A two‐dimensional BEM/FEM coupling applied to viscoelastic analysis of composite domains

Abstract

SUMMARYA coupling between the boundary-element and ÿnite-element methods is studied for the viscoelastic analysis of reinforced media. The viscous behaviour of the composed body is taken into account by an alternative BEM methodology developed for the Boltzmann model. This methodology is based on di erential constitutive relations for viscoelasticity. The reinforcements are modelled by ÿnite elements and are considered elastic. The coupling is based on the sub-region technique due to its generality and easy implementation. The resulting time-marching process is able to represent both the instantaneous and the time-dependent behaviour of a body subjected to general boundary conditions. The method is validated by an experimental result and its accuracy tested by comparing numerical results with analytical solutions. The generality of the method is proved by an inÿnite domain application.

Direct boundary integral procedure for a Boltzmann viscoelastic plane with circular holes and elastic inclusions

“…In deriving (1), the assumption that h k ¼ h l ¼ c is adopted [2,4,7,8], where h k and h l are the hydrostatic and deviatoric viscosity coefficients, respectively, with the dimension of time. This results in a constant Poisson's ratio but allows one to obtain only boundary values in the governing integral equations for the problem.…”

“…3). By substituting (10) and (11) into (8) and performing the analytical integrations (by using complex variables and the residue theorem [1,12]), the displacements can be expressed in terms of the Fourier coefficients for boundary tractions and displacements. Symbolically, the result can be written as:…”

“…The method combines the elastic boundary integral approach for multiple holes and inclusions developed by Crouch and Mogilevskaya [1] and the time-marching approach for viscoelastic analysis described by Mesquita and Coda [2][3][4][5][6][7][8]. An approach based on a Kelvin model is not able to simulate instantaneous behavior of materials, and this is very important in most applications.…”

Wave spectral finite element model for the prediction of sound transmission loss and damping of sandwich panels

“…It is noted here, that both the STL and DLF problems can be solved accurately using the FE and BE methods as described in Refs. [24][25][26].…”

“…Elements are formulated and assembled as in the standard FEM while the base functions are the frequency dependent local solutions of the equations of motion. It is only recently that the potential of this method to handle a wide range of applications has been realized [26,27]. For instance, this method was used to analyze the stationary vibrations in a beam and plate structure [28,29].…”