Analyse dynamique des structures mécaniques par la méthode des éléments finis.

Abstract

The mechanicaldiscrete or continuumstructures are actually of great importance in the application field of contemporary modern industry. However, during their life time these structures are often subjected to considerable external stresses or to high amplitudes of vibrations which can cause them large deformations and internal stresses which can cause them internal cracking or even their total destruction. In order to avoid these types of problems, the concept of static and dynamic analysis of these structures is recommended, and due to the complexity of their shape and size, the finite element method is the most used. The latter is currently recognized as a very powerful technique for the static and dynamic analysis of discrete or continuous structures of complicated form applied in the field of mechanics, aeronautics, civil engineering, maritime or robotics. Consequently, the calculation and dimensioning of these mechanical systems by the finite element method plays an important role at the service of the industry for possible sizing and prediction of their lifetime. Our work consists of static and dynamic analysis of two-dimensional discrete and continuous mechanical systems using the finite element method based on the main elements of bars, beams and plates, under the effect of external excitations with different boundary conditions. The discrete structures considered are twodimensional in metallic framework interconnected to the nodes by welding, riveting or bolted under various boundary conditions. Their elements are modeled comparatively by bar elements and beam elements, while for continuous structures the elements are rectangular thin plates with different boundary conditions. The excitation forces are based on periodic, random or impulsive forces and a numerical solution by development of a program to describe the behavior of these structures is realized. The mass and stiffness matrices of all the structures are determined respectively by assembling the bars, beam and plate elements based on the kinetic and deformation energy for each element. The displacements, the node reactions and the axial forces in all the elements as well as the transverse stresses and the eigenvalues of the structures under different boundary conditions were also calculated and good results were obtained compared to those obtained using other software Already existing. In fact, analysis using the finite element method will allow the proper dimensioning and design of complex industrial mechanical structures according to different boundary conditions, their internal loading and their vibratory level.