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1

Wyznaczanie rozkładów temperatury, gradientów temperatury oraz naprężeń termicznych w zaworze wylotowym pokrytym warstwą nagaru

Hornik Aleksander

Napędy i Sterowanie

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2022

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R. 24, nr 5

38--43

PL

W artykule przedstawiono modelowanie obciążeń cieplnych w zaworze wylotowym pokrytym warstwą nagaru w początkowej fazie pracy doładowanego silnika z zapłonem samoczynnym. W obliczeniach wykorzystano dwustrefowy model procesu spalania, metodę elementów skończonych (MES). Modelowanie przeprowadzono przy użyciu warunków brzegowych III rodzaju. W wyniku przeprowadzonych obliczeń otrzymano rozkłady temperatury, gradientów temperatury oraz naprężeń termicznych. Naprężenia te powodują wzrost mikropęknięć na powierzchni zaworu, które ostatecznie prowadzą do defektów materiału, uszkodzeń zaworu, a w konsekwencji nawet silnika.

EN

This paper presents the model ling of the heat loads in the exhaust valve with using the layer of carbon deposit in initial phase of work of the turbocharged Diesel engine. In calculations used the two-zone combustion model , finite elements method (FEM). Modelling was conducted by use of III kind of the boundary conditions. As a result of the calculations were obtained distributions of temperature, thermal gradients and thermal stresses. These stresses cause the growth of micro cracks in the area of the valve, which finally give occasion to the defect of material, the damage of the valve and engine failure.

2

Thermosensitive response of a functionally graded cylinder with fractional order derivative

Lamba Navneet Kumar

International Journal of Applied Mechanics and Engineering

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2022

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Vol. 27, no. 1

107--124

EN

The present paper deals with thermal behaviour analysis of an axisymmetric functionally graded thermosensitive hollow cylinder. The system of coordinates are expressed in cylindrical-polar form. The heat conduction equation is of time-fractional order02<α≤, subjected to the effect of internal heat generation. Convective boundary conditions are applied to inner and outer curved surfaces whereas heat dissipates following Newton’s law of cooling. The lower surface is subjected to heat flux, whereas the upper surface is thermally insulated. Kirchhoff’s transformation is used to remove the nonlinearity of the heat equation and further it is solved to find temperature and associated stresses by applying integral transformation method. For numerical analysis a ceramic-metal-based functionally graded material is considered and the obtained results of temperature distribution and associated stresses are presented graphically.

3

Thermoelastic analysis of pressurized hollow spherical vessels with arbitrary radial non-homogeneity

Rani Pooja, Singh Kuldip

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 4

192--205

EN

In this study, a general analysis of one dimensional steady-state thermal stresses of a functionally graded hollow spherical vessel with spherical isotropy and spherically transversely isotropy is presented with material properties of arbitrary radial non-homogeneity. The material properties may arbitrarily vary as continuous or piecewise functions. The boundary value problem associated with a thermo-elastic problem is converted to an integral equation. Radial and tangential thermal stress components distribution can be determined numerically by solving the resulting equation. The influence of the gradient variation of the material properties on the thermal stresses is investigated and the numerical results are presented graphically.

4

Thermal stresses due to non-uniform internal heat generation in functionally graded hollow cylinder

Rani P., Singh K., Muwal R.

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 2

186--200

EN

Thermal stresses of a functionally graded hollow thick cylinder due to non-uniform internal heat generation are studied in this paper. Analytical solutions are obtained with radially varying properties by using the theory of elasticity. Thermal stresses distribution for different values of the powers of the module of elasticity and varying power law index of heat generation are studied. The results have been computed numerically and illustrated graphically.

5

Reduced differential transform method for thermoelastic problem in hyperbolic heat conduction domain

Chaudhari K. K., Sutar C. S.

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 1

76--87

EN

In the present study, we have applied the reduced differential transform method to solve the thermoelastic problem which reduces the computational efforts. In the study, the temperature distribution in a two-dimensional rectangular plate follows the hyperbolic law of heat conduction. We have obtained the generalized solution for thermoelastic field and temperature field by considering non-homogeneous boundary conditions in the x and y direction. Using this method one can obtain a solution in series form. The special case is considered to show the effectiveness of the present method. And also, the results are shown numerically and graphically. The study shows that this method provides an analytical approximate solution in very easy steps and requires little computational work.

6

Konstruowanie odlewów obciążanych cieplnie - aspekty technologiczno-ekonomiczne

Maj Maria, Łukasik Jerzy, Stachurski Wacław

Hutnik, Wiadomości Hutnicze

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2021

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Vol. 88, nr 1

22--25

PL

W pracy zaprezentowano, na przykładzie dużego elementu obciążanego cieplnie, w jakim stopniu wybrane kryteria konstrukcyjne prowadzą do spełnienia stawianych mu wymagań. W szczególność pokazany został wpływ obciążenia cieplnego na trwałość, funkcjonalność i koszty eksploatacji dwóch różnych konstrukcji spełniających funkcję pokrywy kadzi pośredniej w linii ciągłego odlewania stali. Omówiono przede wszystkim wpływ konstrukcji oraz zastosowanych materiałów na trwałość płyty pod-wlewnicowej poddawanej bardzo dużym obciążeniom zarówno cieplnym, jak i mechanicznym. Przytoczone różnice uzasadniają przyjęcie do eksploatacji konstrukcji przestrzennej zabezpieczonej odpowiednią izolacją termiczną i ogniotrwałą.

EN

Based on the example of a large thermally loaded component, the study has focused on the problem to what extent the selected design criteria can help meet the requirements set for this component. In particular, the effect of thermal load on the durability, functionality and operating costs of two different designs of the component serving as a tundish cover in a continuous steel casting line is shown. First of all, the impact of the design and type of material on the durability of the plate which should withstand the effect of very high loads, both thermal and mechanical, is discussed. The differences in design justify the use of a spatial structure protected with appropriate thermal and refractory insulation.

7

Power losses and windings temperature of an induction machine under voltage subharmonics

Gnaciński Piotr, Pepliński Marcin, Hallmann Damian

Zeszyty Naukowe Akademii Morskiej w Szczecinie

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2020

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nr 63 (135)

51--57

EN

This paper deals with the effect of voltage subharmonics on power losses and heating of an induction motor. An increase in power losses in stator and rotor windings and their impact on windings temperature is presented for subharmonics of various frequencies. The results of this study’s investigations are provided for subharmonics occurring as a single power quality disturbance and combined with voltage deviation. The appropriate electromagnetic computations were performed with the finite element method, and thermal ones – with an analytical method.

8

Temperature and thermal stresses distributions in a dry friction clutch

Topczewska Katarzyna, Schlattmann Josef, Abdullah Oday Ibraheem

Journal of Theoretical and Applied Mechanics

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2020

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Vol. 58 nr 2

351--360

EN

The aim of this study is to develop an analytical model to determine temperature and thermal stresses distributions in a single plate clutch during the slipping phase. Proposed expressions enable calculation of temperature and thermal stresses on the contact surface as well as at any depth inside the friction material and at any instant during the slipping period. It was investigated how the maximum temperature on the friction surface varies with the thickness of the friction facings of the clutch disc and the intensity of convective cooling.

9

Application of fractional order theory of thermoelasticity in an elliptical disk and associated thermal stresses

Thakare S., Panke Y., Hadke K.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 3

169--180

EN

In this article, a time fractional-order theory of thermoelasticity is applied to an isotropic homogeneous elliptical disk. The lower and upper surfaces of the disk are maintained at zero temperature, whereas the sectional heat supply is applied on the outer curved surface. Thermal deflection and associated thermal stresses are obtained in terms of Mathieu function of the first kind of order 2n. Numerical evaluation is carried out for the temperature distribution, Thermal deflection and thermal stresses and results of the resulting quantities are depicted graphically.

10

Analysis of time-fractional heat transfer and its thermal deflection in a circular plate by a moving heat source

Thakare S., Warbhe M.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 3

158--168

EN

Mathematical modeling of a thin circular plate has been made by considering a nonlocal Caputo type time fractional heat conduction equation of order […], by the action of a moving heat source. Physically convective heat exchange boundary conditions are applied at lower, upper and outer curved surface of the plate. Temperature distribution and thermal deflection has been investigated by a quasi-static approach in the context of fractional order heat conduction. The integral transformation technique is used to analyze the analytical solution to the problem. Numerical computation including the effect of the fractional order parameter has been done for temperature and deflection and illustrated graphically for an aluminum material.

11

Selection of the Technological Ceramic Layer Thickness in an HPDC Machine Plunger in the Aspect of its Strength

Jankowski Jacek, Kołakowski Dariusz, Pisarek Bogusław

Advances in Science and Technology. Research Journal

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2020

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Vol. 14, no 4

11--20

EN

A way of selecting the ceramic coating thickness concerning the axially symmetrical thermal stresses in a casting machine plunger with a horizontal shot sleeve was discussed. Application of a technological ceramic outer layer in the plunger enhances its tribological properties. The condition that stresses in tension in the outer ceramic layer are lower than the tensile strength was proposed as a selection criterion.

12

Thermomechanical Analysis of the Charge Heating in a Rotary Furnace

Gołdasz A., Malinowski Z., Cebo-Rudnicka A.

Archives of Metallurgy and Materials

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2019

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Vol. 64, iss. 4

1377--1384

EN

This paper presents the methodology for determining thermal strains and stresses during heating the charge in a rotary furnace. The calculations were made with the original software, which uses the finite element method. The heat transfer boundary conditions used for computing were verified on the basis of industrial tests. Good compatibility between the experimental data and numerical calculations was obtained. The possibility of the material cracking occurrence was checked for a set exhaust gas temperature distribution on the furnace length. As a result, it was possible to develop steel heating curves characterized by short process times.

13

Thermal Stresses in the Accessories of Heat Treatment Furnaces vs Cooling Kinetics

Bajwoluk A., Gutowski P.

Archives of Foundry Engineering

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2019

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iss. 3

88--93

EN

Depending on the course of the processes of heat treatment and thermo-chemical treatment, the technological equipment of heat treatment furnaces is exposed to different operating conditions, as the said processes differ among themselves in the temperature of annealing and atmosphere prevailing in the furnace chamber, in the duration of a single work cycle and in the type and temperature of the coolant. These differences affect the magnitude of stresses occurring in each cycle of the operation of furnace accessories, and thus play an important role in fatigue processes leading to the destruction of these accessories. The kinetics of temperature changes during each cooling process plays an important role in the formation of thermal stresses on the cross-section of the cooled parts. It depends on many factors, including the initial cooling temperature, the type and temperature of the cooling medium, or the dimensions and shape of the object. This article presents a numerical analysis of the effect of the initial temperature on the distribution of stresses on the cross-section of the grate ribs, generated in the first few seconds of the cooling process carried out in two cooling media, i.e. hardening oil and water. The analysis was carried out by the finite element method, based on the results of experimental testes of temperature changes in the rib during its cooling.

14

Analytical model for investigation of the effect of friction power on thermal stresses in friction elements of brakes

Topczewska K.

Journal of Theoretical and Applied Mechanics

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2018

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Vol. 56 nr 4

1017--1027

EN

The influence of the change with time of friction power on thermal stresses in a friction element of a brake system is investigated. For this purpose, a list of ten different temporal profiles of specific friction power is used, which has been experimentally established for a single braking process. The corresponding profiles of transient temperature fields in the considered element are applied as input parameters to find quasi-static thermal stresses. Numerical analysis concerned with spatio-temporal distributions of the stresses and their evolutions on the heated surface is presented.

15

Thermal micro- and macrostresses in the surface layer of cast steel accessories for carburizing furnaces

Bajwoluk A., Gutowski P.

Inżynieria Materiałowa

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2018

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Vol. 39, nr 5

178--183

EN

High heat resistance and creep resistance make the austenitic Fe–Ni–Cr alloys widely used as a material for accessories of the furnaces for heat treatment and thermochemical treatment. Due to the specific character of furnace operation, its tooling is exposed to the effect of numerous highly unfavourable factors, including high temperature and its rapid changes, strongly carburizing atmosphere as well as mechanical and thermal loads originating from the processed batch of items. As a result of the impact of the above-mentioned factors, in castings made from the Fe–Ni–Cr alloys, cracks and deformations occur, eliminating these castings from further use. The damages are mainly caused by stresses arising in the cast structure during subsequent work cycles. It is generally believed that stresses in furnace accessories are due to the temperature gradient generated during heating or cooling of components and differences in the thermal expansion of the structural constituents of cast steel from which these accessories are made. This article focuses on the results of numerical analysis of the stress distribution in the surface layer of a carburized austenitic alloy undergoing the cooling process. Cases are discussed when the examined sources of stress act as separate and independent factors and also when they operate simultaneously. This provides information about the stress formation and development of stress-initiated cracks on the surface of real castings.

PL

Dobra żaroodporność oraz żarowytrzymałość sprawiają, iż austenityczne stopy Fe–Ni–Cr są powszechnie stosowane jako materiał, z którego wykonywane są elementy osprzętu pieców do obróbki cieplnej i cieplno-chemicznej. Specyfika pracy oprzyrządowania pieców powoduje, że jest ono poddawane cyklicznemu działaniu wielu niekorzystnych czynników, w tym: wysokiej temperatury oraz jej gwałtownym zmianom, silnie nawęglającej atmosfery oraz obciążeniom mechanicznym i cieplnym pochodzącym od obrabianego wsadu, przyspieszającym procesy zmęczenia cieplnego. Pomimo dość dobrych właściwości wytrzymałościowych, którymi charakteryzują się austenityczne stopy niklowo-chromowe w podwyższonej temperaturze, w elementach z nich wykonanych dochodzi w wyniku wzajemnego oddziaływania wymienionych czynników do odkształceń oraz pęknięć eliminujących je z dalszego użytkowania. Za główne źródła naprężeń powodujących niszczenie odlewów (rys. 1, 2) użytkowanych w piecach uważa się różną rozszerzalność cieplną składników strukturalnych występujących w staliwie, z którego są one wykonane oraz gradient temperatury tworzący się na przekroju podczas chłodzenia lub nagrzewania. Celem pracy było przeprowadzenie analiz numerycznych rozkładów naprężeń powstających w warstwie wierzchniej gwałtownie chłodzonego, nawęglonego elementu wykonanego ze stopu Fe–Ni–Cr z uwzględnieniem równoczesnego występowania obydwóch tych źródeł.

16

On an approach to the thermo-elasto-plastic failure based on the Burzynski criterion

Banaś K., Badur J.

Transactions of the Institute of Fluid-Flow Machinery

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2017

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nr 136

65--76

EN

In this paper the comparison of material eort models: the classic Huber-Mises-Hencky approach and the Burzynski condition was presented. Burzynski yield condition is pressure sensitive and naturally takes into account the strength dierential eect, which has been observed in nickel-base super alloys such as Inconel 718. Investigation was performed during thermal-uidstructure interaction analysis of a power turbine guide vane of turbine helicopter engine PZL- 10W. Firstly, computational uid dynamics conjugate heat transfer analysis was carried out, then stress analysis was performed with boundary conditions obtained via computational uid dynamics analysis. During stress analysis, two mentioned above equivalent stress denitions were applied and dierence in material eort modelling by them was shown.

17

A novel approach to thermal and mechanical stresses in a FGM cylinder with exponentially-varying properties

Celebi K., Yarımpabuc D., Keles I.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 1

343—351

EN

A novel approach is employed to a general solution for one-dimensional steady-state thermal and mechanical stresses in a hollow thick cylinder made of a functionally graded material (FGM). The temperature distribution is assumed to be a function of radius, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the cylinder. The material properties, except Poisson’s ratio, are assumed to be exponentially-varying through the thickness. Forcing functions applied to the inner boundary are internal pressures which may be in form of steps. These conditions result in governing differential equations with variable coefficients. Analytical solutions to such equations cannot be obtained except for certain simple grading functions and pressures. Numerical approaches must be adopted to solve the problem in hand. The novelty of the present study lies in the fact that the Complementary Functions Method (CFM) is employed in the analysis. The Complementary Functions method (CFM) will be infused into the analysis to convert the problem into an initial-value problem which can be solved accurately. Benchmark solutions available in the literature are used to validate the results and to observe the convergence of the numerical solutions. The solution procedure is well-structured, simple and efficient and it can be readily applied to cylinders. It is also well suited for problems in which mechanical properties are graded.

18

Analiza rozkładu temperatury w ścianie żelbetowego zbiornika, uwzględniająca dwuwymiarowy przepływ ciepła

Garbalińska H., Strzałkowski J., Stolarska A.

Czasopismo Inżynierii Lądowej, Środowiska i Architektury / Journal of Civil Engineering, Environment and Architecture

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2017

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z. 64, nr 3/I

31--38

PL

Artykuł prezentuje wybrane aspekty projektowania żelbetowych zbiorników na ciecze z uwagi na obciążenia termiczne, pojawiające się w trakcie ich eksploatacji. Obciążenia termiczne wynikają z występowania dużych różnic temperatur między cieczą wypełniającą zbiornik a jego otoczeniem. W szczególności problem ten ujawnia się w przypadku ścian zbiornika, wyniesionych ponad poziom terenu. Wartości obliczeniowych temperatur podane w normie EC1-1-5 ustalone zostały na ekstremalnie niskim poziomie dla warunków zimowych (w przeprowadzonych obliczeniach przyjmowano -30ºC), natomiast dla okresu letniego na poziomie ekstremalnie wysokim (w obliczeniach przyjmowano +38ºC oraz +56ºC, na ścianach zbiornika wyeksponowanych na działanie słońca). W obliczeniach zaprezentowanych w artykule poddano analizie 4 warianty rozwiązania ściany zewnętrznej zbiornika – bez izolacji termicznej oraz z ułożoną na zewnątrz izolacją ze styropianu o grubości 5, 10 i 15 cm. Obliczenia rozkładów temperatur w ścianie zbiornika wykonano przy użyciu oprogramowania CFD, używanego do symulacji stacjonarnych i niestacjonarnych procesów cieplnych. Porównanie danych otrzymanych z symulacji dwuwymiarowych z wynikami obliczeń zakładających jednowymiarowy przepływ ciepła, wskazuje na występowanie wyraźnie wyższych gradientów temperatur. Problem ten jest szczególnie istotny w ścianach z termoizolacją, gdzie różnice temperatury są nawet pięciokrotnie większe w rozpatrywanych przekrojach, niż w modelu jednowymiarowym. Przekłada się to w dalszej kolejności na naprężenia występujące w obrębie ściany zbiornika, a wywołane zmianami temperatury.

EN

The article presents the selected aspects of designing reinforced concrete tanks for liquids considering the high thermal loads occurring during tanks’ exploitation. Thermal loads often are a consequence of occurrence of high differences in temperature between the liquid, which fills the tank, and the tank’s surroundings. This problem is strongly visible in case of the tank’s walls erected high above ground level. The calculation values of temperatures presented by EC1-1-5 norm have been established on extremely low levels of winter conditions (during the calculations, the assumed temperature was -30ºC), and extremely high levels of summer conditions (during the calculations, the assumed temperature was +38ºC and +56 ºC on the tank’s walls exposed to sunlight). The calculations presented in the article included 4 variants of solutions for the tank’s external walls – devoid of thermal isolation and with isolation of 5, 10 and 15 cm thick polystyrene layers laid out externally. Calculations of temperature distribution in the tank wall were made with application of CFD software which is used to simulate stationary and non-stationary heat processes. The comparison of data obtained from the two-dimensional simulation with results assuming one-dimensional heat flow indicates the appearance of clearly higher temperature gradients. The problem is particularly important in walls with thermal insulation, where temperature differences are even five times higher in the section in question than in the one-dimensional model. It further results in stresses appearing within the tank walls, which are caused by temperature changes.

19

The Effect of Cooling Agent on Stress and Deformation of Charge-loaded Cast Pallets

Bajwoluk A., Gutowski P.

Archives of Foundry Engineering

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2017

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Vol. 17, iss. 4

13--18

EN

The results of research on the effect of the type of cooling agent used during heat treatment and thermal-chemical treatment on the formation of temperature gradient and stress-deformation distribution in cast pallets, which are part of furnace accessories used in this treatment, are disclosed. During operation, pallets are exposed to the effect of the same conditions as the charge they are carrying. Cyclic thermal loads are the main cause of excessive deformations or cracks, which after some time of the cast pallet operation result in its withdrawal due to damage. One of the major causes of this damage are stresses formed under the effect of temperature gradient in the unevenly cooled pallet construction. Studies focused on the analysis of heat flow in a charge-loaded pallet, cooled by various cooling agents characterized by different heat transfer coefficients and temperature. Based on the obtained temperature distribution, the stress distribution and the resulting deformation were examined. The results enabled drawing relevant conclusions about the effect of cooling conditions on stresses formed in the direction of the largest temperature gradient.

20

Propagation of a thermoelastic wave in a half-space of a homogeneous isotropic material subjected to the effect of gravity field

Abd-Alla A. M., Abo-Dahab S. M., Alotaibi H. A.

Archives of Civil and Mechanical Engineering

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2017

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Vol. 17, no. 3

564--573

EN

The propagation of thermoelastic waves in a homogeneous, isotropic elastic semi-infinite space is subjected to a gravitational field, which is at temperature T0 initially, and whose boundary surface is subjected to heat source and load moving with finite velocity. Temperature and stress distribution occurring due to heating or cooling and have been determined using certain boundary conditions. Numerical results have been given and illustrated graphically in each case considered. The results indicate that the effect of gravity field is very pronounced. Comparison is made with the results predicted by the theory of thermoelasticity in the absence of gravity. The results indicate that the effect of the gravity is very pronounced.