Combining Finite Elements Method and Particle Swarm Optimization in the Analysis of Nonlinear 2D Frames
nonlinear geometric, 2D frames, finite element, PSO
This research develops and explores the possibility of resolution, considering the effects of geometric non-linearity, of beams and planar porticoes, combining the Finite Element Method in the Positional Formulation (MEF-P) and Particle Swarm Optimization (OEP), known in the specialized literature by Particle Swarm Optimization (PSO). The deformations of several structures are analyzed, comparing them with the values of deformations presented when solved by the MEF in the positional formulation, using the method of Newton Raphson. A comparison is also made with the results provided by the Classical Beam Kinematics (Euler-Bernoulli), in cases where the structures were in a regime of small displacements. Processing cost and accuracy are also presented in charts for various structures. Particle swarm optimization was able to find adequate values for the deformation of several structures, however the cost of processing fell short of expectations, contradicting several records in the specialized literature. Considerations about the result and proposals for deepening are recorded, highlighting that the coupling of such different methods (MEF and EPO), being a deterministic and another stochastic, is an open proposal that considers the need to test interdisciplinary solutions to problems each time More complex in the area of structural analysis.