Axisymmetric mechanical and thermal stresses in thick short length FGM cylinders

Jabbari, Mohsen; Bahtui, A.; Eslami, M. R.

doi:10.1016/j.ijpvp.2008.12.002

Cited by 102 publications

(51 citation statements)

References 18 publications

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“…Shao et al (2008) used complex Fourier series and Laplace transform techniques to investigate transient heat conduction and thermo-mechanical stresses in an FGM hollow cylinder. Jabbari et al (2002Jabbari et al ( , 2003Jabbari et al ( , 2009) derived the exact solution for one-dimensional and two dimensional steady-state thermoelastic problems of functionally graded hollow cylinders where material properties varied with the power product form of the radial coordinate variable. Recently Ruhi et al (2005) studied thermoelastic analysis of thick walled finite length cylinders of functionally graded materials and achieved results for stress, strain and displacement components through the thickness and along the length.…”

Section: Introductionmentioning

confidence: 99%

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

Çelebi

Yarımpabuç

Keles

2017

jtam

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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.

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Section: Introductionmentioning

confidence: 99%

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

Çelebi

Yarımpabuç

Keles

2017

jtam

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“…Вопросы распространения гармонических волн в цилиндрических термоупругих телах изучались многими авторами [1][2][3][4][5][6][7][8][9][10]. Распространение про-дольных термоупругих волн обсуждалось в рабо-тах [1; 2].…”

Section: Introductionunclassified

Equations of Dynamics for Prestressed Thermoelastic Cylinder

Sheydakov¹,

Belyankova²,

Sheydakov³

et al. 2018

Sc. South Russ.

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Аннотация. В рамках теории наложения малых деформаций на конечную проведена последователь-ная линеаризация определяющих соотношений нелинейной механики термоупругой сплошной среды. В процессе преобразований была использована материальная система координат Лагранжа, связанная с естественной конфигурацией тела. Предполагалось, что начальное напряженное состояние термо-упругого полуограниченного тела обусловлено как воздействием механических усилий, так и влиянием температуры (преднагрев). В линеаризованных тензорах напряжений Пиолы и Кирхгофа, участвующих в уравнениях движения и граничных условиях, удержаны все члены, которые содержат высшие степени начальной деформации и квадраты температуры. Выражения, определяющие линеаризованный закон состояния преднапряженной среды, а также линеаризованные уравнения, описывающие движение тер-моупругой среды при больших начальных деформациях, представлены в тензорном виде с последу-ющим переходом к компонентному представлению всех соотношений в цилиндрической ортогональ-ной системе координат. Для конкретной формы термоупругого потенциала при однородной начальной деформации приведены окончательные выражения, определяющие линеаризованный закон состояния преднапряженной среды, а также линеаризованные уравнения, описывающие движение термоупругой среды при больших начальных деформациях. Полученные представления позволяют эффективно ис-следовать влияние начальных напряжений и температуры на характеристики динамического процесса в термоупругом цилиндре.Ключевые слова: преднапряженный термоупругий цилиндр, начальная деформация, начальные напряжения, предварительный нагрев, термодинамический потенциал, термоупругие волны. Within the theory of small deformations superposed on a finite one, a step-by-step linearization of the constitutive relations for the nonlinear mechanics of a thermoelastic medium is carried out using a cylindrical coordinate system. In the transformations, the Lagrangian material coordinate system, connected with the natural configuration of the body, is used. It is assumed that the initial stress state of a thermoelastic semibounded body is both due to the action of mechanical forces and the effect of temperature (preheating). In the linearized Piola and Kirchhoff stress tensors involved in the equations of motion and boundary conditions, all terms that contain higher degrees of initial deformation and squares of temperature are retained. The expressions that determine the linearized constitutive law of a prestressed medium, as well as the linearized equations describing the motion of a thermoelastic medium with large initial deformations, are presented in the tensor form with the subsequent transition to the component representation of all relations in a cylindrical orthogonal coordinate system. For the specific form of the thermoelastic potential and for homogeneous initial deformation, the final expressions that determine the linearized constitutive law of the prestressed medium are given, as well as the linearized equations describing the motion of the thermoel...

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“…The effect of centrifugal load also was studied on the electro-magneto-elastic responses of the problem. Two dimensional theory of elasticity has been employed in order to investigate the thermo-elastic behavior of a FG cylinder under thermal and mechanical loads by Jabbari et al (2009). Sarfaraz Khabbaz et al (2009) investigated the nonlinear analysis of FG plates under pressure based on the higher-order shear deformation theory.…”

Section: Introductionmentioning

confidence: 99%

A complete set of equations for piezo-magnetoelastic analysis of a functionally graded thick shell of revolution

Arefi

2014

Lat. Am. j. solids struct.

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Tensor analysis and an orthogonal curvilinear coordinate system have been used to derive a complete set of equations for piezomagneto-elastic analysis of a functionally graded (FG) thick shell of revolution with variable thickness and curvature. The mentioned structure can be subjected to mechanical, electrical and magnetic fields. It was assumed that all material properties (mechanical, electrical and magnetic properties) change functionally throughout the three axis of employed coordinate system. Kinetic and potential energies of the system have been evaluated in order to constitute the functional of the system. Final partial differential equations of the system can be derived by using minimization of the energy functional with respect to five employed functions of the system. For validation, the obtained differential equations have been reduced to two previously studied problems i.e. functionally graded piezoelectric materials and functionally graded piezomagnetic cylinders. Furthermore, numerical results are evaluated for a case study.

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Axisymmetric mechanical and thermal stresses in thick short length FGM cylinders

Cited by 102 publications

References 18 publications

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

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

Equations of Dynamics for Prestressed Thermoelastic Cylinder

A complete set of equations for piezo-magnetoelastic analysis of a functionally graded thick shell of revolution

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