Analysis of Slender Aircraft Structures using the Finite Element Method - Fraqueiro, Filipe José Robalo (2020)
At present there is a great demand for structural analysis to be as realistic as possible and highly reliable. In the aeronautical industry this is translated into a reduction of the aircrafts weight and maintaining the desired safety factors. However, this type of analysis is a time-consuming and labor-intensive process and sometimes it is necessary to have a faster, but less reliable, solution that can be used as a starting point in the preliminary design. There are several methods for solving the different structural problems. When the cases are simple it is possible to have an analytical solution, however these cases are reduced and involves the resolution of differential equations. Thus it is necessary to use numerical methods of interpolation or approximation. One of these methods is the finite element method. This method consists in dividing the problem domain into small fractions, called elements, and applying approximations in each of these fractions taking into account the results of the surrounding fractions. In the case of this dissertation this method is applied from a one-dimensional (1D) point of view, ie, the structures are of the type: beam, bar and rod and the elements are represented by straight line segments. The start and end points of these segments are called nodes and allow the continuity of the structure and they are connected to the adjacent elements. Two major tasks were performed in this work. Initially the mathematical method of the finite elements was adjusted for a structural analysis, more concretely in structures that can be considered in one dimension, and to determine the deformation of the structure under certain loads and boundary conditions. It is still possible to calculate the free vibration modes of the structure. Then this method was applied to an algorithm so that it could be programmed and applied to several cases. In order to verify the reliability of the developed code some cases with different initial data were studied. These initial data refers to: the size and cross-section of the structure, material, loads and boundary conditions. The results are compared with programs that already exist in the market, thus verifying if they are plausible.