Wave Propagation Analysis as a Global Stiffness Measurement in the Investigation of Fiber Orientation Effect of Orthotropic Beam

Abstract

As products made of composite materials become more applicable in many engineering sectors throughout the years, arises the need for advanced numerical methods which can enhance project development regarding innovation in these areas. Specifically for applications of constant cross section parts, i.e pultruded structures, understanding which and how geometric design aspects and material properties change the stiffness is a key point for the design of the springs. Such parameter can be influenced by several design variables such as fiber orientations and its distribution along the cross-section since the orthotropic behavior of composite materials are mainly guided by it. Methodologies to numerically evaluate the stiffness of structures often use the finite element method, in which the results are highly dependent on symmetry and shapes of boundary conditions. To overcome this, a global analysis can be carried out by solving an eigenvalue problem using the wave propagation approach, which relates the wave speed propagation inside the structure with its stiffness. In that sense, this work presents a numerical evaluation of the fiber orientation effect in wave propagation phenomenon to globally analyze the stiffness of a straight, orthotropic and perfectly coupled beam. SAFE and Block-Floquet methodologies are carried out together with the finite element method to obtain the elastodynamic behavior and the results are validated with modal analysis, which is used to study and compare the fundamental modes: bar, shaft and beam modes. Once validated, different sections and fiber orientations are explored while maintaining the same beam cross-section properties: area and moment of inertia. Results demonstrate how bending and longitudinal stiffness are decreased to increase torsion stiffness when fiber orientation or cross-sectional shape changes. Finally, this paper successfully delivers the study of how the combination of geometrical aspects and fiber orientation globally affects stiffness, employing a relatively simple methodology