Análise modal assintótica da estabilidade de estruturas reticuladas espaciais - Alves, Ricardo Valeriano (1989)
This work presents a solution, by the Finite Element Method, for non-linear asymptotic analysis of elastic stability for space frames under conservative loads. The general non-linear equilibrium and critical equilibrium equations are obtained through a Lagrangian formulation, by analysing the variation of the total potential energy resulting from incremental displacements. The perturbation technique in a matrix form allows asymptotic approaches of primary and secondaries paths, to be calculated in an adequate form for computational purposes. The linearized critical equilibrium analysis is used in an alternative plus consistent form, yielding critical loads and modes that are usually better approximations than those from a conventional procedure. As a consequence of the asymptotic expantions, an automatic selection of a reduced number of modes is obtained for the non-linear model analysis, which also permits the study of the influence of small geometric imperfections.