Wave propagation in functionally graded and layered materials

Aksoy, H. G.; Şenocak, E.

doi:10.1016/j.finel.2009.06.025

Cited by 28 publications

(8 citation statements)

References 20 publications

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“…For the numerical solution of the boundary value problem in Section 2, we solve the system of 4M + 2N linear algebraic equations given by (18) (with P = M + N), (28), (29) or (30), and (32). If one wishes to solve a smaller system of linear algebraic equations, one may substitute (29) or (30) together with (32) directly into (28). This will reduce the number of unknowns and the number of equations in the formulation to 2M + 2N.…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…The proposed solution approach based on boundary integral and radial basis function approximations provides an interesting and viable alternative to the existing numerical methods for analyzing heat and mass transfer in anisotropic media with spatially varying material properties. It may be explored further and extended to solve more complicated problems involving anisotropic media such as those considered in the works of Aksoy andŞenocak, 29 Baron, 30 Lin et al, 31 Marin and Lesnic, 32 and Fahmy. 33,34 How to cite this article: Ang W-T. A boundary element and radial basis function approximation method for a second order elliptic partial differential equation with general variable coefficients.…”

Section: Summary and Final Remarksmentioning

confidence: 99%

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A boundary element and radial basis function approximation method for a second order elliptic partial differential equation with general variable coefficients

Ang

2019

Engineering Reports

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A numerical method based on boundary integral equation and radial basis function approximation is presented for solving boundary value problems governed by a second‐order elliptic partial differential equation with variable coefficients. The equation arises in the analysis of steady‐state anisotropic heat or mass diffusion in nonhomogeneous media with properties that vary according to general smoothly varying functions of space. The method requires only the boundary of the solution domain to be discretized into elements. To check the validity and accuracy of the numerical solution, some specific problems with known solutions are solved.

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Section: Numerical Proceduresmentioning

confidence: 99%

Section: Summary and Final Remarksmentioning

confidence: 99%

A boundary element and radial basis function approximation method for a second order elliptic partial differential equation with general variable coefficients

Ang

2019

Engineering Reports

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“…26 analyzed one-dimensional wave propagation in the FGM using the spectral ﬁnite elements and transfer matrix methods. Aksoy and Senocak 27 analyzed two-dimensional wave propagation in FGMs using Galerkin method. Further, Golub et al.…”

Section: Introductionmentioning

confidence: 99%

A numerical investigation on ultrasonic bulk wave propagation features in functionally graded plates

Farahmand

Soorgee

2019

Journal of Composite Materials

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The goal of this research is to numerically look for a proper feature for functionally graded materials mechanical property distribution function evaluation based on through transmitted ultrasonic bulk wave amplitude variation. A numerical approximation called homogenous layers approximation is introduced and employed for wave propagation formulation in functionally graded plate, followed by finite element utilization for verification. As the amplitude of the propagated ultrasonic wave is affected by acoustic impedance and wave divergence angle variation in the functionally graded material plate thickness, while neglecting the attenuation phenomenon, numerical investigation has been performed in order to quantify the contribution of each mechanism on the wave amplitude behavior. One-dimensional investigations, using homogenous layers approximation and finite element method, show that the final value of the wave amplitude is the same for all functionally graded material property distribution function power index, while two-dimensional results, obtained from finite element method, provide a suitable amplitude variation manner based on the wave divergence angle variation in functionally graded material thickness direction. The final results shows that it is possible to calibrate the received wave amplitude distribution on the receiving side of the plate, in a through transmission test, for the material property distribution function power index evaluation. Moreover, the concept of functionally graded material ultrasonic shoe is introduced, suitable for beam focusing applications instead of expensive phased array systems.

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“…They controlled the oscillations in the shock wave by adding an artificial viscosity to the hydrostatic pressure and showed that the optimum value of the linear artificial viscosity enabled to minimize the relative error in computed stresses. Aksoy and Senocak [21] applied a space-time discontinuous Galerkin method to investigate the wave propagation in 2-D functionally graded materials and layered materials under impact loads. Shariyat et al [22] investigated the elastodynamic response of long thick-walled functionally graded cylinders subjected to arbitrary dynamic and shock pressures.…”

Section: Introductionmentioning

confidence: 99%