Showing papers in "Mechanics of Advanced Materials and Structures in 2008"
TL;DR: In this article, the authors deal with classical and mixed variational statements for the analysis of layered structures under the effect of four different fields: mechanical, thermal, electrical, and magnetic.
Abstract: This work deals with classical and mixed variational statements for the analysis of layered structures under the effect of four different fields: mechanical, thermal, electrical and magnetic. Constitutive equations, in terms of coupled mechanical-thermal-electrical-magnetic filed variables, are obtained on the basis of a thermodynamics approach. The Principle of Virtual Displacements (PVD) and the Reissner's Mixed Variational Theorem (RMVT) are employed. The latter permits interlaminar variables, such as transverse stresses, transverse electrical displacements, etc. to be assumed “a priori.” A number of particular cases of the considered variational statements are proposed. A new condensed notation is introduced into the Unified Formulation (UF) framework, which leads to governing equations and finite element matrices in terms of a few fundamental nuclei. The Finite Element (FE) case for multilayerd plates has been addressed. Variable kinematics, as well as layer-wise and equivalent single layer descripti...
76 citations
TL;DR: In this paper, the microstructural evolution of closed-cell polymethacrylimide foam was simulated in compression undergoing elastic, compaction, and densification stages.
Abstract: Closed-cell foams in compression exhibit complex deformation characteristics that remain incompletely understood. In this paper the microstructural evolution of closed-cell polymethacrylimide foam was simulated in compression undergoing elastic, compaction, and densification stages. The three-dimensional microstructure of the foam is determined using Micro-Computed Tomography (μ-CT), and is converted to material points for simulations using the material point method (MPM). The properties of the cell-walls are determined from nanoindentation on the wall of the foam. MPM simulations captured the three stages of deformations in foam compression. Features of the microstructures from simulations are compared qualitatively with the in-situ observations of the foam under compression using μ-CT. The stress-strain curve simulated from MPM compares reasonably with the experimental results. Based on the results from μ-CT and MPM simulations, it was found that elastic buckling of cell-walls occurs even in the elastic...
58 citations
TL;DR: In this article, a three-dimensional analysis of a functionally graded plate is presented, where the plate is subjected to normal and shear tractions of arbitrary form on the lower and upper surfaces while edge boundary conditions are given as simply supported.
Abstract: Three-dimensional analysis of a functionally graded plate is presented in this paper. The plate is subjected to normal and shear tractions of arbitrary form on the lower and upper surfaces while edge boundary conditions are given as simply supported. The problem is formulated on the assumption that the elastic modulus depends on the z-coordinate along the thickness direction. Plevako's solution of the general three-dimensional governing equations is used and the corresponding physical quantities are expanded into Fourier series. Closed-form solutions are obtained for some specific variations of material modulus. The influence of different functionally graded models and plate configurations on the stress and displacement fields is studied through numerical examples.
48 citations
TL;DR: In this article, a mixed finite element model for the nonlinear bending analysis of laminated composite plates is presented, which is obtained using a mixed variational formulation of the first-order shear deformation theory of plates in which displacements and bending moments are treated as independent fields.
Abstract: A mixed finite element model for the nonlinear bending analysis of laminated composite plates is presented. The finite element model is obtained using a mixed variational formulation of the first-order shear deformation theory of plates in which displacements and bending moments are treated as independent fields. A p-type Lagrangian basis is used to approximate the nodal degrees of freedom that consist of three displacements, two rotations, and three moment resultants. The geometric nonlinearity in the sense of the von Karman is included in the plate theory. The mixed plate element developed herein is employed in the linear and nonlinear bending analysis of a variety of layered composite rectangular plates. The effects of transverse shear deformation, material anisotropy, and bending-stretching coupling on deflections and stresses are investigated. The predictive capability of the present model is demonstrated by comparison with analytical, experimental, and numerical solutions available in the literature...
46 citations
TL;DR: In this article, a modified model combining EMI technique and reverberation matrix method (RMM) is proposed to quantitatively correlate crack parameters in continuous beams with high-frequency signatures for structural health monitoring.
Abstract: Electro-mechanical impedance (EMI) is very effective for detecting the local incipient damages including small cracks in structures and has been validated by many experimental investigations. Meanwhile, some analytical models have been proposed to deal with dynamics of structures for health monitoring. However, there is little analytical work done to relate EMI signatures with crack parameters at ultrasonic frequencies. In this paper, a modified model combining EMI technique and reverberation matrix method (RMM) is proposed to quantitatively correlate crack parameters in continuous beams with high-frequency signatures for structural health monitoring. The model is based on Timoshenko beam theory with the crack treated as a massless rotational spring. The bonded PZT wafers are restricted to one-dimensional axial vibration. A shear lag model is adopted to simulate the interfacial bonding between PZT patches and the host beam. For the first time, an analytical expression of impedance (or admittance) involvin...
34 citations
TL;DR: In this article, a universally applicable hybrid approach utilizing finite fracture mechanics is employed to model crack initiation at stress concentrations, which overcomes deficiencies of classical criteria and is implemented in a versatile finite element procedure.
Abstract: As potential locations for failure initiation, stress concentrations require sophisticated analysis models. In composites, not only geometrical discontinuities may cause high local stresses, but also material discontinuities or even a combination of both. A universally applicable hybrid approach utilizing finite fracture mechanics is employed in this study to model crack initiation at stress concentrations. It overcomes deficiencies of classical criteria. The model is implemented in a versatile finite element procedure. Examples demonstrate the capability of the model to cover relevant effects for simple configurations as well as for glass-ceramic sealing joints in solid oxide fuel cells subject to thermomechanical loading.
34 citations
TL;DR: At the macroscale, wood materials show great variability and diversity as mentioned in this paper. At the nanoscale, however, they exhibit common (universal) building blocks which build up universal organizational patterns.
Abstract: At the macroscale, wood materials show great variability and diversity. At the nanoscale, however, they exhibit common (universal) building blocks which build up universal organizational patterns o...
31 citations
Metz1
TL;DR: In this paper, an accurate shell finite element (FE) formulation is presented to model composite shell structures with embedded viscoelastic and piezoelectric layers and an integrated active damping control mechanism.
Abstract: This paper presents an accurate shell finite element (FE) formulation to model composite shell structures with embedded viscoelastic and piezoelectric layers and an integrated active damping control mechanism. The five-layered finite element introduced in this paper uses the first order shear deformation theory in the viscoelastic core and Kirchoff theory for the elastic and piezoelectric layers. The corresponding coupled FE formulation is derived starting from the shell kinematic and electromechanical governing equations. Assuming a linear strain field through each layer and exactly the same transverse displacement and the rotations in the elastic and piezoelectric layers, the number of degree of freedoms (dof) per node is reduced to 8. All the eight of these dofs are mechanical in nature. Constant velocity and constant displacement feedback control algorithms are used to actively control the dynamic response of the adaptive structure. Based on this formulation, a finite element code is implemented and t...
28 citations
TL;DR: In this paper, a micromechanics model is developed for hexagonal honeycomb structures by using a modified couple stress theory, which is based on structural analysis of repeating units and a homogenization procedure.
Abstract: A micromechanics model is developed for hexagonal honeycomb structures by using a modified couple stress theory. The formulation is based on structural analysis of repeating units and a homogenization procedure. Both bending and axial deformations of cell walls are considered here, unlike earlier models. The closed-form expressions for five effective in-plane elastic constants (including two Young's moduli, one shear modulus and two Poisson's ratios) of a honeycomb structure are derived in terms of the Young's modulus of the cell wall material and the slenderness (length-to-thickness) ratio of the cell wall. The formulas for two length scale parameters are obtained in terms of the slenderness ratio and thickness of the cell wall, thereby providing a direct measure of the microstructure of the honeycomb. The constitutive relations for the two-dimensional couple stress continuum equivalently representing the discrete honeycomb structure are provided using the five effective elastic constants and two length ...
26 citations
TL;DR: In this paper, a meshless local Petrov-Galerkin (MLPG) formulation is applied to solve the 2D problem of shear deformable shallow shells with orthotropic material properties and continuously varying material properties through the shell thickness.
Abstract: The first-order shear deformation theory is used for description of shear deformable shallow shells with orthotropic material properties and continuously varying material properties through the shell thickness. Static and dynamic loads are considered here. For transient elastodynamic cases the Laplace-transform is used to eliminate the time dependence of the field variables. The first-order shear deformation theory reduces the original three-dimensional (3-D) problem into a two-dimensional (2-D) one. A meshless local Petrov-Galerkin (MLPG) formulation is applied to solve the 2-D problem. A weak formulation with a unit test function transforms the set of governing equations into local integral equations on local subdomains in the basic plane of the shell. Nodal points are randomly spread in that domain and each node is surrounded by a circular subdomain to which local integral equations are applied. The meshless approximation based on the Moving Least-Squares (MLS) method is employed for the implementation...
24 citations
TL;DR: In this article, a variational principle for the motion and deformation of a regular region of hygrothermopiezoelectric materials in the elastic range was derived under a quasi-static approximation of the electric field.
Abstract: In this study Hamilton's principle is stated for the motion and deformation of a regular region of hygrothermopiezoelectric materials in the elastic range, and a four-field variational principle is obtained under the quasi-static approximation of the electric field. The variational principle is modified through an involuntary transformation and a generalized variational principle is derived in analogy to the Hu-Washizu variational principle of elasticity. Likewise, a variational principle is formulated for the region with a fixed internal surface of discontinuity, and another one for the region containing any number of perfectly bonded dissimilar materials. The variational principles are shown to generate, as its Euler-Lagrange equations, all the divergence and gradient equations, the constitutive relations and the natural mixed boundary and continuity (jump) conditions for each region of the dissimilar materials. The admissible states of the variational principles have Cauchy's second law of motion and t...
TL;DR: In this article, the adhesive bonding of elastic bodies when the adhesive is a phase-transforming material was modeled using the Fremond model, including only two variants of martensite.
Abstract: It is proposed to model the adhesive bonding of elastic bodies when the adhesive is a phase-transforming material. For this purpose, the (isothermal) Fremond model is adopted, including only two variants of martensite. In the first part of this paper, asymptotic expansions are used to study the asymptotic behavior of the adhesive as its thickness and elastic coefficients tend toward zero. In the second part, the energy minimization approach is used and the equilibrium of a one-dimensional bar is studied in detail. The simplified one-dimensional context adopted here makes it possible to compute contact laws taking nucleation and the kinetics of the phase transformation explicitly into account.
TL;DR: In this paper, the authors presented the geometrically exact assumed stress-strain four-node piezoelectric solid-shell element with six displacement degrees of freedom per node on the basis of the first-order equivalent single-layer theory.
Abstract: This paper presents the geometrically exact assumed stress-strain four-node piezoelectric solid-shell element with six displacement degrees of freedom per node on the basis of the first-order equivalent single-layer theory. The proposed piezoelectric laminated shell formulation is based on the objective strain-displacement relationships, written in curvilinear reference surface coordinates, and generalizes the authors' purely mechanical finite element formulation. The mechanical and piezoelectric degrees of freedom are coupled via constitutive equations and the electric potential is assumed to be linear through the thickness of the piezoelectric layer. To overcome shear and membrane locking and have no spurious zero energy modes, the assumed strain and stress resultant fields are invoked. In order to circumvent thickness locking, the ad hoc modified laminate stiffness matrix, corresponding to the generalized plane stress condition, is employed. The elemental stiffness matrix has six zero eigenvalues and r...
TL;DR: In this article, a genetic algorithm is used to investigate the relationship of the viscoelastic layer thickness, the constraining layer thickness and the number of cuts initiated in the passive constrained layer damping (PCLD) treatment as they all relate to optimum damping of beams.
Abstract: The optimization of geometry and material properties of Passive Constrained Layer Damping (PCLD) treatments has been the subject of many research efforts in recent years. In this study, a genetic algorithm is used to investigate the relationship of the viscoelastic layer thickness, the constraining layer thickness, and the number of cuts initiated in the PCLD treatment as they all relate to optimum damping of beams. Genetic algorithms mimic the biological evolution process where potential solutions compete for survival based on their relative fitness. As a measure of the fitness of the PCLD treatment, a finite element model is used to compute the loss factor for the first mode of vibration with the capability of segmenting the treatment. It is found that, while the loss factor increases asymptotically with the increase in the viscoelastic layer thickness, an optimum constraining layer thickness for each viscoelastic layer thickness exists. The number of cuts in the segmented treatment tends to decrease wi...
TL;DR: In this paper, the degradation of surface layers of continuous caster rolls under service conditions is studied and it is found that the damage of the surface layers, estimated by means of a homogeneity coefficient, is 60-72% greater than the damage at the depth h = 9-32 mm.
Abstract: Degradation of surface layers of continuous caster rolls under service conditions is studied. The roll material is steel 25 Kh1M1F. A statistical analysis of size, orientation and distribution of surface cracks is carried out. Microhardness measurements are performed and structural degradation of the material surface layers is evaluated as a function of the distance to the roll surface. It is found that the damage of the surface layers, estimated by means of a homogeneity coefficient, is 60–72% greater than the damage at the depth h = 9–32 mm. The evolution of the roll material microstructure under tensile deformation is studied as well.
TL;DR: In this article, a contact analysis between a deformable sphere and a rigid flat by finite element method was carried out beyond elastic limit, until the inception of plasticity for various materials with different radii.
Abstract: This paper presents a contact analysis between a deformable sphere and a rigid flat by finite element method. Analysis is carried out beyond elastic limit, until the inception of plasticity for various materials with different radii. Results are compared with previous elastic-plastic models. It is found those materials with Young's modulus to yield stress (E/Y) ratio less than 300 show strikingly different contact phenomena. Equations for hardness and interference in terms of E/Y ratio for these materials are presented. Also it is noted that materials with E/Y ratio more than 300 and less than 1000 exhibit similar elastic plastic contact phenomena. New nondimensional relationships for contact load, area and contact stress for a wide range of interferences are also presented.
TL;DR: In this article, an optimal design methodology based on planning experiments and response surface technique has been developed for an active twist of helicopter rotor blades consisting of C-spar made of unidirectional GFRP, skin made of +45°/−45° GfrP, foam core, MFC actuators embedded into the skin and balance weight.
Abstract: The active twist control of helicopter rotor blades by an application of macro-fiber composite (MFC) actuators leads to significant vibration and noise reduction without the need for complex mechanisms in the rotating systems For environmental improvement an optimal design methodology based on planning experiments and response surface technique has been developed for an active twist of helicopter rotor blades consisting of C-spar made of unidirectional GFRP, skin made of +45°/−45° GFRP, foam core, MFC actuators embedded into the skin and balance weight The structural static analysis with thermal load, static torsion analysis and modal analysis using 3D finite element models has been developed using ANSYS for the optimal design In this case thermal strain analogy between piezoelectric strains and thermally induced strains is used to model piezoelectric effects The optimization results have been obtained for four design solutions connected with the application of active materials
TL;DR: In this article, an analytical closed-form solution is developed based on the asymptotic method, using the assumptions laid out by earlier researchers (e.g.,... ).
Abstract: Adhesively bonding is one of the most commonly and widely used joining methods in various engineering applications. Many fiber-reinforced plastic (FRP) structural components nowadays are joined by adhesives. As a result many researchers have expended considerable effort in developing analytical solutions and computational procedures to assess the stress distribution in such joints. Most of the works however have considered joints that are balanced, formed with a thin layer of adhesive, mainly useful in characterizing joints in aerospace structural applications. However, in many applications, especially in marine and civil infrastructure applications, the adhesive layers are relatively thick, and the joints are usually unbalanced. Therefore seeking an accurate and robust analytical solution for characterizing such adhesively bonded joints is desirable. In this paper, an analytical closed-form solution is developed based on the asymptotic method, using the assumptions laid out by earlier researchers (e.g., ...
TL;DR: In this article, the authors present the current status of design and optimization of the Active Trailing Edge (ATE) actuator and the resulting optimal actuator design, the sensitivity of the optimal design to manufacturing and material constraints and some key performance characteristics like aeroservoelastic airfoil polars and Mach-number influence on aerodynamic effectiveness.
Abstract: A new concept is proposed for individual blade control: the Active Trailing Edge (ATE). The objective of this paper is to present the current status of design and optimization of the ATE. Due to the specific nature of the subject an inherently multi-disciplinary approach is taken. The aeroservoelastic optimization of the ATE actuator is based on evolutionary algorithm. The resulting optimal actuator design, the sensitivity of the optimal design to manufacturing and material constraints and some key performance characteristics like aeroservoelastic airfoil polars and Mach-number influence on aerodynamic effectiveness are presented. For the purpose of comprehensive rotor dynamics simulation including the dynamic and aeroservoelastic behaviour of the ATE actuator, a reduced-order model is developed. The paper concludes with a presentation of active helicopter benefit analysis.
TL;DR: In this article, the static analysis of simply supported cross-ply substrate plates integrated with a layer of piezoelectric fiber reinforced composite material undergoing nonlinear deformations is presented.
Abstract: This paper is concerned with the static analysis of simply supported cross-ply substrate plates integrated with a layer of piezoelectric fiber reinforced composite material undergoing nonlinear deformations. The von Karman type nonlinear strain displacement relations and first order shear deformation theory are used to formulate the variational model of this electromechanical coupled problem. Subsequently, Galerkin procedure is employed to derive the nonlinear algebraic governing equations which are solved by usingNewton-Raphson method. The results suggest the potential use of PFRC material for distributed control of nonlinear deformations of smart composite structures. The effect of variation of piezoelectric fiber orientation on the actuating capability of the PFRC actuator for counteracting the nonlinear deformations of the smart composite plates has also been investigated.
TL;DR: In this article, the influence of the magnetic configuration on the behavior of magneto-electro-elastic bimorph beams is analyzed by using a boundary element approach, which is formulated by using the generalized displacements and generalized tractions.
Abstract: The influence of the magnetic configuration on the behavior of magneto-electro-elastic bimorph beams is analyzed by using a boundary element approach. The problem is formulated by using the generalized displacements and generalized tractions. The boundary integral equation formulation is obtained by extending the reciprocity theorem to magneto-electro-elastic problems; it is numerically implemented by using the boundary element method multidomain technique to address problems involving nonhomogeneous configurations. Results under different magnetic configurations are compared highlighting the characteristic features of magnetopiezoelectric behavior particularly focusing on the link between interlaminar stress and magnetic induction.
TL;DR: In this paper, an axisymmetric problem for a near-surface circular crack in a semi-infinite composite, which is subjected to initial (residual) stresses parallel to the crack plane, is considered.
Abstract: In the present study, an axisymmetric problem for a near-surface circular crack in a semi-infinite composite, which is subjected to initial (residual) stresses parallel to the crack plane, is considered. Normal and radial shear loads are applied. An analytical approach within the framework of the three-dimensional linearized mechanics of solids is used. The problems are reduced to systems of Fredholm integral equations of the second kind, where the solutions are identified with harmonic potential functions. The stress intensity factors at the crack tips for two types of composites are analyzed. These are a laminated composite made of aluminum/boron/silicate glass with epoxy-maleic resin and a carbon/plastics composite with stochastic reinforcement by short ellipsoidal carbon fibers. The influence of the residual stresses and of the geometrical parameters of the system are illustrated.
TL;DR: In this article, the authors investigated chemically stimulated polymer gels in a solution bath and derived models based on the statistical theory and porous media theory, as well as a coupled multi-field model and a discrete element formulation.
Abstract: Polyelectrolyte gels are a very attractive class of actuation materials with remarkable electronic and mechanical properties with a great similarity to biological contractile tissues. They consist of a polymer network with ionizable groups and a liquid phase with mobile ions. Absorption and delivery of solvent lead to a large change of volume. This mechanism can be triggered by chemical (change of salt concentration or pH of solution surrounding the gel), electrical, thermal or optical stimuli. Due to this capability, these gels can be used as actuators for technical applications, where large swelling and shrinkage is desired. In the present work chemically stimulated polymer gels in a solution bath are investigated. To adequately describe the different complicated phenomena occurring in these gels, they can be modeled on different scales. Therefore, models based on the statistical theory and porous media theory, as well as a coupled multi-field model and a discrete element formulation are derived and emp...
TL;DR: In this paper, a meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2D), orthotropic and linear elastic solids with continuously varying material properties.
Abstract: A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-D), orthotropic and linear elastic solids with continuously varying material properties. Both quasi-static thermal and transient elastodynamic problems are considered. For time-dependent problems, the Laplace-transform technique is utilized. A unit step function is used as the test functions in the local weak-form. It leads to local boundary integral equations (LBIEs) involving only a domain-integral in the case of transient dynamic problems.The analyzed domain is divided into small subdomains with a circular shape. The moving least-squares (MLS) method is adopted for approximating the physical quantities in the LBIEs. The accuracy of the present method for computing the mode-I stress intensity factors is discussed by comparison with available analytical or numerical solutions.
TL;DR: In this article, a shape control method is proposed to find a distributed actuation such that a structure assumes a desired shape, which is called undistended shape. But, the shape control is concerned with finding a distributed actuator such that the structure assumes the desired shape.
Abstract: Adaptive and smart structures have become a major subject of contemporary research. Smart structures are structures that—like human beings—are capable of automatically reacting to disturbances exerted upon them by the environment they are operating in. Typically, smart structures are put into practice by embedding or attaching smart materials to a substrate structure. These materials have both actuating and sensing capabilities; a popular example would be piezoelectric materials that exhibit the direct and the converse piezoelectric effect. As many of the structures, which are considered as candidates for implementing smart materials, are continuous structures, there is an inherent need for properly distributing the actuation as well as the sensing. A method that has been successfully utilized for the design of distributed actuators is shape control. In general, shape control is concerned with finding a distributed actuation such that a structure assumes a desired shape. The latter shape may be the undist...
TL;DR: In this paper, the structural properties of single-walled carbon nanotubes (SWCNTs) are evaluated by a new continuum modeling method, called the dynamic continuum modelling method (DCMM), where a repeating cell unit isolated from a SWCNT is represented as an equivalent continuum beam element.
Abstract: The structural properties of single-walled carbon nanotubes (SWCNTs) are evaluated by a new continuum modeling method, called the dynamic continuum modeling method (DCMM). In the DCMM, a repeating cell unit isolated from a SWCNT is represented as an equivalent continuum beam element by using the energy equivalence principle. The method may allow us to accomplish the static or dynamic analysis for SWCNTs without needing to assume their wall thickness. The structural rigidities of armchair SWCNTs evaluated by using the DCMM are within the range predicted by using the Young's moduli reported in existing references. It is also found that SWCNTs have quite high transverse shear rigidity, but with negligible coupling rigidities.
TL;DR: In this article, an eight node plate with one electrical potential degree of freedom for each interface of piezoelectric layers is presented, where the usual FSDT theory is combined with a field compatibility methodology to avoid the transverse shear locking for thin plates.
Abstract: The aim of this work is to develop a simple and very efficient tool to simulate the active control of laminated plates, and in a next step, to optimize the geometry and number of sensors and actuators. A new piezoelectric Finite Element is presented. It is an eight node plate with one electrical potential degree of freedom for each interface of piezoelectric layers. The usual FSDT theory is combined with a “field compatibility” methodology to avoid the transverse shear locking for thin plates. A LQR control method including a state observer is used to compute the control. Four examples are presented. The quasi-static correction and the use of collocated sensor/actuator are discussed.
TL;DR: The interaction integral method is an accurate and robust scheme for evaluating mixed-mode stress intensity factors as mentioned in this paper, which makes use of a conservation integral in an elastic orthotropic and co...
Abstract: The interaction integral method is an accurate and robust scheme for evaluating mixed-mode stress intensity factors. The method makes use of a conservation integral in an elastic orthotropic and co...
TL;DR: In this article, a fiber inclination model is applied to predict the effective stiffness matrix of the braided composite plate and asymptotic solutions are obtained for simply supported rectangular plates by using an improved perturbation approach and Galerkin technique.
Abstract: This paper studies the nonlinear vibration and dynamic response of three-dimensional braided composite plates produced by the four-step procedure. It is assumed that the yarn is transversely isotropic and the matrix is isotropic. A fiber inclination model is applied to predict the effective stiffness matrix of the braided composite plate. Theoretical formulations are based on Reddy's higher-order shear deformation plate theory and von Karman-type nonlinear kinematics. Asymptotic solutions are obtained for simply supported rectangular plates by using an improved perturbation approach and Galerkin technique.Numerical illustrations are given in both tabular and graphical forms, showing the effects of the fiber volume fraction, the braiding angle, and the inclination angle on the linear and nonlinear vibration frequencies and the dynamic response of braided composite plates.
TL;DR: In this paper, the stability of a generic three-layered truncated conical shell containing a functionally graded (FG) layer subjected to uniform external pressure is investigated, where the material properties of the functionally graded layer are assumed to vary continuously through the thickness of the shell.
Abstract: In this study, the stability of a generic three-layered truncated conical shell containing a functionally graded (FG) layer subjected to uniform external pressure is investigated. The material properties of the functionally graded layer are assumed to vary continuously through the thickness of the shell. The variation of the properties follows an arbitrary distribution in terms of the volume fractions of the constituents. The fundamental relations, the stability and compatibility equations of three-layered truncated conical shells containing a FG layer are obtained, first. Then, applying Galerkin's method, the closed form solution for critical external pressure is obtained. The results show that the critical parameters are affected by the configurations of the constituent materials, the variations of the thickness of the FG layer and the variation of the shell geometry. Comparing the results with those in the literature validates the present analysis.