Raoofian Naeeni - Academia.edu (original) (raw)

Papers by Raoofian Naeeni

Research paper thumbnail of Computation of the changes in gravitational gradient components from GRACE observations and analytical model

Acta Geodaetica et Geophysica, 2015

Research paper thumbnail of Analytical solution of the asymmetric transient wave in a transversely isotropic half-space due to both buried and surface impulses

Soil Dynamics and Earthquake Engineering, 2016

Research paper thumbnail of A new idea to alert of Tsunami using of satellites altimetry and MSL

In this paper using of Satellite altimetry (e.g. Topex/Poseidon) and MSL (Mean Sea Level) a new a... more In this paper using of Satellite altimetry (e.g. Topex/Poseidon) and MSL (Mean Sea Level) a new approach presents to alert of tsunami. That in memory of Satellites there is a model of MSL, that using of matching technique and coincide of two components of MSL (hj) (observation of sea displacement at model) and height instantaneously displacement of sea measured with satellite (hi), different between two components is determined. If difference between hj and hi is big, the system alert the occurring the Tsunami using the radio waves.

Research paper thumbnail of کاربرد تنسور گرادیان جاذبه در حذف خطای نواری مشاهدات ثقل سنجی ماهواره ای گریس

Research paper thumbnail of Deformation analysis of the Earth crust based on manifold intrinsic geometry Case Study: Deformation analysis of the geodynamic network of Iran within 1999 - 2005

Unlike the classical deformation analysis of the Earth crust, which derives the planar and vertic... more Unlike the classical deformation analysis of the Earth crust, which derives the planar and vertical strains separately, in this study, we have offered a method for 3-D deformation study based on intrinsic geometry of the manifolds on the topographic surface of the Earth. In this way, our method would be based on the 2-D metric tensor of horizontal * ‫راﺑﻂ‬ ‫ﻧﮕﺎرﻧﺪه‬ : ‫ﺗﻠﻔﻦ‬ : 61114383 -021 ‫دورﻧﮕﺎر‬ : 88337642 -021 ardalan@ut.ac.ir E-mail: 126 ‫دوره‬ ‫ﻓﻀﺎ،‬ ‫و‬ ‫زﻣﻴﻦ‬ ‫ﻓﻴﺰﻳﻚ‬ ‫ﻣﺠﻠﺔ‬ 37 ‫ﺷﻤﺎره‬ ، 4 ، 1390

Research paper thumbnail of تعیین پارامترهای گسل مسبب زلزله با آنالیز موجک مشاهدات ثقل سنجی ماهواره ای گریس

‫بیست‬ ‫دومین‬ ‫و‬ ‫ژئوماتیك‬ ‫ملي‬ ‫همایش‬ -‫اردیبهشت‬ 4931 ‫بیست‬ ‫دومین‬ ‫و‬ ‫ژئوماتیك‬ ‫ملي‬ ... more ‫بیست‬ ‫دومین‬ ‫و‬ ‫ژئوماتیك‬ ‫ملي‬ ‫همایش‬ -‫اردیبهشت‬ 4931 ‫بیست‬ ‫دومین‬ ‫و‬ ‫ژئوماتیك‬ ‫ملي‬ ‫همایش‬ -‫اردیبهشت‬ 4931 ‫بیست‬ ‫دومین‬ ‫و‬ ‫ژئوماتیك‬ ‫ملي‬ ‫همایش‬ -‫اردیبهشت‬ 4931 J J J J J ‫بیست‬ ‫دومین‬ ‫و‬ ‫ژئوماتیك‬ ‫ملي‬ ‫همایش‬ -‫اردیبهشت‬ 4931

Research paper thumbnail of On the Application of the Gravity Gradient Tensor in a Reduction of the Striping Error of Grace Gravity Observation

In this study we will review potential and gravity gradient changes due to Sumatra's 9.1-magn... more In this study we will review potential and gravity gradient changes due to Sumatra's 9.1-magnitude earthquake on 26 th Dec 2004 using data collected from GRACE Satellite. Also we find the second derivative of the gravitational potential and then we use these values for co-seismic deformation which are caused by the Sumatra earthquake. The gravity gradients clearly show rupture line and mass distribution. In this study we find changes in co-seismic gradient components without using filter and with these gradients we eliminate GRACE strip errors in ∅ direction however in the direction of λ would cause fluctuations to intensify in east-west direction. Because í µí° ¶ 20 coefficient has a negligible contribution in the calculation of gravity changes determination due to the low accuracy of these coefficients, this coefficient will be replaced by SLR coefficients.

Research paper thumbnail of A proposal for deformation analysis via direct computation of strain tensor elements from the time-wise changes in the distances and angles in a geodetic network Case study: Deformation computation of the geodynamic network of Iran

A method for deformation computation based on strain tensor elements, as an alternative to the us... more A method for deformation computation based on strain tensor elements, as an alternative to the usual way of application of gradient of displacement vector, is proposed. The method computes directly the strain tensor elements from the computed/observed changes in distances and angles between the stations of a geodetic network in two epochs of

Research paper thumbnail of Are the gravimetry measurments necessary in the pricies levelling?

In this paper we presented the suitable criterion which shows the necessity for taking account of... more In this paper we presented the suitable criterion which shows the necessity for taking account of gravity field on the precise leveling observations. Our criterion is based on the required accuracy for gravity measurements which is a function of potential accuracy, height difference and height difference accuracy, and can be obtained via this simple formulaDeltaw = g × DeltaH. By taking sigmaw = 0.01m2 s2, sigmaDeltaH = .0001m, and DeltaH and g maximum values of height difference and gravity acceleration in the desired region, respectively, we can obtain the required accuracy for gravity measurement. By comparing this quantity with the maximum variations of gravity over the region, if these changes are smaller than the accuracy of gravity measurements, we won't require to consider the gravity in the computation of height by way of precise levelling and vice versa.

Research paper thumbnail of Analytical solution for axisymmetric thermoelastodynamic problems in a transversely isotropic half-space under a surface loading

In the present study, the theory of coupled thermoelastodynamic is applied to determine the displ... more In the present study, the theory of coupled thermoelastodynamic is applied to determine the displacement, temperature and stress (DTS) fields of a torsionless axisymmetric transversely isotropic half-space under a surface loading. The basic equations of coupled thermoelasticity consist of the equations of motion and the energy equation, which forms a set of completely coupled partial differential equations for the displacement and temperature fields. Potential method is employed for uncoupling the set of basic equations of coupled thermoelasticity. With the aid of a potential function existed in the literature, the system of equations are uncoupled, where a sixth order partial differential equation is received. Displacement components and temperature are written with respect to the potential function in cylindrical coordinate system. The Laplace and Hankel integral transforms are employed to suppress the time and radial variables, respectively. One may apply the inverse Hankel and L...

Research paper thumbnail of Wavelet and Gaussian Approaches for Estimation of Groundwater Variations Using GRACE Data

Research paper thumbnail of A comparative study among computation techniques for deformation analysis based on repeated geodetic observations

Considering the relative movement of points on the Earth's surface as a source of information... more Considering the relative movement of points on the Earth's surface as a source of information for deformation analysis of the crust via strain analysis, geodetic obser-vations (ground based, and satellite) can provide the required geometrical data. In the literatures so far various computational techniques have been introduced to the defor-mation analysis based on repeated geodetic observations. In this paper we present a comparative study over those computations techniques. Strain component computa-tions based on displacement vector, strain component computation based on changes in the distances and angles between geodetic network stations in two epoch of time, strain component computation on the topographic surface of the Earth, and strain com-ponent computation on the map projection planes are among the those computational techniques that have been studied for their efficiency and reliability in deformation analysis, in this paper.

Research paper thumbnail of Performance comparison of numerical inversion methods for Laplace and Hankel integral transforms in engineering problems

Applied Mathematics and Computation, 2015

Research paper thumbnail of Asymmetric motion of a transversely isotropic thermoelastic half-space under time-harmonic buried source

Zeitschrift für angewandte Mathematik und Physik, 2013

With the aid of complete representations in terms of two scalar potential functions, the governin... more With the aid of complete representations in terms of two scalar potential functions, the governing equations of coupled thermoelasticity are uncoupled into a sixth-and second-order partial differential equations in cylindrical coordinate system, which are solved by virtue of Fourier series expansion and Hankel integral transforms. Utilizing the transformed stresses-, displacements-and temperature-potential functions relationships, these functions are derived and represented in terms of improper line integrals. The general solutions are changed for point and circular patch load and heat flux Green's functions in order to derive the related displacement and temperature Green's functions. Some numerical evaluations of Greens functions are represented to portray the dependency of response on thermo-mechanical coupling as well as the anisotropy of the medium.

Research paper thumbnail of How to obtain the optimum digree/order in the expansion of geopotential model for geoid computation problem?

One of the discrepancy issues among the contemporary geodesist is the manner of implementation of... more One of the discrepancy issues among the contemporary geodesist is the manner of implementation of geopotential models for solving of boundary value problems. Some of them believe that it's better to use the low order in the expansion of geopotential models and instead, increase the domain of integration in the terrain correction. However, the other emphasize that we should take the order of expansion in the geopotential models as high as possible and consequently lessen the domain of integration over the remain local masses. In this paper we have comprehensively studied this matter and illustrated it's result on the various geopotential models.

Research paper thumbnail of Frequency Domain Analysis of an Axisymmetric Thermoelastic Transversely Isotropic Half-Space

Journal of Engineering Mechanics, 2013

By virtue of a new complete scalar potential function, an analytical formulation is presented to ... more By virtue of a new complete scalar potential function, an analytical formulation is presented to determine displacements, stresses, and temperature in an axisymmetric linear thermoelastic transversely isotropic half-space affected by time harmonic surface axisymmetric vertical traction and/or surface heat flux. With the use of only one scalar potential function in a cylindrical coordinate system, the coupled partial differential equations in thermoelasticity are transformed to a sixth-order partial differential equation governing the potential function. Then, by using the Hankel integral transforms, a sixth-order ordinary differential equation is received, which after solving, results in the displacements, stresses, and temperature fields. To prove the validation of the analytical solution presented in this paper, the solutions are reduced to the case of elastodynamics in transversely isotropic half-space and in a quasi-static thermoelastic isotropic half-space, where exact agreements with the solutions reported in the literature are achieved. Because of complexity of the integrands, numerical evaluations of the integrals involved in this paper are carried out using a suitable quadrature scheme by Mathematica software. To show the accuracy and efficiency of the numerical algorithm, the solution of this study is compared with the results of an existing elastodynamic transversely isotropic half-space, where an excellent agreement is achieved.

Research paper thumbnail of Dynamic Green's Functions of an Axisymmetric Thermoelastic Half-Space by a Method of Potentials

Journal of Engineering Mechanics, 2013

With the aid of a new complete scalar potential function, an analytical formulation for thermoela... more With the aid of a new complete scalar potential function, an analytical formulation for thermoelastic Green's functions of an axisymmetric linear elastic isotropic half-space is presented within the theory of Biot's coupled thermoelasticity. By using the potential function, the governing equations of coupled thermoelasticity are uncoupled into a sixth-order partial differential equation in a cylindrical coordinate system. Then, by using Hankel integral transforms to suppress the radial variable, a sixth-order ordinary differential equation is received. By solving this equation and considering boundary conditions, displacements, stresses, and temperature are derived in the Hankel integral transformed domain. By applying the theorem of inverse Hankel transforms, the solution is obtained generally for arbitrary surface timeharmonic traction and heat distribution. Subsequently, point-load Green's functions for the displacements, temperature, and stresses are given in the form of some improper line integrals. For more investigations, the solutions are also determined analytically for uniform patch-load and patch-heat distributed on the surface. For validation, it is shown that the derived solutions could be degenerated to elastodynamic and quasistatic thermoelastic cases reported in the literature. Numerical evaluations of improper integrals, which have some branch points and pole, are carried out using a suitable quadrature scheme by Mathematica software. To show the accuracy and efficiency of numerical algorithm, a numerical evaluation from this study is compared with the results of an existing elastodynamic case, where excellent agreement is achieved.

Research paper thumbnail of Analytical Solution of Coupled Thermoelastic Axisymmetric Transient Waves in a Transversely Isotropic Half-Space

Journal of Applied Mechanics, 2013

A half-space containing transversely isotropic thermoelastic material with a depth-wise axis of m... more A half-space containing transversely isotropic thermoelastic material with a depth-wise axis of material symmetry is considered to be under the effects of axisymmetric transient surface thermal and forced excitations. With the use of a new scalar potential function, the coupled equations of motion and energy equation are uncoupled, and the governing equation for the potential function, is solved with the use of Hankel and Laplace integral transforms. As a result, the displacements and temperature are represented in the form of improper double integrals. The solutions are also investigated in detail for surface traction and thermal pulses varying with time as Heaviside step function. It is also shown that the derived solutions degenerate to the results given in the literature for isotropic materials. Some numerical evaluations for displacement and temperature functions for two different transversely isotropic materials with different degree of anisotropy are presented to portray the dependency of response on the thermal properties as well as the degree of anisotropy of the medium.

Research paper thumbnail of Coupled thermoviscoelastodynamic Green's functions for bi-material half-space

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2013

By virtue of the representations of displacements, stresses, and temperature fields in terms of t... more By virtue of the representations of displacements, stresses, and temperature fields in terms of two scalar potential functions and the use of correspondence principle, an analytical derivation of fundamental Green's functions for bi-material halfspace composed of a transversely isotropic thermo-elastic layer and an isotropic thermo-visco-elastic half-space affected by finite surface or interfacial sources is presented. With the aid of the potential function relationships, the coupled equations of motion and energy equation in both the half-space and the layer are uncoupled and solved with the aid of Fourier series and Hankel integral transforms. Responses of the medium are derived in the form of improper line integrals related to Hankel inversion transforms. To show the effects of anisotropy and viscoelasticity on the propagation of coupled thermoviscoelastic waves, the derived integrals for displacements, stresses, and temperature Green's functions are evaluated by a numerical scheme.

Research paper thumbnail of Transient response of a thermoelastic half-space to mechanical and thermal buried sources

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2013

With the aid of a complete set of two scalar potential functions, the transient responses of an i... more With the aid of a complete set of two scalar potential functions, the transient responses of an isotropic thermoelastic halfspace subjected to time dependent tractions and heat flux applied to a finite patch at an arbitrary depth below a free surface are derived. Using the displacements-and temperature-potential function relationships, the coupled equations of motion and energy equation are uncoupled, resulting in two (6th and 2nd order) partial differential equations in the cylindrical coordinate system, which are solved with the aid of Fourier series expansion and joint Hankel-Laplace integral transforms. The solutions are also investigated in details for tractions varying with time in terms of a Heaviside step function and heat flux as a Dirac delta function, which may be used as a kernel in any integral based method for more complicated thermoelastodynamic initial-boundary value problems. Due to the complexity of the integrands involved in the general case, the integrals cannot be resolved analytically and thus an appropriate numerical algorithm is used for the inversion of the Laplace and Hankel integral transforms. To demonstrate the pattern of deformations as well as the distribution of change of temperature at the free surface of the half-space, numerical evaluations for these functions are presented for an isotropic material.

Research paper thumbnail of Computation of the changes in gravitational gradient components from GRACE observations and analytical model

Acta Geodaetica et Geophysica, 2015

Research paper thumbnail of Analytical solution of the asymmetric transient wave in a transversely isotropic half-space due to both buried and surface impulses

Soil Dynamics and Earthquake Engineering, 2016

Research paper thumbnail of A new idea to alert of Tsunami using of satellites altimetry and MSL

In this paper using of Satellite altimetry (e.g. Topex/Poseidon) and MSL (Mean Sea Level) a new a... more In this paper using of Satellite altimetry (e.g. Topex/Poseidon) and MSL (Mean Sea Level) a new approach presents to alert of tsunami. That in memory of Satellites there is a model of MSL, that using of matching technique and coincide of two components of MSL (hj) (observation of sea displacement at model) and height instantaneously displacement of sea measured with satellite (hi), different between two components is determined. If difference between hj and hi is big, the system alert the occurring the Tsunami using the radio waves.

Research paper thumbnail of کاربرد تنسور گرادیان جاذبه در حذف خطای نواری مشاهدات ثقل سنجی ماهواره ای گریس

Research paper thumbnail of Deformation analysis of the Earth crust based on manifold intrinsic geometry Case Study: Deformation analysis of the geodynamic network of Iran within 1999 - 2005

Unlike the classical deformation analysis of the Earth crust, which derives the planar and vertic... more Unlike the classical deformation analysis of the Earth crust, which derives the planar and vertical strains separately, in this study, we have offered a method for 3-D deformation study based on intrinsic geometry of the manifolds on the topographic surface of the Earth. In this way, our method would be based on the 2-D metric tensor of horizontal * ‫راﺑﻂ‬ ‫ﻧﮕﺎرﻧﺪه‬ : ‫ﺗﻠﻔﻦ‬ : 61114383 -021 ‫دورﻧﮕﺎر‬ : 88337642 -021 ardalan@ut.ac.ir E-mail: 126 ‫دوره‬ ‫ﻓﻀﺎ،‬ ‫و‬ ‫زﻣﻴﻦ‬ ‫ﻓﻴﺰﻳﻚ‬ ‫ﻣﺠﻠﺔ‬ 37 ‫ﺷﻤﺎره‬ ، 4 ، 1390

Research paper thumbnail of تعیین پارامترهای گسل مسبب زلزله با آنالیز موجک مشاهدات ثقل سنجی ماهواره ای گریس

‫بیست‬ ‫دومین‬ ‫و‬ ‫ژئوماتیك‬ ‫ملي‬ ‫همایش‬ -‫اردیبهشت‬ 4931 ‫بیست‬ ‫دومین‬ ‫و‬ ‫ژئوماتیك‬ ‫ملي‬ ... more ‫بیست‬ ‫دومین‬ ‫و‬ ‫ژئوماتیك‬ ‫ملي‬ ‫همایش‬ -‫اردیبهشت‬ 4931 ‫بیست‬ ‫دومین‬ ‫و‬ ‫ژئوماتیك‬ ‫ملي‬ ‫همایش‬ -‫اردیبهشت‬ 4931 ‫بیست‬ ‫دومین‬ ‫و‬ ‫ژئوماتیك‬ ‫ملي‬ ‫همایش‬ -‫اردیبهشت‬ 4931 J J J J J ‫بیست‬ ‫دومین‬ ‫و‬ ‫ژئوماتیك‬ ‫ملي‬ ‫همایش‬ -‫اردیبهشت‬ 4931

Research paper thumbnail of On the Application of the Gravity Gradient Tensor in a Reduction of the Striping Error of Grace Gravity Observation

In this study we will review potential and gravity gradient changes due to Sumatra's 9.1-magn... more In this study we will review potential and gravity gradient changes due to Sumatra's 9.1-magnitude earthquake on 26 th Dec 2004 using data collected from GRACE Satellite. Also we find the second derivative of the gravitational potential and then we use these values for co-seismic deformation which are caused by the Sumatra earthquake. The gravity gradients clearly show rupture line and mass distribution. In this study we find changes in co-seismic gradient components without using filter and with these gradients we eliminate GRACE strip errors in ∅ direction however in the direction of λ would cause fluctuations to intensify in east-west direction. Because í µí° ¶ 20 coefficient has a negligible contribution in the calculation of gravity changes determination due to the low accuracy of these coefficients, this coefficient will be replaced by SLR coefficients.

Research paper thumbnail of A proposal for deformation analysis via direct computation of strain tensor elements from the time-wise changes in the distances and angles in a geodetic network Case study: Deformation computation of the geodynamic network of Iran

A method for deformation computation based on strain tensor elements, as an alternative to the us... more A method for deformation computation based on strain tensor elements, as an alternative to the usual way of application of gradient of displacement vector, is proposed. The method computes directly the strain tensor elements from the computed/observed changes in distances and angles between the stations of a geodetic network in two epochs of

Research paper thumbnail of Are the gravimetry measurments necessary in the pricies levelling?

In this paper we presented the suitable criterion which shows the necessity for taking account of... more In this paper we presented the suitable criterion which shows the necessity for taking account of gravity field on the precise leveling observations. Our criterion is based on the required accuracy for gravity measurements which is a function of potential accuracy, height difference and height difference accuracy, and can be obtained via this simple formulaDeltaw = g × DeltaH. By taking sigmaw = 0.01m2 s2, sigmaDeltaH = .0001m, and DeltaH and g maximum values of height difference and gravity acceleration in the desired region, respectively, we can obtain the required accuracy for gravity measurement. By comparing this quantity with the maximum variations of gravity over the region, if these changes are smaller than the accuracy of gravity measurements, we won't require to consider the gravity in the computation of height by way of precise levelling and vice versa.

Research paper thumbnail of Analytical solution for axisymmetric thermoelastodynamic problems in a transversely isotropic half-space under a surface loading

In the present study, the theory of coupled thermoelastodynamic is applied to determine the displ... more In the present study, the theory of coupled thermoelastodynamic is applied to determine the displacement, temperature and stress (DTS) fields of a torsionless axisymmetric transversely isotropic half-space under a surface loading. The basic equations of coupled thermoelasticity consist of the equations of motion and the energy equation, which forms a set of completely coupled partial differential equations for the displacement and temperature fields. Potential method is employed for uncoupling the set of basic equations of coupled thermoelasticity. With the aid of a potential function existed in the literature, the system of equations are uncoupled, where a sixth order partial differential equation is received. Displacement components and temperature are written with respect to the potential function in cylindrical coordinate system. The Laplace and Hankel integral transforms are employed to suppress the time and radial variables, respectively. One may apply the inverse Hankel and L...

Research paper thumbnail of Wavelet and Gaussian Approaches for Estimation of Groundwater Variations Using GRACE Data

Research paper thumbnail of A comparative study among computation techniques for deformation analysis based on repeated geodetic observations

Considering the relative movement of points on the Earth's surface as a source of information... more Considering the relative movement of points on the Earth's surface as a source of information for deformation analysis of the crust via strain analysis, geodetic obser-vations (ground based, and satellite) can provide the required geometrical data. In the literatures so far various computational techniques have been introduced to the defor-mation analysis based on repeated geodetic observations. In this paper we present a comparative study over those computations techniques. Strain component computa-tions based on displacement vector, strain component computation based on changes in the distances and angles between geodetic network stations in two epoch of time, strain component computation on the topographic surface of the Earth, and strain com-ponent computation on the map projection planes are among the those computational techniques that have been studied for their efficiency and reliability in deformation analysis, in this paper.

Research paper thumbnail of Performance comparison of numerical inversion methods for Laplace and Hankel integral transforms in engineering problems

Applied Mathematics and Computation, 2015

Research paper thumbnail of Asymmetric motion of a transversely isotropic thermoelastic half-space under time-harmonic buried source

Zeitschrift für angewandte Mathematik und Physik, 2013

With the aid of complete representations in terms of two scalar potential functions, the governin... more With the aid of complete representations in terms of two scalar potential functions, the governing equations of coupled thermoelasticity are uncoupled into a sixth-and second-order partial differential equations in cylindrical coordinate system, which are solved by virtue of Fourier series expansion and Hankel integral transforms. Utilizing the transformed stresses-, displacements-and temperature-potential functions relationships, these functions are derived and represented in terms of improper line integrals. The general solutions are changed for point and circular patch load and heat flux Green's functions in order to derive the related displacement and temperature Green's functions. Some numerical evaluations of Greens functions are represented to portray the dependency of response on thermo-mechanical coupling as well as the anisotropy of the medium.

Research paper thumbnail of How to obtain the optimum digree/order in the expansion of geopotential model for geoid computation problem?

One of the discrepancy issues among the contemporary geodesist is the manner of implementation of... more One of the discrepancy issues among the contemporary geodesist is the manner of implementation of geopotential models for solving of boundary value problems. Some of them believe that it's better to use the low order in the expansion of geopotential models and instead, increase the domain of integration in the terrain correction. However, the other emphasize that we should take the order of expansion in the geopotential models as high as possible and consequently lessen the domain of integration over the remain local masses. In this paper we have comprehensively studied this matter and illustrated it's result on the various geopotential models.

Research paper thumbnail of Frequency Domain Analysis of an Axisymmetric Thermoelastic Transversely Isotropic Half-Space

Journal of Engineering Mechanics, 2013

By virtue of a new complete scalar potential function, an analytical formulation is presented to ... more By virtue of a new complete scalar potential function, an analytical formulation is presented to determine displacements, stresses, and temperature in an axisymmetric linear thermoelastic transversely isotropic half-space affected by time harmonic surface axisymmetric vertical traction and/or surface heat flux. With the use of only one scalar potential function in a cylindrical coordinate system, the coupled partial differential equations in thermoelasticity are transformed to a sixth-order partial differential equation governing the potential function. Then, by using the Hankel integral transforms, a sixth-order ordinary differential equation is received, which after solving, results in the displacements, stresses, and temperature fields. To prove the validation of the analytical solution presented in this paper, the solutions are reduced to the case of elastodynamics in transversely isotropic half-space and in a quasi-static thermoelastic isotropic half-space, where exact agreements with the solutions reported in the literature are achieved. Because of complexity of the integrands, numerical evaluations of the integrals involved in this paper are carried out using a suitable quadrature scheme by Mathematica software. To show the accuracy and efficiency of the numerical algorithm, the solution of this study is compared with the results of an existing elastodynamic transversely isotropic half-space, where an excellent agreement is achieved.

Research paper thumbnail of Dynamic Green's Functions of an Axisymmetric Thermoelastic Half-Space by a Method of Potentials

Journal of Engineering Mechanics, 2013

With the aid of a new complete scalar potential function, an analytical formulation for thermoela... more With the aid of a new complete scalar potential function, an analytical formulation for thermoelastic Green's functions of an axisymmetric linear elastic isotropic half-space is presented within the theory of Biot's coupled thermoelasticity. By using the potential function, the governing equations of coupled thermoelasticity are uncoupled into a sixth-order partial differential equation in a cylindrical coordinate system. Then, by using Hankel integral transforms to suppress the radial variable, a sixth-order ordinary differential equation is received. By solving this equation and considering boundary conditions, displacements, stresses, and temperature are derived in the Hankel integral transformed domain. By applying the theorem of inverse Hankel transforms, the solution is obtained generally for arbitrary surface timeharmonic traction and heat distribution. Subsequently, point-load Green's functions for the displacements, temperature, and stresses are given in the form of some improper line integrals. For more investigations, the solutions are also determined analytically for uniform patch-load and patch-heat distributed on the surface. For validation, it is shown that the derived solutions could be degenerated to elastodynamic and quasistatic thermoelastic cases reported in the literature. Numerical evaluations of improper integrals, which have some branch points and pole, are carried out using a suitable quadrature scheme by Mathematica software. To show the accuracy and efficiency of numerical algorithm, a numerical evaluation from this study is compared with the results of an existing elastodynamic case, where excellent agreement is achieved.

Research paper thumbnail of Analytical Solution of Coupled Thermoelastic Axisymmetric Transient Waves in a Transversely Isotropic Half-Space

Journal of Applied Mechanics, 2013

A half-space containing transversely isotropic thermoelastic material with a depth-wise axis of m... more A half-space containing transversely isotropic thermoelastic material with a depth-wise axis of material symmetry is considered to be under the effects of axisymmetric transient surface thermal and forced excitations. With the use of a new scalar potential function, the coupled equations of motion and energy equation are uncoupled, and the governing equation for the potential function, is solved with the use of Hankel and Laplace integral transforms. As a result, the displacements and temperature are represented in the form of improper double integrals. The solutions are also investigated in detail for surface traction and thermal pulses varying with time as Heaviside step function. It is also shown that the derived solutions degenerate to the results given in the literature for isotropic materials. Some numerical evaluations for displacement and temperature functions for two different transversely isotropic materials with different degree of anisotropy are presented to portray the dependency of response on the thermal properties as well as the degree of anisotropy of the medium.

Research paper thumbnail of Coupled thermoviscoelastodynamic Green's functions for bi-material half-space

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2013

By virtue of the representations of displacements, stresses, and temperature fields in terms of t... more By virtue of the representations of displacements, stresses, and temperature fields in terms of two scalar potential functions and the use of correspondence principle, an analytical derivation of fundamental Green's functions for bi-material halfspace composed of a transversely isotropic thermo-elastic layer and an isotropic thermo-visco-elastic half-space affected by finite surface or interfacial sources is presented. With the aid of the potential function relationships, the coupled equations of motion and energy equation in both the half-space and the layer are uncoupled and solved with the aid of Fourier series and Hankel integral transforms. Responses of the medium are derived in the form of improper line integrals related to Hankel inversion transforms. To show the effects of anisotropy and viscoelasticity on the propagation of coupled thermoviscoelastic waves, the derived integrals for displacements, stresses, and temperature Green's functions are evaluated by a numerical scheme.

Research paper thumbnail of Transient response of a thermoelastic half-space to mechanical and thermal buried sources

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2013

With the aid of a complete set of two scalar potential functions, the transient responses of an i... more With the aid of a complete set of two scalar potential functions, the transient responses of an isotropic thermoelastic halfspace subjected to time dependent tractions and heat flux applied to a finite patch at an arbitrary depth below a free surface are derived. Using the displacements-and temperature-potential function relationships, the coupled equations of motion and energy equation are uncoupled, resulting in two (6th and 2nd order) partial differential equations in the cylindrical coordinate system, which are solved with the aid of Fourier series expansion and joint Hankel-Laplace integral transforms. The solutions are also investigated in details for tractions varying with time in terms of a Heaviside step function and heat flux as a Dirac delta function, which may be used as a kernel in any integral based method for more complicated thermoelastodynamic initial-boundary value problems. Due to the complexity of the integrands involved in the general case, the integrals cannot be resolved analytically and thus an appropriate numerical algorithm is used for the inversion of the Laplace and Hankel integral transforms. To demonstrate the pattern of deformations as well as the distribution of change of temperature at the free surface of the half-space, numerical evaluations for these functions are presented for an isotropic material.