Modified Compression Field Theory Based 2D Non-linear Finite Element Analysis Of Reinforced Concrete

The nonlinear finite element analysis of reinforced concrete structure is one of the important tasks in the nonlinear analysis field at all times. How to deal with concrete cracking and how to simulate the stress-strain relationships of concrete and reinforcement under complex loading conditions are the focuses and difficult problems of this field that the domestic and international researchers always take care about. Such as the stress-strain relationships of concrete and reinforcement under reversed cyclic load. The NAP procedure proposed in this paper is applied in the nonlinear analysis of reinforced concrete 2-D members, based on the modified compression field theory (MCFT) with the smeared rotating crack models. It has been used to analyze the reinforced concrete 2-D members under monotonic loading and reversed cyclic loading, considering the combinations of axial load, bend and shear. And the method can provide accurate simulations of the behaviors of RC members in the loading process. These work have established a good basis for the study group to do the next research. The primary work that has finished in this paper is: ①The secant stiffness matrix and global stiffness matrix of the plane rectangular element and of truss element have been educed in the paper, based on the MCFT with the smeared rotating crack; at the same time, from the basic theory of mechanics of materials, particularly expatiate the material secant stiffness of the principal strain direction and the principal stress direction and the element transformation matrix; they provide the theory basis of the procedure presented in this paper. ②Through improving the displacement loading control method based on the tangent stiffness, this paper has presented displacement loading control method based on the secant stiffness. ③Through properly improving the Newton-Raphson method of solving system of equations based on the tangent stiffness, this paper presented Newton-Raphson incremental-iterative mixed method based on the secant stiffness. ④Based on the established analysis theory in this paper, NAP procedure has proposed with C++ language, and has successfully solved the special problems to deal with the memory and judgment of element history conditions, the abnormity of the secant stiffness matrix. ⑤Based on the transformation of the element history conditions proposed by Bolong Zhu, this paper has improved and extended the judgment of the element history conditions with the change characteristic of element conditions. ⑥It has simulated and analyzed the behaviors of slabs, walls and simply supported beams subjected to monotonic loading and the hysteretic behaviors of shear walls subjected to low reversed cyclic loads. Conclusions acquired from the work that this paper has complete: ①This paper has used the NAP procedure to simulate the response of large numbers of shear walls and simply supported beams subjected to axial loads, bend and shears. The procedure is based on the Modified Compression Field Theory (MCFT) with the smeared rotating crack model, the low-unit and the displacement loading control method with secant stiffness. The results of analysis are well coincident with the results of tests, and the validity and reliability of the theory in the paper that used to analyze 2-D members subjected to complex load conditions have proved. ②The NAP procedure has successfully simulated the behaviors of the 2-D members subjected to complex load conditions included axial loads, bend and shear. And also has effectively solved the complex problems that can't be dealt with the common macroscopic analytical models. ③In order to solve the singularity of the secant stiffness in simulating the behaviors of 2-D members, the total strains of reinforcement and concrete are partitioned into the elastic strain component and the plastic strain component, then formed the element equivalent joint load vector. This method is proved rationality. ④The NAP procedure in this paper has offered a very powerfully analytical measure and tool for researching the nonlinear behavior of 2-D members.