Geometric Nonlinear Analysis using the Two-cycle Method in Ftool

With recent advances in design and material technology, increasingly slender structures are being conceived, which makes nonlinear analysis an important task for efficient and safe projects. Geometrically nonlinear problems are usually solved using the Finite Element Method (FEM) along with iterative numerical schemes, in which the structure response is directly influenced by the level of discretization and the nonlinear solution algorithm used. Thus, nonlinear analysis demands some experience from the analyst in terms of the parameters involved in the solution algorithms and structural behavior in general. To reduce the discretization dependence, exact solutions based on the deformed infinitesimal element equilibrium can be used as interpolation functions. To circumvent the difficulties in dealing with parameters related to the numerical methods, the two-cycle method can be used, since it is not dependent on load or displacement steps. The structural analysis software Ftool, widely used by Civil Engineers and students was adapted to perform two-cycle analyses employing frame elements based on solutions of the differential equations obtained from the deformed configuration. The results in terms of displacements and rotations for the examples studied are identical to the analytical solutions, showing that the combination of the two-cycle method with the exact element formulation is promising and can diminish the need for discretization and the use of complicated nonlinear solution algorithms.