• Advances in nano research
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• v.12 no.4
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• pp.405-414
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• 2022

In this study, the elastic plane problem of a layered composite containing an internal or edge crack perpendicular to its boundaries in its lower layer is examined using numerical analysis. The layered composite consists of two elastic layers having different elastic constants and heights. Two bonded layers rest on a homogeneous elastic half plane and are pressed by a rigid cylindrical stamp. In this context, the Finite Element Method (FEM) based software called ANSYS is used for numerical solutions. The problem is solved under the assumptions that the contacts are frictionless, and the effect of gravity force is neglected. A comparison is made with analytical results in the literature to verify the model created and the results obtained. It was found that the results obtained from analytical formulation were in perfect agreements with the FEM study. The numerical results for the stress-intensity factor (SIF) are obtained for various dimensionless quantities related to the geometric and material parameters. Consequently, the effects of these parameters on the stress-intensity factor are discussed. If the FEM analysis is used correctly, it can be an efficient alternative method to the analytical solutions that need time.

• The Journal of the Acoustical Society of Korea
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• v.17 no.3E
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• pp.35-42
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• 1998

Transient acoustic and elastic wave propagation in inhomogeneous media are studied by using the Fourier method. It is known that the fourier method has advantages in memory requirements and computing speed over conventional methods such as FDM and FEM, because the Fourier method needs less grid points for achieving the same accuracy. To verify the proposed numerical scheme, several examples having analytic solutions are considered, where two different semi-infinite media are in contact along a plane boundary. The comparisons of numerical results by the Fourier method and analytic solutions show good agreements. In addition, the fourier method is applied to a layered half-plane, in which an elastic semi-infinite medium is covered by an elastic layer of finite thickness. It is showed how to derive the analytic solutions by using the Cagniard-de Hoop method. The numerical solutions are in excellent agreements with analytic results.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1998.10a
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• pp.399-406
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• 1998

Transient acoustic and elastic wave propagation in inhomogeneous media are studied by using the Fourier method. To verify the proposed numerical scheme, several examples having analytic solutions are considered, where two different semi-infinite media are in contact along a plane boundary. The comparisons of numerical results by the Fourier method and analytic solutions show good agreements. In addition, the Fourier method is applied to a layered half-plane, in which an elastic semi-infinite medium is covered by an elastic layer of finite thickness. It is showed how to derive the analytic solutions by using the Cagniard-de Hoop method. The numerical solutions are in excellent agreements with analytic results.

• Geomechanics and Engineering
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• v.16 no.1
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• pp.11-19
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• 2018

Propagation of the generalized Rayleigh waves in an elastic half-space covered by an elastic layer for different initial stress combinations and imperfect contact conditions is investigated. Three-dimensional linearized theory of elastic waves in initially stressed bodies in plane-strain state is employed, the corresponding dispersion equation is derived and an algorithm is developed for numerical solution to this equation. Numerical results on the influence of the initial stress patterns and on the influence of the contact conditions are presented and discussed. The case where the external forces are "follower forces" is considered as well. These investigations provide some theoretical foundations for the study of the near-surface waves propagating in layered mechanical systems and can be successfully used for estimation of the degree of the bonded defects between layers, fault characteristics and study of the behavior of seismic surface waves propagating under the bottom of the oceans.

• Advances in aircraft and spacecraft science
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• v.7 no.1
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• pp.41-52
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• 2020

The effect of relaxation times is studied on plane waves propagating through semiconductor half-space medium by using the eigen value approach. The bounding surface of the half-space is subjected to a heat flux with an exponentially decaying pulse and taken to be traction free. Solution of the field variables are obtained in the form of series for a general semiconductor medium. For numerical values, Silicon is considered as a semiconducting material. The results are represented graphically to assess the influences of the thermal relaxations times on the plasma, thermal, and elastic waves.

• Proceedings of the Acoustical Society of Korea Conference
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• 1998.06c
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• pp.327-330
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• 1998

Wave propagation in inhomogeneous elastic media is studied by using the Fourier method, where the spatial derivatives are computed by the FFT algorithm, while the time derivatives are expanded into the second order finite different expansion. For numerical examples, wave propagation in the layered half-plane are investigated. The comparisons of numerical and analytic results shows good agreement.

• Structural Engineering and Mechanics
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• v.66 no.3
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• pp.329-341
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• 2018

This paper considers the smooth receding contact problem between a homogeneous half-plane and a composite laminate composed of an inhomogeneously coated elastic layer. The inhomogeneity of the elastic modulus of the coating is approximated by an exponential function along the thickness dimension. The three-component structure is pressed together by either a concentrated force or uniform pressures applied at the top surface of the composite laminate. Both semianalytical and finite element analysis are performed to solve for the extent of contact and the contact pressure. In the semianalytical formulation, Fourier integral transformation of governing equations and boundary conditions leads to a singular integral equation of Cauchy-type, which can be numerically integrated by Gauss-Chebyshev quadrature to a desired degree of accuracy. In the finite element modeling, the functionally graded coating is divided into homogeneous sublayers and the shear modulus of each sublayer is assigned at its lower boundary following the predefined exponential variation. In postprocessing, the stresses of any node belonging to sublayer interfaces are averaged over its surrounding elements. The results obtained from the semianalytical analysis are successfully validated against literature results and those of the finite element modeling. Extensive parametric studies suggest the practicability of optimizing the receding contact peak stress and the extent of contact in multilayered structures by the introduction of functionally graded coatings.

• Structural Engineering and Mechanics
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• v.56 no.3
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• pp.491-506
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• 2015

Propagation of the generalized Rayleigh waves in an initially stressed elastic half-space covered by an elastic layer is investigated. It is assumed that the initial stresses are caused by the uniformly distributed normal compressional forces acting on the face surface of the covering layer. Two different cases where the compressional forces are "dead" and "follower" forces are considered. Three-dimensional linearized theory of elastic waves in initially stressed bodies in plane-strain state is employed and the elasticity relations of the materials of the constituents are described through the Murnaghan potential where the influence of the third order elastic constants is taken into consideration. The dispersion equation is derived and an algorithm is developed for numerical solution to this equation. Numerical results for the dispersion of the generalized Rayleigh waves on the influence of the initial stresses and on the influence of the character of the external compressional forces are presented and discussed. These investigations provide some theoretical foundations for study of the near-surface waves propagating in layered mechanical systems with a liquid upper layer, study of the structure of the soil of the bottom of the oceans or of the seas and study of the behavior of seismic surface waves propagating under the bottom of the oceans.

• Advances in nano research
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• v.8 no.4
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• pp.265-276
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• 2020

A study that primarily focuses on nonlocal strain gradient plate model for the sole purpose of vibration examination, for graphene sheets under linearly variable in-plane mechanical loads. To study a better or more precise examination on graphene sheets, a new advance model was conducted which carries two scale parameters that happen to be related to the nonlocal as well as the strain gradient influences. Through the usage of two-variable shear deformation plate approach, that does not require the inclusion of shear correction factors, the graphene sheet is designed. Based on Hamilton's principle, fundamental expressions in regard to a nonlocal strain gradient graphene sheet on elastic half-space is originated. A Galerkin's technique is applied to resolve the fundamental expressions for distinct boundary conditions. Influence of distinct factors which can be in-plane loading, length scale parameter, load factor, elastic foundation, boundary conditions, and nonlocal parameter on vibration properties of the graphene sheets then undergo investigation.

• Tribology and Lubricants
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• v.18 no.3
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• pp.219-227
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• 2002

A linear elastic fracture mechanics analysis of double subsurface cracks propagation in a half-space subjected to moving thermomechanical surface traction was performed using the finite element method. The effect of frictional heat at the sliding surface on the crack growth behavior is analyzed in terms of the thermal load and peclet number. The crack propagation direction is predicted in light of the magnitudes of the maximum shear and tensile stress intensity factor ranges. When moving thermomechanical surface traction exists, subsurface horizontal cracks are propagation in-plane crack growth rate at the beginning but they are propagation out-of-plane crack growth rate by the frictional heat which is occurrence by the repeated sliding contact.