Ftool version 5: What are the new features

This work presents a new version of Ftool, a program for structural analysis of two-dimensional frame models, widely used by Civil Engineers and students. The new features of this version are: second-order non-linear geometric analysis using the two-cycle method, stability eigenvalue analysis, natural mode vibration eigenvalue analysis, semi-rigid connections with moment-rotation linear-elastic behavior, and consideration of structural member deformation constraints, such as inextensible and rigid members, using Lagrange multipliers. Ftool was adapted to perform two-cycle analyses employing frame elements based on solutions of the differential equations obtained from the deformed configuration. The results of displacements and rotations for the examples studied are identical to the analytical solutions, showing that combining 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. The stability analysis provides structural critical loads and buckling modes, while the natural mode vibration analysis provides natural frequencies, vibration modes, mode participation factors, and mode effective masses.  The new version simulates a semi-rigid connection by inserting a rotational spring finite element with linear-elastic behavior. An essential characteristic of this implementation is that the stiffness matrix of a connection finite element is not condensed to the beam element that contains the joint, as is usually done. Instead, a fictitious node with only one additional rotational degree of freedom is created for each semi-rigid connection in the planar case. The advantage of this approach is that, in the future, the physically nonlinear behavior of a semi-rigid connection may be isolated from the elastic behavior of the beam elements. It is also implemented in the new version of Ftool, a methodology for considering structural member deformation constraints using Lagrange multipliers. It consists of adding strain constraints into the total potential energy minimization, leading to a quadratic programming problem. In addition, this approach is very suitable for computational implementation because it does not affect the generic characteristic of a matrix structural analysis. The solution gives rise to one Lagrange multiplier per constraint, which is essential for computing member internal forces.