Analysis of Mechanical Structures Using Beam Finite Element Method

Abstract

The finite element method is used to solve problems by dividing the deformable body in a complicated assembling sub domain form or by constructing single elements and the approximate solutions in the form of a combination of shape functions and compact support. Our paper is mainly based on the application of this method to examine the mechanical structures using beam finite element method. The excitation forces are based on periodic, random or impulsive ones. In our case, we present a numerical solution to describe the dynamic behavior of discrete structures which have applications of big importance in many sectors of the industry, such as the space or aerodynamic structures, mechanical constructions, robotics and civil engineering. Nowadays, this method is a powerful tool, available for reasonable costs with a reduced time of execution used for the analysis of these structures. In this work, we have developed PASCHAL language program, to calculate the displacements, reactions in the axial strengths in elements and the clean fashions of the structure. Examples of verification of our language have been made, under different loads and boundary conditions. Good results have been obtained compared to those using SAP 2000 and Robot 2009 software programs. The discrete structures are composed of bar, beam elements riveted or welded to each other at points called nodes, and subjected to external forces or moments. Under the effect of these forces, the structure may be deformed and the internal stresses in each element may occur. These structures are characterized by a finite number of unknown displacements and the forces at the nodes parameters. This method is used also to analyze continuum three dimensional bodies or cylindrical bodies using plate, triangular or shell elements. In fact, this method is based on the discretization of the structure or continuous body into infinitesimal elements limited by nodes and then by assembling them in order to obtain the overall and the entire structure (1). Thus, the shape of the structure or the body is obtained in respecting its conditions with the initial limits and applied efforts. In general, the behavior of all the assembled basic members describes all of the behavior of the whole structure or body. The present work consists on the use of this method for static and dynamic analysis of structures under the influence of outside excitation with different boundary conditions. The stiffness and mass matrix of each element is