ABSTRACT
Problems in structural mechanics have, for a long time, been solved using linear or linearized equations representing their behavior. The solutions obtained based on these linear models were considered adequate for many practical and engineering purposes although it was recognized that linearized equations provide no more than a first approximation to the actual situations. Linearized models are inadequate, however, if for example, the vibrations of an elastic body involve amplitudes which are not very small. In addition, problems treated by nonlinear theory exhibit new phenomena–for example, the dependence of frequency of vibration on amplitude–that cannot be predicted by means of linear theories. It is often recognized that there is an increasing demand for more realistic models to predict the responses of elastic bodies. Such demands combined with the availability of superior computational facilities have enabled researchers to abandon the linear theories in favor of nonlinear methods of solution.
