INCAS BULLETIN, Volume 9, Issue 4/ 2017, pp. 3 – 10 (P) ISSN 2066-8201, (E) ISSN 2247-4528 Integral Method for Static, Dynamic, Stability and Aeroelastic Analysis of Beam-like Structure Configurations Viorel ANGHEL* *Corresponding author “POLITEHNICA” University of Bucharest, Strength of Materials Department, Splaiul Independenţei 313, 060042, Bucharest, Romania, vanghel10@gmail.com DOI: 10.13111/2066-8201.2017.9.4.1 Received: 23 October 2017/ Accepted: 31 October 2017/ Published: December 2017 Copyright©2017. Published by INCAS. This is an “open access” article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Abstract: 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. Key Words: Integral Method, Green Functions, Collocation, Static, Dynamic, Stability, Aeroelasticity 1. INTRODUCTION The use of the structural influence functions (Green’s functions) in the structural and aeroelastic analysis are presented in [1]. In Romania this approach is widely used by Professor A. Petre in his works on aeroelasticity in fixed wing aircraft [2, 3]. In the case of the rotating beams and blades the method using Green’ s functions was presented for simple configurations in order to obtain the natural frequencies for the bending and bending-torsion vibration analysis [4, 5]. The coupled bending vibration analysis in the case of pretwisted blades was presented in [6]. Then, a general case of the coupled bending-bending-torsion vibration analysis of straight beams and blades was described in [7]. The papers [8, 9] concern the dynamic analysis of rotating beams with tip mass. Other works related to the dynamic analysis of rotating beams and blades are [10, 11]. The method of Green’s functions was then applied for composite beams both for dynamic analysis [12] and static analysis [13]. Other applications are then presented in [14, 15]. In [15] a short application concerning the buckling analysis of a straight uniform beam was also performed. Aspects concerning the aeroelastic analysis of wings are presented in work [16]. New developments of the methods based on Green’s functions in dynamic analysis of beams and blades are recently reported in [17, 18].