tested to simulate the seismic behavior. The test results are also compared with the analytical results of SAP2000 and the developed nonlinear shell element. The seismic capacity of the test model and the analytical models was similar at 31 tons. The developed element can be effectively used for modelling and nonlinear hybrid simulation of RC buildings and can also be applied to prestressed concrete structures for tendon modelling.