M. R. Eslami

• Professor
• Professor at Amirkabir University of Technology

In this research, the thermally induced vibration of the plates on the elastic foundation has been investigated. The plate is made of functionally graded materials (FGMs) that is graded along the thickness. All mechanical and thermal properties dependent on temperature are taken into account. To apply the temperature dependence of thermomechanical...

The current research deals with the rapid surface heating of cylindrical panels made of functionally graded materials (FGMs). The investigation encompasses the temperature-dependent nature of all thermo-mechanical properties within the FG media. Applying the uncoupled linear thermoelasticity theory establishes a one-dimensional transient heat condu...

This paper addresses the investigation of axisymmetric thermally induced vibrations in Functionally Graded Material (FGM) cylindrical shells. It considers temperature-dependent (TD) properties and geometric non-linearity (the von Karman effect). The study systematically solves a transient heat conduction equation using finite differences method and...

The current work investigates the geometrically nonlinear dynamic response of a functionally graded material conical–cylindrical–conical joint shell construction exposed to rapid surface heating. Considering the dependence on position and temperature, the material properties are determined using the Voigt and Touloukian models.To determine the ther...

The present study examines the geometrically non-linear dynamic response of hermetic capsule construction made of functionally graded materials subjected to thermal shock. The Voigt and Toloukian models are used to derive the material properties, where dependence of the properties to position and temperature is included. The one-dimensional transie...

Geometrically non-linear thermally induced vibrations of functionally graded material (FGM) joined spherical-conical shells are analyzed in the current research. Thermo-mechanical properties of the shells are assumed to be temperature and position dependent. The system of joined spherical-conical shells is subjected to thermal shock on the ceramic-...

Geometrically nonlinear thermally induced vibrations of functionally graded material (FGM) joined conical–conical shells is analyzed in the current research. Thermo-mechanical properties of the shell are assumed to be temperature and position dependent. The system of joined conical–conical shells is subjected to thermal shock on the ceramic-rich su...

This paper concentrates on axisymmetric free vibration of functionally graded (FG) sandwich annular plates obtained using a quasi-3D plate theory. Motion equations and corresponding boundary conditions are established via the mentioned plate theory which takes into consideration the non-uniform shear strains across the thickness and also stretching...

The present study deals with the phenomenon of thermally induced vibrations in a conical panel. The considered conical panel is made of functionally graded materials. All thermal and mechanical properties of the panel are distributed through the thickness direction. The properties of two constituents are considered to be temperature-dependent. A vo...

In this article, nonlinear analysis of pin-ended isotropic homogeneous deep arches under rapid heating is considered. Arch is subjected to thermal shock on one surface while the other surface is kept at the reference temperature. One-dimensional heat conduction equation across the thickness of the arch was solved analytically to obtain the temperat...

In this paper, dynamic buckling response of a shallow arch constructed from functionally graded materials under thermal shock is investigated. It is assumed that one surface of the beam is subjected to sudden temperature elevation while the other surface is kept at reference temperature. To solve the one-dimensional Fourier heat transfer equation,...

Geometrically nonlinear thermally induced vibrations of functionally graded material beams resting on a two-parameter elastic foundation is analyzed in the current research. Thermo-mechanical properties of the beam are assumed to be temperature and position dependent. The foundation medium is assumed to be linear, homogeneous, and isotropic. It is...

In this article, thermally induced vibrations of shallow functionally graded material arches is considered and analyzed. The arch is subjected to sudden thermal loading on one surface while the other surface is kept at a constant temperature. Based on the uncoupled thermoelasticity assumptions, the one-dimensional heat conduction equation is establ...

The purpose of this paper is to investigate the effect of stress classification on cyclic viscoplastic response of a structure (here, a thick spherical vessel which has an application in pressure vessel technology). The response is either reverse plasticity and shakedown or ratcheting behavior of a structure. The viscoplastic behavior of thick sphe...

In the current research, application of generalized differential quadrature element (GDQE) method is presented to analyze the free vibration of L-shaped plates. It is considered that the laminated composite plate is reinforced by graphene platelets (GPLs). Furthermore, the GPLs are randomly oriented and uniformly dispersed in each lamina. The GPL w...

Free vibration response of a cylindrical shell closed with two hemispherical caps at the ends (hermit capsule) is analysed in this research. It is assumed that the system of joined shell is made from functionally graded materials (FGM). Properties of the shells are assumed to be graded through the thickness. Cylindrical and hemispherical shells are...

The current article deals with the nonlinear free vibration of nanocomposite circular plates reinforced with graphene platelets (GPL). The functionally graded (FG) plate is considered over a three parameter non-linear elastic foundation. In this research, three types of gradings are assumed for reinforcing the plate by GPLs. The Halpin-Tsai microme...

In this paper, thermally induced vibration of annular sector plate made of functionally graded materials is analyzed. All of the thermomechanical properties of the FGM media are considered to be temperature dependent. Based on the uncoupled linear thermoelasticity theory, the one-dimensional transient Fourier type of heat conduction equation is est...

By proposing the unifier factors, a unified formulation for the generalized coupled thermo-visco-elasticity response of hollow spheres based on the Lord–Shulman, Green–Lindsay, and Green–Naghdi models is developed. Kelvin–Voigt model is used in the current research to consider the viscoelastic response of the sphere. This formulation is used to cap...

Natural frequencies of a conical–spherical functionally graded material (FGM) shell are obtained in this study. It is assumed that the conical and spherical shell components have identical thickness. The system of joined shell is made from FGMs, where properties of the shell are graded through the thickness direction. The first order shear deformat...

An imperfection sensitivity analysis for the nonlinear post-buckling behavior of functionally graded (FG) porous micro-tubes is performed in this research. The case of geometrically imperfect micro-tubes surrounded by a nonlinear elastic medium under axial compressive load is analyzed. Properties of the micro-tube with uniform distributed porosity...

Free vibration response of a joined shell system including cylindrical and spherical shells is analyzed in this research. It is assumed that the system of joined shell is made from a functionally graded material (FGM). Properties of the shells are assumed to be graded through the thickness. Both shells are unified in thickness. To capture the effec...

This study deals with the nonlinear bending analysis of elastic tubes made of functionally graded (FG) porous material based on modified couple stress theory. Immovable simply supported and clamped boundary conditions are assumed for the FG porous microtubes resting on nonlinear elastic foundation. Transverse pressure load is applied uniformly on t...

In the current investigation, large amplitude free vibration behavior of shallow curved pipes (tubes) made of functionally graded materials is investigated. Properties of the tube are distributed across the radius of the tube and are obtained by means of a power law function. It is also assumed that all thermo-mechanical properties are temperature...

Considering the modified couple stress theory, nonlinear vibration and snap-buckling analyses of porous FG curved micro-tubes are performed in this research. Curved micro-tubes with shallow curvature resting on nonlinear elastic foundation are analysed. Properties of the micro-tube with uniform distributed porosity are graded across the radius of c...

Based on the modified couple stress theory, an analytical approach is presented to study vibrations of thermally pre/post-buckled functionally graded (FG) tubes. The case of simply supported FG micro-tubes with uniform distributed porosity surrounded by nonlinear elastic medium in uniform temperature field is analyzed. Thermomechanical properties a...

An analysis on thermal buckling of composite laminated annular sector plates reinforced with the graphene platelets is examined in this research. It is assumed that the graphene platelets fillers are randomly oriented and uniformly distributed in each ply of the composite media. Effective elasticity modulus of the nanocomposite media is extracted u...

Analysis of nonlinear response of thick FGM beams subjected to either thermal or mechanical load is performed. Beam is in contact with a three-parameter elastic foundation. Nonlinear component of the foundation may be of the hardening or softening type. Equilibrium equations of the clamped beam are obtained within the framework of von Karman assump...

Present study deals with the dynamic snap-through phenomenon of an isotropic shallow spherical cap under transient type of thermal loading. The inner surface of the shell is subjected to sudden temperature elevation, whereas the outer surface is kept at reference temperature. Transient thermal shock is applied uniformly and shell thickness is assum...

An attempt is made in the current research to obtain the fundamental buckling torque and the associated buckled shape of an annular plate. The plate is subjected to a torque on its outer edge. An isotropic homogeneous plate is considered. The governing equations of the plate in polar coordinates are established with the aid of the Mindlin plate the...

Current investigation deals with the small and large amplitude free vibrations of a curved beam (arch) resting on a nonlinear elastic foundation. The arch is made of a functionally graded material, where the properties are graded across the thickness. Uniform temperature elevation in the arch is also considered and material properties are assumed t...

In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate subjected to uniform compression on both inner and outer edges is analysed. It is further assumed that the plate is rotatingwith a constant angular speed. Formulation is based on the first order shear deformation plate theory, which is valid for thin and...

In this paper, the generalized thermoelastic response of a beam subjected to a partial lateral thermal shock is analysed. The beam is made of homogeneous and isotropic material and is assumed to follow the Hooke law for its constitutive material. The displacement gradient is small and the linear form of strain-displacement relations is used for the...

Considering the third-order shear deformation and physical neutral plane theories, thermal postbuckling analysis for functionally graded (FG) porous beam are performed in this research. The cases of shear deformable functionally graded materials (FGM) beams with initial deflection and uniformly distributed porosity are considered. Geometrically imp...

Considering the uncoupled thermoelasticity assumptions, a thermally induced vibration analysis for functionally graded material (FGM) conical shells is performed in this research. Thermo-mechanical properties of the conical shell are assumed to be temperature and position dependent. The conical shell is under rapid heating with various cases of the...

In the current investigation, the small and large amplitude free vibration characteristics of long cylindrical panels made of FGMs is investigated using the higher order shear deformation shell theory and Donnell kinematic assumptions. The interaction of the panel with a nonlinear hardening/softening foundation in also included into the formulation...

In the present research, thermally induced vibration of shallow spherical shells made of functionally graded materials is investigated. The thermomechanical properties of the FGM media are assumed to be temperature dependent. Based on the uncoupled thermoelasticity theory, the one-dimensional heat conduction equation is established. The top and bot...

Based on the modified couple stress theory, nonlinear thermally induced large deflection analysis of shallow sandwich arches is studied. A functionally graded material (FGM) micro-arch with piezoelectric layers integrated into the surfaces and with immovable pinned and fixed edges is analyzed. Temperature and position dependence of the thermomechan...

An attempt is made in this research to analyse the nonlinear response of functionally graded material shallow arches with both edges clamped. The arch is resting on a three parameter nonlinear elastic foundation during deformation and is subjected to uniform lateral pressure and uniform temperature rise. Material properties are expressed according...

Based on the modified couple stress theory, an attempt is made in this study to analyze the nonlinear snap-through instability of shallow sandwich arches. The microstructure-dependent functionally graded material (FGM) arch with surface bonded piezoelectric actuator layers is analyzed. The piezo-FGM sandwich arch is subjected to uniform transverse...

In this article, the current status of research in Iran has been evaluated with a focus on the field of engineering and especially mechanical engineering. To achieve this goal, the quantity and quality of research have been studied and compared with developed and developing countries. The number of scientific publications has been used as the main...

Based on the nonlinear dynamic analysis, thermally induced vibrations of the FGM shallow arches subjected to different sudden thermal loads are studied. Temperature and position dependence of the material properties are taken into account. Based on the uncoupled thermoelasticity assumptions, The non-linear one-dimensional transient heat conduction...

Not all types of temperature changes in a solid continuum result in creation of thermal stresses. The chapter begins with the discussion of the condition on what type of temperature distribution causes thermal stresses. The analogy of temperature gradient with body forces is stated. Then the theoretical analysis of thermal stress problems is presen...

The basic laws of thermoelasticity, similar to those of the theory of elasticity, include the equations of motion, the compatibility equations, and the constitutive law. This chapter begins with the derivation of the basic laws of linear thermoelasticity, where the linear strain–displacement relations are obtained, following the general discussion...

Because the analytical solutions to coupled and generalized thermoelasticity problems are mathematically complicated, the numerical methods, such as the finite and the boundary element methods, have become powerful means of analysis. This chapter presents a new treatment of the finite and the boundary element methods for this class of problems. The...

As an application of the theory of thermoelasticity, thermal stress analysis of beams based on the elementary beam theory is the objective of this chapter. It begins with the derivation of formulas for axial thermal stresses and thermal lateral deflections in beams, and the associated boundary conditions are stated, see [1, 2]. The discussion on tr...

Under the combination of elevated temperature and mechanical loads, structural members tend to creep. Basic laws of creep are presented, and the effect of temperature changes in the constitutive law of creep is discussed. The rheological models of two important engineering concepts of stress, namely the load- and the deformation-controlled stresses...

A structure under thermal shock load, when the period of shock is of the same order of magnitude as the lowest natural frequency of the structure, should be analyzed through the coupled form of the energy and thermoelasticity equations. Analytical solutions of this class of problems are mathematically complex and are limited to those of an infinite...

A new presentation of the thermodynamic principles for solid elastic continuum is given. The first and the second laws of thermodynamics in variational form are stated, and the variational principle of thermodynamics in terms of entropy follows. The principle of thermoelasticity linearization is discussed and the classical, coupled, as well as the...

The ability of obtaining the temperature distribution in an elastic continuum through the solutions of the heat conduction equation is an essential tool for the analysis of thermal stress problems. The analytical methods of solution of heat conduction problems may be classified as the differential, the lumped, and the integral formulations. This ch...

Piping systems, such as those installed in refineries, are transmitters of high-pressure fluids or gases at high temperatures, and failure of such systems may cause catastrophic damage. Advanced design codes have been developed to provide safety instructions for designers. Piping systems are initially installed at reference temperature. At working...

Thick cylinders, spheres, and disks are components of many structural systems. Due to their capacity to withstand high pressures, radial loads, and radial temperature gradients, the problem of thermal stress calculations is an important design issue. This chapter presents the method to calculate thermal stresses in such structural members which are...

This chapter presents thermally induced vibrations of isotropic and homogeneous beams and shallow arches and functionally graded beams. The vibration occurs when the heat conduction equation is of parabolic type and the first-order time derivative of temperature function is involved in the heat conduction equation. This equation may be solved with...

Present research deals with the large amplitude thermally induced vibrations of an annular plate made of functionally graded materials (FGMs). One surface of the plate is subjected to rapid surface heating while the other surface is either thermally insulated or kept at reference temperature. The material properties of the constituents are assumed...

Natural frequencies of circular deep arches made of functionally graded materials (FGMs) with general boundary conditions are obtained in this research based on the unconstrained higher-order shear deformation theory taking into account the depth change, complete effects of shear deformation, and rotary inertia. The material properties are assumed...

Present research deals with the thermal buckling and post-buckling analysis of the geometrically imperfect functionally graded tubes on nonlinear elastic foundation. Imperfect FGM tube with immovable clamped–clamped end conditions is subjected to thermal environments. Tube under different types of thermal loads, such as heat conduction, linear temp...

In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate subjected to uniform compression on both inner and outer edges is analysed. It is further assumed that the plate is rotating with a constant angular speed. Formulation is based on the first order shear deformation plate theory, which is valid for thin and...

The analysis of large amplitude thermally induced vibrations of a shallow curved beam is considered in this article. The beam is made from an isotropic homogeneous material. One surface of the arch is subjected to rapid surface heating while the other surface is kept at reference temperature. The temperature profile is evaluated by means of the 1D...

Present research aims to analyze the nonlinear bending response of the functionally graded material curved tube subjected to the uniform lateral pressure. The effect of thermal environment is also included. Properties of the arch are distributed through the radial direction using a power law function. Thermomechanical properties of the media are as...

In the present investigation, geometrically nonlinear response of a shallow curved tube subjected to thermal loading is analyzed. The tube is made of a functionally graded material (FGM), where properties are distributed across the tube radius. Thermomechancal properties of the constituents are assumed to be temperature dependent. The simple case o...

The present research considers the free vibration characteristics of a joined shell system that consists of three segments. The joined shell system contains two conical shells at the ends and a cylindrical shell at the middle. All shell elements are made from isotropic homogeneous material. The shell elements are unified in thickness. With the aid...

The present investigation deals with the large amplitude response of shallow thick circular arches subjected to thermal, mechanical, or thermomechanical loads. The structure is resting on a three-parameter elastic foundation containing the Winkler springs, the shear Pasternak layer, and hardening nonlinear springs. The arch is made of a through-the...

In this paper, the generalized thermo-elastic response of a beam subjected to a uniform lateral thermal shock is analyzed. The beam is made of homogeneous and isotropic materials and is assumed to follow the Hook's law for its constitutive behavior. The displacement field of the beam is approximated according to the first-order shear deformation th...

In the present research, dynamic buckling of a shallow arch subjected to transient type of thermal loading is investigated following the Budiansky–Hutchinson criterion. Arch is subjected to thermal shock on one surface while the other surface is kept at reference temperature. Transient heat conduction equation across the arch thickness is establish...

Present research deals with the geometrically nonlinear bending of a long cylindrical panel made of a through-the-thickness functionally graded material subjected to thermal load. A panel under the action of uniform temperature rise loading is considered. Formulation of the shell is based on the third-order shear deformation shell theory, where the...

The present paper is aimed to make a detail analysis on the correct simulation of the associated natural thermal boundary conditions and their interesting effects on the thermally nonlinear generalized thermoelastic response of a continuum medium. The paper presents some explanations regarding the literally conventional thermal boundary conditions...

Spherical shells, as part of structural systems, are frequently used in many structural design problems. This type of shells is capable to stand high internal or external pressures and is especially quite stable under external pressures. The behavior of deep spherical shells, in particular, under external pressure is quite unique and the bifurcatio...

The chapter presents basic concepts of the structural stability under the external applied loads. The applied loads may be in form of the mechanical or thermal loads, where the latter create thermal stresses due to the temperature gradient in the structure. When the applied loads result into the compressive stresses, the structural member may fail...

The stability of rectangular plates with induced in-plane compressive stresses resulting from the mechanical or thermal loads is discussed in this chapter. The kinematical relations, constitutive law, the equilibrium equations, and the stability equations for a rectangular plate are derived and the classical boundary conditions are presented. The c...

Conical shells under the mechanical and thermal loads are considered in this chapter. The basic governing equations of the shell including the nonlinear strain-displacement relations of Sanders assumption, the constitutive law, the nonlinear equilibrium equations, and the linear stability equations are derived employing the variational principle. T...

The stability of circular and annular plates under mechanical and thermal loads are presented in this chapter. The chapter begins with the presentation of the strain-displacement relations based on the von Karman and Kirchhoff assumptions employing the classical plate theory. The linear thermoelastic constitutive relations between the stress and st...

This chapter presents buckling and post-buckling analysis of straight beams under thermal and mechanical loads. The Euler and Timoshenko beam theories are considered and buckling and postbuckling behaviors are discussed. The buckling analysis of beams with piezoelectric layers is presented and the effect of piezo-control on the beam stability is an...

The buckling and post-buckling of curved beams under mechanical distributed and concentrated loads and thermal loads with different types of boundary conditions are discussed in detail in this chapter. The existence of bifurcation points are examined for each type of loading. For those cases that bifurcation do not occur, the limit load is discusse...

This chapter is devoted to the stability behavior of thin cylindrical shells. The basic governing equations of thin circular cylindrical shells employing the Donnell theory with the von-Karman geometrical non-linearity are derived. The nonlinear strain-displacement relations, the nonlinear equilibrium equations, and the linear stability equations a...

This book contains eight chapters treating the stability of all major areas of the flexural theory. It covers the stability of structures under mechanical and thermal loads and all areas of structural, loading and material types. The structural element may be assumed to be made of a homogeneous/isotropic material, or of a functionally graded materi...

In this investigation, the asymmetrical buckling behaviour of FGM annular plates resting on partial Winkler-type elastic foundation under uniform temperature elevation is investigated. Material properties of the plate are assumed to be temperature dependent. Each property of the plate is graded across the thickness direction using a power law funct...

Free vibration behaviour of a shear deformable conical shell with intermediate ring support is analysed in this research. It is assumed that the conical shell is made from a linearly elastic isotropic homogeneous material. To capture the through-the-thickness shear deformations and rotary inertia effects, first order shear deformation theory of she...

This article addresses a clarification study on the thermally nonlinear Fourier/ non-Fourier dynamic coupled (generalized) thermoelasticity. Based on the Maxwell-Cattaneo’s heat conduction law and the infinitesimal theory of thermoelasticity, governing equations for the thermally nonlinear small deformation type of generalized thermoelasticity are...

The present research deals with the nonaxisymmetric buckling behaviour of isotropic homogeneous annular plates subjected to simultaneous effects of uniform temperature rise and constant angular speed. First-order shear deformation plate theory is used to obtain the complete set of governing equations and the associated boundary conditions. Pre-buck...

Thermoelastic analysis of an isotropic homogeneous layer within the framework of Lord-Shulman theory of generalized thermoelasticty is performed in this research. Two coupled partial differential equations, namely; the energy and equation of motion are established. The energy equation is kept in its original nonlinear form and the assumption made i...

This study deals with the response of an FGM annular plate under lateral thermal shock load. The equations of motion are obtained using the first order shear deformation plate theory. The governing equations are solved using the Laplace transformation and Galerkin finite element method. Finally, numerical inversion of the Laplace transform is carri...

This study evaluates the plastic responses of thick cylinders made of transversely isotropic materials under mechanical cyclic loads, using the kinematic hardening theory of plasticity. The Hill yield criterion is adapted to the kinematic hardening theory of plasticity. The constitutive equations of plastic strains are obtained using the adapted yi...

In this investigation, the asymmetrical buckling behavior of isotropic homogeneous annular plates resting on a partial Winkler-type elastic foundation under uniform temperature elevation is investigated. First-order shear deformation plate theory is used to obtain the governing equations and the associated boundary conditions. Prebuckling deformati...

Generalized thermoelasticity response of an annular disk subjected to thermal shock on its inner surface is analyzed in this research. The Lord–Shulman theory, which accounts for one relaxation time in the conventional Fourier law, is used to avoid for the infinite speed of thermal wave propagation. Unlike the other available works in which the fir...

The present research deals with the thermoelastic response of a thick sphere based on the Lord-Shulman theory of generalized thermoelasticity. Unlike the other available works in which energy equation is linearised, the assumption of ignorance of temperature change in comparison to the reference temperature is not established in this research resul...

Thermally induced vibrations of functionally graded material rectangular plates are investigated in this research. The thermomechanical properties of the plate are assumed to be temperature and position dependent. Dependency on temperature is expressed based on theTouloukian formula, and position dependency is written as a power-law function. The c...

This study presents the buckling analysis of radially loaded solid circular plate made of porous material. Properties of the porous plate, where pores are assumed to be saturated with fluid, vary across its thickness. The boundary condition of the plate is assumed to be clamped and the plate is assumed to be geometrically perfect. The higher order...

The unsymmetrical buckling of clamped shallow spherical shells made of functionally graded material (FGM) and surface-bonded piezoelectric actuators under thermal load is studied in this paper. The governing equations are based on classical shell theory and the Sanders nonlinear kinematic equations. It is assumed that properties of the functionally...

Mechanical and Thermal Stresses In FGPPM Hollow Cylinder Due to Radially Symmetric Loads

In this paper, non-linear stability behavior of functionally graded (FG) circular shallow arches subjected to a uniform radial pressure is investigated by an analytical method. For this purpose, the classical single layer assumption is used to approximate the displacement field through the arch. Donnell׳s non-linear model for shallow shells is empl...