INCREMENTAL APPROACH TO THE SOLUTION OF SNAPPING AND BUCKLING PROBLEMS

This paper is concerned with the numerical solution of systems of equations of discrete variables, which represent the nonlinear behaviour of elastic systems under conservative loading conditions. In particular, an incremental approach to the solution of buckling and snapping problems is explored. The topics that are covered can be summarized as follows:-The computation of nonlinear equilibrium paths with continuation through limit points and bifurcation points.-The determination of critical equilibrium states. Characteristic to the procedures employed is the use of the length of the equilibrium path as control parameter. This feature, together with the second order iteration method of Newton, offers a reliable basis for the procedures described. Actual computations, carried out on a finite element model of a shallow circular arch, illustrate the effectiveness of the methods proposed. © 1979.