New Approach for Seismic Nonlinear Analysis of Inelastic Framed Structures

A novel approach for seismic nonlinear analysis of inelastic framed structures is presented in this paper. The nonlinear analysis refers to the evaluation of structural response considering P-delta effect, which is in the form of geometric nonlinearity, and inelastic behavior refers to material nonlinearity. This novel approach uses finite element formulation to derive the elemental stiffness matrices, particularly to derive the geometric stiffness matrix in a general form. At the same time, this approach separates the inelastic displacement from total deflection of the structure by applying two additional constant matrices, namely, the force–recovery matrix and the moment-restoring matrix in the force analogy method. The benefit behind this treatment is explicitly locating and calculating the inelastic response, together with strategically separating the coupling effect between the material nonlinearity and geometric nonlinearity, during the time history analysis. Comparison with the traditional incremental methods shows that the proposed method is very time efficient as well as straightforward. One portal frame and one five-story frame are used as numerical examples to illustrate and verify the robustness of current approach.