Comparison study between FEM and SEM for wave propagation models applied to solids
Wave propagation is a field whose application has spread across many disciplines. In the field of structural engineering, wave propagation methods have focused their attention specifically in the area of structural health monitoring and active control of vibrations and noise. Likewise, the development of new methods and their application have been successful in the area of material science with a special emphasis on the field of structural integrity evaluation of anisotropic and inhomogeneous structures (laminated composite structures). The current available analysis tools are inadequate to handle the modeling of complex structures. One-dimensional wave propagation problems in solids are still a prevalent mean to approximate solutions for more sophisticated problems in mechanics. Fundamental solutions to one-dimensional problems provide the basis for understanding the fundamental principles that govern multidimensional wave propagation behavior. As boundary conditions become non-trivial and the quest of analytical closed-form solutions to the equations becomes cumbersome, D'Alembert's approach to wave propagation problems may involve a complex procedure that may render the quest for the solution very difficult if not impossible. Although many transformation approaches may seem promising, utilization of numerical procedures such as finite element analysis or the newest spectral element method has quickly become the academic norm for analysis of propagation problems. The aim of this study is to gain insight in the analytical, numerical and experimental aspects that FE and SE wave propagation models provide. For the first part of this paper we will study wave propagation through a cylindrical rod, although it has been treated extensively in literature because of its simple structural shape, studying these types of problems allows us to compute accurate analytical and numerical solutions. The study of these problems provides the fundamentals to understand and interpret solutions that lead toward accurate multidimensional extension of the wave propagation theory. For the second part of this study, we will extend our models to two-dimensional wave propagation in plates. SEM and FEM plate models were developed based on different levels of spatial and temporal discretization. If not assessed carefully, numerical models may be often affected by phenomena not present in the physical system that has been introduced due to round-off errors, incompatibility of time integrations schemes, and/or ill-conditioned matrices. Proper identification and correction of any factors that may lead to unstable systems is necessary. Based on the models presented in this paper, a conclusion regarding the choice of the best-suited method for the modeling and assessment of wave propagation problems has been drawn based on their respective conditioning and stability characteristics.
Civil engineering|Mechanical engineering
Castillo Ponton, Shaddy Roberto, "Comparison study between FEM and SEM for wave propagation models applied to solids" (2012). ETD Collection for University of Texas, El Paso. AAI1533214.