Finite Element Flexibility Method Based 3D Inelastic Seismic Response Analysis Of Reinforced Concrete Frames

The law of 3D inelastic seismic response of structures is always among the important problems in the seismic research field. Owing to the restriction of the scale and quantity of the test structure, for the whole structure prototype, the computer simulation analysis becomes the main mean to study this problem, but the experimentation is very useful at studying the structural member and small-scale structure. As to reinforced concrete frames, existing research findings are still not able to meet fully the actual demands,and many problems remain to be solved. In this paper several key problems of 3D inelastic seismic response analysis of RC frames are studied. These problems are how to guarantee the demand of objectivity of input parameters and to solve a series of complicated problems such as axial force and two-way bending moment coupling for RC column under complicated loading path,as well as the effect of high axial load ratio or variable axial force, RC column softening, inelastic buckling etc. This paper centers on aforementioned problems, the main achievements are as follows:â‘  Based on the basic theory of nonlinear finite element stiffness method and flexibility method for member structures respectively and adopting fiber models to simulate the complicated nonlinear relation between member section forces and deformations on multi-axial loading conditions, two spatial beam-column elements applicable to material and geometry dual nonlinear analysis are built. On this basis,a program is developed for 3D inelastic seismic response analysis of RC frames. Every different fiber that the member element has in the program may have different material characteristics so as to deal with this type of problem such as the RC member composed of different materialï¼›Users do nothing but inputting material uniaxial stress-strain relation, which conforms to the demand of objectivity and handiness of parameter inputï¼›Besides a great deal of the usual information on structure, element and section, the program is also able to output such detail information as the stress or strain history of the specified fiber, and convenient for researchers to study the seismic behavior of structures. â‘¡ Systematic comparisons between finite element stiffness-based and flexibility- based nonlinear spatial beam-column elements are drawn. The results show that since the stiffness-based two-node beam-column elements are usually based on cubicpolynomial Hermit interpolation for transversal displacement and Lagrangian linear interpolation for axial displacement,which only can satisfy deformation compatibility condition and nodal equilibrium condition, thus it can hardly describe the actual deformation behavior of RC member in strong nonlinear phase, can not exactly satisfy element interior equilibrium condition, and a series of complicated physical phenomena such as axial force and two-way bending moment coupling for RC column under complicated loading path as well as RC column softening, inelastic buckling etc are impracticable to simulate effectively. Although these problem can be solved theoretically by means of refining the grid, namely one element is subdivided into a number of elements again, this way certainly results in series-like increase in computational effort, moreover, may lead to numerical instability and convergence issues in relatively large structure computation. However, flexibility method takes the postulate of element section force field as starting point of element to be built. For beam-columns depending mainly on axial and bending deformations, the postulate usually is able to obtain exact satisfaction and not influenced by nonlinear behavior of elements. Even to strong nonlinear problem that elements have come into soften phase later, element interior equilibrium condition is still able to get exact satisfaction. Thus compared with stiffness method,flexibility method enhances largely computational efficiency and effectiveness.â‘¢ Finite element flexibility method applicable to only material nonlinear proble...