Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
Analysis of equilibrium in elasticity using a regular perturbation technique
Submission Author:
Lucas Rocha , SP , Brazil
Co-Authors:
Adair Aguiar, Julián Bravo-Castillero, Lucas Rocha
Presenter: Lucas Rocha
doi://10.26678/ABCM.COBEM2021.COB2021-0588
Abstract
Numerical methods, such as the finite element method, are often used to obtain approximate solutions of problems whose exact solutions are not known. In this work, we adopt a different approach; we employ an analytical method, namely, the regular perturbation method, to construct approximate solutions in the form of truncated power series in a small parameter ε. We apply the method to obtain approximate solutions for the problem of a cylindrically orthotropic disk in equilibrium subjected to a compressive prescribed displacement along its boundary. This problem has an exact solution that has a singular derivative at the center of the disk and predicts inversion of material. The approximate solutions reproduce those behaviors and tend to the exact solution as either ε decreases or the number of terms in the truncated series increases. In addition, the approximate solutions can be cast in a very concise form. The approach presented in this work can also be used to validate numerical solutions and to obtain insight on the solutions of complex problems that are not known in closed form.
Keywords
Linear Elasticity, orthotropy, Asymptotic Analysis, Regular Perturbation Method
