Integral Method for Static, Dynamic, Stability and Aeroelastic Analysis of Beam-like Structure Configurations

摘要

This work presents a synthesis of the use of an integral approximate method based on structural influence functions (Green’s functions) concerning the behavior of beam-like structures. This integral method is used in the areas of static, dynamic, aeroelasticity and stability analysis. The method starts from the differential equations governing the bending or/and torsional behavior of a beam. These equations are put in integral form by using appropriate Green’s functions, according to the boundary conditions. Choosing a number of n collocation points on the beam axis, each integral are then computed by a summation using weighting numbers. This approach is suitable for conventional Euler-Bernoulli beams and also for the thin-walled open or closed cross-section beams which can have bending-torsion coupling. Generally, for a static analysis this approach leads to a linear system of equations (the case of the lift aeroelastic distribution analysis) or to an eigenvalues and eigenvectors problem in the case of dynamic, stability or divergence analysis.