Introdução à teoria da estabilidade com implementação numérica - Souza, Yargo Pezzin (2018)
One of the main structural engineering goals has been to make the slenderest and cheapest structure by reducing its weight and material consumption without compromising their stability. Increasing the elements slenderness makes them even more susceptible to large side deflections before they break. Stability analysis of slender structural systems usually involves the use of Finite Element Method (FEM). As a result, a non-linear algebraic system is obtained and its solution, in most of cases, can be found by iterative incremental procedures. This work aims to present in a modern way this important theme for structural engineering. Computational numerical procedures for analysis of non-linear systems stability with one and two degrees of freedom are shown, aiming to facilitate the understanding, since they bring the basic concepts and the necessary numerical implementations for the solution of more complex problems with many degrees of freedom. All examples are solved analytically by the Principle of Stationary Total Potential Energy and numerically by the Newton-Raphson method. The method of arc length is deduced and applied in the system of one degree of freedom which presents a load limit point Details of the computational implementation, stability concepts, and analytical solution of a material and geometric non-linear system will be introduced. Numeric examples and their implementations codes in computational language are made available.