PEDAGOGICAL APPROACH FOR STRUCTURAL STABILITY WITH NUMERICAL IMPLEMENTATION

Resumo

This article aims to present a Stability Theory in a compact pedagogical way, where important concepts, analytical, and numerical procedures are included. The strong point of this article is the simplicity of the presentation of the nonlinear geometric analysis. Numerical computational procedures are presented for geometric nonlinear system analysis in order to facilitate understanding for those who intend to study the subject because it brings the basic concepts and the numerical implementations that can be used for the solution of more complex problems. Computational implementation details and analytical solutions are presented for two examples: single and multiple degree of freedom systems (SDOF and MDOF systems, respectively). The first one, the single degree of freedom scalar problem, is presented because it contains a limit load point, a dynamic jump, and the geometric imperfections influence, besides incorporating additional important concepts. The second one, a MDOF system, represented by a two degrees of freedom problem, is presented to introduce to matrix algebra.