Analysis of Nonlinear Structures

A method of analyzing nonlinear structural systems is presented in this paper. The method of displacements is used, and with this formulation, the characteristic equations are shown to be equivalent to a set of simultaneous nonlinear first order ordinary differential equations in which the generalized displacements are the dependent variables and the applied loading is the independent variable. The solution of these differential equations for a given set of initial conditions and loading on the structure yields the complete displacement pattern of the structure. In general, only numerical solutions of these equations are feasible or practical because of the large number of variables involved. With the displaced configuration of the structure known, the internal load distribution in the structure may be easily determined. The method is illustrated through the analysis of several structures to demonstrate its feasibility for systems of practical size and interest. Although only material nonlinearities are considered, the method may be extended to include geometric nonlinearities.