Analysis of Nonlinear Structures: Force Method

A method for analyzing nonlinear structural systems using the force (flexibility) method is presented herein. Using a differential point of view, the analysis of a nonlinear system is treated as an initial value problem. The equations developed for structural systems are a set of simultaneous nonlinear first-order ordinary differential equations in which the indeterminate quantities are the dependent variables and the applied loading is the independent variable. Integration of these equations for a given set of initial conditions (forces) yields the internal force distribution in the structure. With the force distribution known, the complete displacement pattern of the structure may be easily determined. The method is illustrated through the solution of several problems to demonstrate its feasibility and applicability to systems of practical size and interest. The numerical integration scheme of Runge-Kutta was used to solve the nonlinear equations. The results are compared with those obtained using the displacement method of analysis.