Consider the system shown in Fig. 1.3.la with no dynamic excitation subjected to an externally applied static force fs along the DOF u as shown. The internal force re sisting the displacement u is equal and opposite to the external force fs (Fig. 1.3.lb). It is desired to determine the relationship between the force fs and the relative dis placement u associated with deformations in the structure. This force-displacement relation would be linear at small deformations but would become nonlinear at larger deformations (Fig. 1.3.lc); both nonlinear and linear relations are considered (Fig. 1.3.lc and d).