Eventos Anais de eventos
MECSOL 2022
8th International Symposium on Solid Mechanics
Displacement response of a 3D full-space due to time-harmonic, biquadratic loads
Submission Author:
Josue Labaki , SP
Co-Authors:
Edivaldo Romanini, Josue Labaki, Iago Cavalcante, EUCLIDES MESQUITA
Presenter: Josue Labaki
doi://10.26678/ABCM.MECSOL2022.MSL22-0179
Abstract
This article presents solutions for the displacement fields of full-spaces subjected to external vertical loads. In this problem, the full-space is a three-dimensional, viscoelastic, isotropic, unbounded medium. The solution method consists of writing the coupled Navier-Cauchy differential equations describing the medium in terms of independent vector fields, in the sense of a Helmholtz decomposition. A subsequent Fourier transformation enables boundary conditions corresponding to the external loads to be incorporated algebraically. In this paper, the external loads are time-harmonic and have a biquadratic distribution over a rectangular area of the full-space. Expressions for these loads in the Fourier domain are derived and presented. Since closed-form, non-singular, analytical expressions were able to be obtained for these loads, the final displacement solutions can be used in the context of boundary element and meshless methods without the issue of singularities resulting from collocation, which is a major application of these solutions. In addition to this advantage, the fact that the solutions consider biquadratic loads enables an improved representation of sharply-varying contact traction fields, which are common in many engineering applications. Final expressions for displacement fields are presented in terms of double Fourier integrals. The paper discusses strategies for their accurate numerical evaluation, and presents selected numerical results.
Keywords
Green's functions, Boundary Element Method
