A Point Heat Source on the Surface of a Semi-Infinite Transversely Isotropic Piezothermoelastic Material

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Peng-Fei Hou ◽  
Wei Luo ◽  
Andrew Y. T. Leung
Keyword(s):  
Heat Source ◽  
Cadmium Selenide ◽  
Harmonic Functions ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Numerical Results ◽  
Point Heat Source ◽  
Elementary Functions ◽  
General Solutions ◽  
Coupled Field

We use the compact harmonic general solutions of transversely isotropic piezothermoelastic materials to construct the three-dimensional Green’s function of a steady point heat source on the surface of a semi-infinite transversely isotropic piezothermoelastic material by four newly introduced harmonic functions. All components of the coupled field are expressed in terms of elementary functions and are convenient to use. Numerical results for cadmium selenide are given graphically by contours.

Fundamental solution for a two-dimensional problem in transversely isotropic micropolar thermoelastic media

2017 ◽  
Vol 13 (3) ◽  
pp. 409-423 ◽  
Author(s):  
Vijay Chawla ◽  
Sanjeev Ahuja ◽  
Varsha Rani
Keyword(s):  
General Solution ◽  
Fundamental Solution ◽  
Heat Source ◽  
Harmonic Functions ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Two Dimensional ◽  
Point Heat Source ◽  
Content Type ◽  
Thermoelastic Material

Purpose The purpose of this paper is to study the fundamental solution in transversely isotropic micropolar thermoelastic media. With this objective, the two-dimensional general solution in transversely isotropic thermoelastic media is derived. Design/methodology/approach On the basis of the general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic micropolar thermoelastic material is constructed by six newly introduced harmonic functions. Findings The components of displacement, stress, temperature distribution and couple stress are expressed in terms of elementary functions. From the present investigation, a special case of interest is also deduced and compared with the previous results obtained. Practical implications Fundamental solutions can be used to construct many analytical solutions of practical problems when boundary conditions are imposed. They are essential in the boundary element method as well as the study of cracks, defects and inclusions. Originality/value Fundamental solutions for a steady point heat source acting on the surface of a micropolar thermoelastic material is obtained by seven newly introduced harmonic functions. From the present investigation, some special cases of interest are also deduced.

scholarly journals A General Study of Fundamental Solutions in Aniotropicthermoelastic Media with Mass Diffusion and Voids

2020 ◽  
Vol 25 (4) ◽  
pp. 22-41
Author(s):  
Vijay Chawla ◽  
Deepmala Kamboj
Keyword(s):  
General Solution ◽  
Fundamental Solution ◽  
Harmonic Functions ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Mass Diffusion ◽  
Point Heat Source ◽  
General Study ◽  
Elementary Functions ◽  
Special Cases

AbstractThe present paper deals with the study of a fundamental solution in transversely isotropic thermoelastic media with mass diffusion and voids. For this purpose, a two-dimensional general solution in transversely isotropic thermoelastic media with mass diffusion and voids is derived first. On the basis of the obtained general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic thermoelastic material with mass diffusion and voids is derived by nine newly introduced harmonic functions. The components of displacement, stress, temperature distribution, mass concentration and voids are expressed in terms of elementary functions and are convenient to use. From the present investigation, some special cases of interest are also deduced and compared with the previous results obtained, which prove the correctness of the present result.

scholarly journals General solution and fundamental solution for two-dimensional problem in orthotropic thermoelastic media with voids

2014 ◽  
Vol 41 (4) ◽  
pp. 247-265
Author(s):  
Rajneesh Kumar ◽  
Vijay Chawla
Keyword(s):  
General Solution ◽  
Fundamental Solution ◽  
Heat Source ◽  
Harmonic Functions ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Point Heat Source ◽  
Elementary Functions ◽  
Thermoelastic Material ◽  
Special Case

The aim of the present paper is to study the fundamental solution in orthotropic thermoelastic media with voids. With this objective, firstly the two-dimensional general solution in orthotropic thermoelastic media with voids is derived. On the basis of general solution, the fundamental solution for a steady point heat source on the surface of a semiinfinite orthotropic thermoelastic material with voids is constructed by six newly introduced harmonic functions. The temperature and voids distribution and components of displacement and stress are expressed in terms of elementary functions. From the present investigation, a special case of interest is also deduced and compared with the previous results obtained. Since all the components are expressed in terms of elementary functions, it is convenient to use them.

scholarly journals Heat Source Modeling in Selective Laser Melting

Materials ◽  
2019 ◽  
Vol 12 (13) ◽  
pp. 2052 ◽  
Author(s):  
Elham Mirkoohi ◽  
Daniel E. Seivers ◽  
Hamid Garmestani ◽  
Steven Y. Liang
Keyword(s):  
Temperature Field ◽  
Steady State ◽  
Heat Source ◽  
Material Properties ◽  
Physical Phenomenon ◽  
Three Dimensional ◽  
Moving Heat Source ◽  
Point Heat Source ◽  
Laser Melting ◽  
Source Models

Selective laser melting (SLM) is an emerging additive manufacturing (AM) technology for metals. Intricate three-dimensional parts can be generated from the powder bed by selectively melting the desired location of the powders. The process is repeated for each layer until the part is built. The necessary heat is provided by a laser. Temperature magnitude and history during SLM directly determine the molten pool dimensions, thermal stress, residual stress, balling effect, and dimensional accuracy. Laser-matter interaction is a crucial physical phenomenon in the SLM process. In this paper, five different heat source models are introduced to predict the three-dimensional temperature field analytically. These models are known as steady state moving point heat source, transient moving point heat source, semi-elliptical moving heat source, double elliptical moving heat source, and uniform moving heat source. The analytical temperature model for all of the heat source models is solved using three-dimensional differential equations of heat conduction with different approaches. The steady state and transient moving heat source are solved using a separation of variables approach. However, the rest of the models are solved by employing Green’s functions. Due to the high temperature in the presence of the laser, the temperature gradient is usually high which has a substantial impact on thermal material properties. Consequently, the temperature field is predicted by considering the temperature sensitivity thermal material properties. Moreover, due to the repeated heating and cooling, the part usually undergoes several melting and solidification cycles, and this physical phenomenon is considered by modifying the heat capacity using latent heat of melting. Furthermore, the multi-layer aspect of the metal AM process is considered by incorporating the temperature history from the previous layer since the interaction of the layers have an impact on heat transfer mechanisms. The proposed temperature field models based on different heat source approaches are validated using experimental measurement of melt pool geometry from independent experimentations. A detailed explanation of the comparison of models is also provided. Moreover, the effect of process parameters on the balling effect is also discussed.

Three-dimensional stress distributions in hexagonal aeolotropic crystals

1948 ◽  
Vol 44 (4) ◽  
pp. 522-533 ◽  
Author(s):  
H. A. Elliott ◽  
N. F. Mott
Keyword(s):  
Harmonic Functions ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Quadratic Equation ◽  
Stress Distributions ◽  
Third Order ◽  
Isotropic Solid ◽  
Single Stress ◽  
Image Position ◽  
Special Case

The conditions for equilibrium in an elastically stressed hexagonal aeolotropic medium (transversely isotropic) are formulated, and solutions are found in terms of two ‘harmonic’ functions ø1, ø2, which are solutions ofν1, ν2 being the roots of a certain quadratic equation.It is also shown that in the case of axially symmetrical stress systems the solution may be expressed in terms of the third-order differential coefficients of a single stress function Φ.The solutions for an isotropic medium may be deduced as a special case.The problems of nuclei of strain in such a hexagonal solid are solved, and the results for zinc and magnesium contrasted with those for an isotropic solid.

scholarly journals Heat Source Modeling in Selective Laser Melting

2019 ◽  
Author(s):  
Elham Mirkoohi ◽  
Daniel E. Seivers ◽  
Hamid Garmestani ◽  
Steven Y. Liang
Keyword(s):  
Temperature Field ◽  
Steady State ◽  
Heat Source ◽  
Material Properties ◽  
Physical Phenomenon ◽  
Three Dimensional ◽  
Moving Heat Source ◽  
Point Heat Source ◽  
Laser Melting ◽  
Source Models

Selective laser melting is an emerging Additive Manufacturing (AM) technology for metals. Intricate three-dimensional parts can be generated from the powder bed by selectively melting the desired location of the powders. The process is repeated for each layer until the part is built. The necessary heat is provided by a laser. Temperature magnitude and history during SLM directly determine the molten pool dimensions, thermal stress, residual stress, balling effect, and dimensional accuracy. Laser-matter interaction is a crucial physical phenomenon in the SLM process. In this paper, five different heat source models are introduced to predict the three-dimensional temperature field analytically. These models are known as steady state moving point heat source, transient moving point heat source, semi-elliptical moving heat source, double elliptical moving heat source, and uniform moving heat source. The analytical temperature model for all of the heat source models are solved using three-dimensional differential equation of heat conduction with different approaches. The Steady state and transient moving heat source are solved using separation of variables approach. However, the rest of models are solved by employing the Green’s functions. Due to the high magnitude of the temperature in the presence of the laser, the temperature gradient is usually high which has a substantial impact on thermal material properties. Consequently, the temperature field is predicted by considering the temperature sensitivity thermal material properties. Moreover, due to the repeated heating and cooling, the part usually undergoes several melting and solidification cycles, this physical phenomenon is considered by modifying the heat capacity using latent heat of melting. Furthermore, the multi-layer aspect of metal AM process is considered by incorporating the temperature history from the previous layer since the interaction of the layers have an impact on heat transfer mechanisms. The proposed temperature field models based on different heat source approaches are validated using experimental measurement of melt pool geometry from independent experimentations. The detailed explanation of the comparison of models is also provided. Moreover, the effect of process parameters on the balling effect is also discussed.

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