The traditional method of structural analysis with geometric nonlinearity uses small displacement theory with the linearized method of geometric stiffness or the approximate method of P-Δ stiffness to capture the reduction in stiffness due to axial forces in the columns of the structure. This often raises a stability question on whether these approaches can accurately predict large displacement response, such as nearing structural collapse in a major seismic event. In this research, the force analogy method combined with the stability functions formulated for nonlinear dynamic analysis will be used to answer this question. Through this combination, the stiffness force is computed by simply multiplying a nonlinear stiffness matrix (due to geometric nonlinearity using stability functions) with a nonlinear displacement vector (due to material nonlinearity using the force analogy method). Although this formulation is still based on small displacement theory, geometric nonlinearity is captured exactly using stability functions and therefore has a better chance of capturing the large displacement response more accurately than other small displacement approaches. A detailed derivation of the nonlinear dynamic analysis procedure using the state space method considering both geometric and material nonlinearity effects is presented to demonstrate the simplicity of the combined method in capturing the structural responses during seismic events.
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