A symmetric Galerkin boundary element method for dynamic frequency domain viscoelastic problems

A Trefftz collocation method is proposed for the analysis of two-dimensional elastodynamic problems subjected to steady-state time-harmonic loads. Trefftz methods are characterized by the use of a superposition of a number of actual solutions of the homogeneous part of governing equations, the so-called T(Trefftz)-functions. This leads to high quality approximations where the unknowns are the weights of each of the T-functions considered. The unknowns are found by matching the approximations to the boundary conditions by following a standard collocation approach.The numerical implementation of the method is briefly described and results are obtained for two anti-plane elastodynamic problems. The results compare quite favourably to other results available in the literature whereby Galerkin and collocation boundary element methods were used.

show abstract

“…The set of examples tested were previously analysed in the works of Domínguez [16], Kitahara [15] and Perez-Gavilan [17].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The numerical validation of the proposed method is achieved by the application to a set of anti-plane elastodynamic problems for which analytic (Kitahara [15]) as well as other numerical solutions are available (Dominguez [16] and Perez-Gavilan and Aliabadi [17]. )…”

Section: Introductionmentioning

confidence: 99%

Trefftz collocation for frequency domain elastodynamic problems

Leitão

Sensale

Rodriguez

2009

Mesh Reduction Methods

View full text Add to dashboard Cite

show abstract

“…Some researchers have studied thermoelasticity of the solids using the BEM (Becker 1992;Gao 2003;Hematiyan 2007). Moreover, numerous researchers have developed BEMs to model behaviors of the homogeneous viscoelastic media (Schanz 1999;Perez-Gavilan and Aliabadi 2001;Huang et al 2006;Mesquita and Coda 2007;Farid 2009, 2010;Cezario et al 2011;Ashrafi et al 2012). They have presented BEM solutions for Laplace transforms of the primary variables of the elastic problems and then returned the solutions to the time domain through proper numerical inversions.…”

Section: Introductionmentioning

confidence: 99%

A time-domain boundary element method for quasistatic thermoviscoelastic behavior modeling of the functionally graded materials

Ashrafi

Shariyat

Asemi

2013

Int J Mech Mater Des

View full text Add to dashboard Cite

In the present paper, a boundary element formulation is presented for two-dimensional thermoviscoelasticity analysis of components fabricated from the functionally graded materials (FGMs). In this regard, a graded viscoelastic element capable of tracing gradual variations of the material properties is developed. Several attempts have been made so far to employ the integral equation approach for the heterogeneous viscoelastic materials. In the present research, Somigliana's displacement identity is considered and implemented numerically for analyzing the two-dimensional exponentially graded viscoelastic components. Employing the common assumptions of the viscoelastic constitutive equations and the weighted residual technique, an efficient boundary element formulation is developed for the heterogeneous Kelvin-Voigt solid viscoelastic models. Finally, three numerical examples are provided to verify the proposed formulation and present practical conclusions.

show abstract

“…In addition to important achievements of the SGBEM for stress and fracture analysis in elastostatics, the SGBEM has recently been developed for elastodynamics (e.g., [13][14][15][16][17][18][19]. However, only damped systems were studied in papers [15][16][17][18][19] as the standard FFT algorithm was used to obtain transient responses.…”

Section: Introductionmentioning

confidence: 99%

Frequency domain analysis by the exponential window method and SGBEM for elastodynamics

et al. 2011

View full text Add to dashboard Cite

Dynamic analysis of a system can be carried out either in the time or frequency domain. Time responses/ histories of this system may be directly obtained using timedomain analysis. In case of frequency domain analysis in the Fourier space, the inverse fast Fourier transform (inverse FFT) would naturally be an appropriate choice for converting frequency solutions to the desired time responses. However, the standard FFT can not be applied to undamped systems as the free-vibration terms of these systems never decay which violates the periodic nature of the standard FFT algorithm. In addition, the FFT may be computationally expensive for lightly damped systems. An alternative to overcome the above limitations is the so-called exponential window method (EWM) commonly used in digital signal processing. This paper presents a combination of the EWM and the symmetric-Galerkin boundary element method for 2-D elastodynamic analysis in the frequency domain of undamped and lightly damped systems. Several numerical examples, including fracture problems, are given to illustrate the efficiency and accuracy of the proposed frequency domain analysis.

show abstract

A symmetric Galerkin boundary element method for dynamic frequency domain viscoelastic problems

Cited by 23 publications

References 14 publications

Trefftz collocation for frequency domain elastodynamic problems

Trefftz collocation for frequency domain elastodynamic problems

A time-domain boundary element method for quasistatic thermoviscoelastic behavior modeling of the functionally graded materials

Frequency domain analysis by the exponential window method and SGBEM for elastodynamics

Contact Info

Product

Resources

About