Research On Nonlinear Dynamic History Analysis Of Reinforced Concrete Structures

The dynamic response of building structures subjected to rare severe earthquake loading has been one of the structural engineering's important research topics for many years. Since many factors should be considered, there is still no perfect solution strategy to this subject. In this dissertation, the fundamental theories and numerical methods for the nonlinear dynamic analysis of building structures are discussed, and some new methods are successfully developed. The main content and contributions are listed as follows:1 Summarized on the existing models developed by other researchers, a new uniaxial hysteresis constitutive model for concrete which is able to consider the influence of complicated stress path and stress history, is proposed. This model consists of two parts: the skeleton curve and the hysteresis rule. The skeleton curve in compression is described by the curvilinear and the broken-line Mander formulae respectively, while the skeleton curve in tension is described by the bi-linear model. The hysteresis curve in compression is described by the linear and curvilinear Mander formulae, while the hysteresis curve in tension is described by the Zhu Bolong's model and the linear models. The new model can be adjusted by the variation of the skeleton curve and the hysteresis rule and even degenerated into different models, to accommodate the various nonlinear dynamic analyses of building structures with different requirements on computational precision and efficiency. Furthermore, this new model can reflect the confinement effects of the hoop reinforcement; fewer parameters required to be calibrated; and can well describe the uniaxial nonlinear behaviors of the concrete under cyclic loading.After studying the existing constitutive models of the steel bar, the bilinear hardening model with the Baushinger effect is selected for the nonlinear dynamic analyses of building structures.2 By combination of the proposed uniaxial constitutive model of concrete, two biaxial hysteretic constitutive models of concrete suitable for simulating the shear-walls and the slabs are established based on the well-known MCFT model and the strain hardening plastic model. These two new models contain fewer easily calibrated parameters only, and can predict the nonlinear behaviors of concrete materials under complicated stress conditions based on the engineering's computational precision requirements.3 The low precision problem of using the traditional shell elements to compute the short-leg shear wall and the slender coupling beam like structures is discussed. Then, a countermeasure is proposed as follows. According to the essence of rational finite element method, a new generalized coordinate beam-shell element is constructed by the generalized conforming theory and the analytical trial function method. All formulations are established in the Cartesian coordinate system directly. Since the analytical solutions of the plane stress problem are taken as the basis functions of the element trial functions for the displacement fields, and the deformation modes of the short-leg shear walls and the slender coupling beams are fully considered, the new element is quite suitable for related finite element analyses. The formulations of the new element are relatively simple, and possess the capacity of describing higher-order displacement fields. When the element is used in a nonlinear analysis, it can effectively predict the shear failure of the short-leg shear wall and the slender coupling beam. Numerical examples show that the new beam-shell element exhibits good performance and is insensitive to mesh distortion. It provides an effective tool for engineering computations of the short-leg shear wall and the slender coupling beam.4 Using the constitutive models of concrete and steel bar proposed in this dissertation, a new RC integral shell element model for nonlinear finite element analyses of various RC shear walls is developed. The new shell element is based on the combination of the ideas of the Altaian's membrane element, thin-thick plate element proposed by Prof. Long Yu-Qiu, and beam-shell element proposed in this dissertation. In the computational model of the distributed RC integral shell element, the boundary elements of the shear walls are simulated by the fiber beam element model; the reinforced concrete Allman's membrane element and the thin-thick plate element are used to simulate in-plane and out-of-plane stiffness of normal shear walls, respectively; and the short-leg shear walls and slender coupling beams are modeled by the beam-shell elements. Since the distributed RC integral shell element is directly based on material model, it can describe the whole elastic-plastic development process of the concrete and the steel bar in the shear walls.The new RC integral shell element model is verified by a comparison between the calculated results and the experimental data of two RC shear wall specimens. The results demonstrate that, for RC shear walls subjected to the combined loadings of bending, shear and compression, the RC integral shell element model can evaluate ultimate loading, coupling effects for nonlinear bending and shear deformations with satisfied accuracy. Compared with other microscopic models such as multi-layered shell element model and solid element model, it is obvious that the present model has the fewest degrees-of-freedom and the highest computational efficiency. It can be concluded that the present model is suitable for the RC shear walls in the time history analysis of building structures under the current computer hardware conditions.5 A 3-D spatial model for the nonlinear time-history analyses of the building structures subjected to earthquake loading is proposed. In this model, the beams, the columns and the braces are simulated by the fiber beam element model, while the RC shear walls are simulated by the distributed RC integral shell element model. Such a spatial model, which is imposed on fewer simplification hypotheses, not only can consider the multi-dimensional responses of building structures subjected to multi-dimensional earthquake loading, but also possesses high computational precision and efficiency.6 The stability, precision, efficiency and robustness of different time integration algorithms for equations of structural dynamics are discussed. A comparison of the characters and the problems which may happen in the nonlinear time-history analyses of building structures between the explicit and the implicit algorithms is also given. Then, a comprehensive solution scheme for the nonlinear dynamic response of the building structures subjected to the earthquake loading is proposed. This scheme includes the solution strategy of the initial stresses when the construction simulation of building structures under gravity load is considered, the implicit solution strategy (generalizedαmethod), and the explicit solution strategy (central difference method) for the nonlinear dynamic response of the building structures under the earthquake loading. Based on the above models and theories, a computer program of the nonlinear dynamic time-history analysis for the buildings structures subjected to earthquake loading is developed. The validity and availability of this program and its related algorithms are demonstrated by various numerical examples. All the results can be references by engineering designers.7 The traditional precise time integration algorithms usually occupy many memory resources, and their computation costs are also relatively high. In order to overcome these disadvantages, an enhanced algorithm is successfully developed. By partitioning of the matrix and exchanging computational sequence, the memory demand can be reduced effectively, and the computational efficiency is also improved. Numerical examples demonstrate the validity of the new algorithm.