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Penta-graphene, a new monolayer of carbon atoms, has been synthesized with ideal strength and temperature resistance. However, the mechanical behavior of penta-graphene has not been fully investigated yet. This paper presents an analytical investigation on the nonlinear large amplitude vibration of imperfect three-dimensional (3D) penta-graphene plates subjected to uniformly distributed external pressure with simply supported and immovable edges in thermal environments. The elastic constants and the thermal expansion coefficients of the 3D penta-graphene plate are determined using the density functional theory. The motion and compatibility equations are established based on the Reddy’s higher-order shear deformation plate theory in which the effect of von Karman nonlinear terms, the initial imperfection and the Pasternak elastic foundation are taken into consideration. The Galerkin method is applied to determine the closed-form expressions of linear frequency and nonlinear to linear frequency ratio while the dynamic response of the plate is obtained by using the fourth-order Runge–Kutta method. The Bees Algorithm is used to determine the optimum value of the natural frequency which depends on five variables including the thickness, the length and the width of penta-graphene plates and two stiffness coefficients of elastic foundations. The numerical results show the effects of width-to-thickness ratio, elastic foundations coefficients, initial imperfection parameter and temperature increment on the nonlinear vibration of the 3D penta-graphene plates.

In this article, the vibration and nonlinear dynamic response of imperfect advanced sandwich nanocomposite plate subjected to uniformly distributed pressure has been studied using fourth-order Rung...

In this work we investigated the nonlinear vibration of nanocomposite multilayer perovskite solar cell (NMPSC) subjected to the combination of mechanical and thermal loadings. The model of organic solar cell is assumed to consist seven functional layers: Au, Spiro-OMeTAD, PEDOT:PSS, Graphene oxide, MAPbI3, TiO­2 and IOT, and glass substrate. The governing equations are established basing on the classical plate theory taking into account the effect of elastic foundations and initial imperfection. Four edges of the NMPSC are assumed to be supported immovably in a transverse plane. The relationship between deflection amplitude and time as well as the expression of natural frequency of NMPSC are obtained by using the Galerkin and Runge – Kutta methods. The numerical results showed that the nonlinear dynamic response and the natural frequency of NMPSC have been strongly influenced by the geometrical and material parameters, initial imperfection, temperature increment and elastic foundations. Keywords: Perovskite solar cell; nonlinear vibration; elastic foundations; initial imperfection; thermal environment

The newly developed penta-graphene is a two-dimensional (2D) carbon allotrope with promising mechanical properties. This paper investigates the nonlinear post-buckling and vibration of imperfect three-dimensional penta-graphene composite plates resting on elastic foundations and subjected to uniform external pressure and axial compressive load. The elastic constants of the single-layer penta-graphene are fully determined by the density functional theory by fitting the equation of strain energy to the density functional theory energy. Specifically, the elastic constant $$C_{66}$$ which has not been considered by other authors is also determined. The motion and compatibility equations are derived based on the classical plate theory taking into account von Karman geometrical nonlinearity, initial geometrical imperfection and Pasternak type elastic foundations. For nonlinear post-buckling, the Bubnov–Galerkin method is applied to obtain the load–deflection amplitude curves while the Runge–Kutta method and harmonic balance method are used to obtain the deflection amplitude–time curves and the amplitude–frequency curves for nonlinear vibration. Numerical results show the effects of geometrical parameters, initial imperfection and elastic foundations on the nonlinear post-buckling and vibration of the imperfect 2D penta-graphene plates. The present results are also compared to others to validate the accuracy of the applied method and approach.

This paper aims to investigate the nonlinear buckling and post-buckling of eccentrically oblique stiffened sandwich functionally graded double curved shallow shells resting on elastic foundations in thermal environment. The shells are reinforced by functionally graded eccentrically oblique stiffeners with deviation angles. Two types of sandwich functionally graded double curved shallow shells with the differences of distribution of functionally graded face sheets and homogeneous core are considered. Material properties of the sandwich shells and stiffeners are assumed to vary continuously and smoothly in the thickness direction according to Sigmoid power law. The formula of force and moment resultants and the nonlinear equilibrium equations are established based on the improved Donnell theory and Lekhnitskii's smeared stiffeners technique. The analytical displacement solutions are chosen based on the trigonometric forms satisfying the boundary conditions. The value of critical buckling loads and the load – deflection curves of the shells are obtained by using the Bubnov – Galerkin method. In numerical results; effect of geometrical parameters, elastic foundations, temperature increment, compressive load and oblique stiffeners on the critical buckling loads and post-buckling load – deflection curves of the shells are studied specifically. The obtained results are also compared with others from literature to validate the accuracy of the present method and approach.

This paper investigated the nonlinear vibration and dynamic response of the carbon nanotube polymer composite elliptical cylindrical shells on elastic foundations in thermal environment. The material properties of the nanocomposite elliptical cylindrical shells are assumed to depend on temperature and graded in the thickness direction according to various linear functions. The shell is subjected to the combination of the uniformly distributed transverse load in harmonic form and the uniform temperature rise. The motion and geometrical compatibility equations are derived based on the Reddy’s higher order shear deformation shell theory. The natural frequencies and the deflection amplitude–time curves of the shell are determined by using the Galerkin method and fourth-order Runge–Kutta method. The numerical results show not only the positive influences of carbon nanotube volume fraction and elastic foundations but also the negative influences of initial imperfection and temperature increment on the nonlinear vibration and dynamic response of the carbon nanotube polymer composite elliptical cylindrical shells. The reliability of the present results is verified by comparing with other publications.

Analytical solutions for the nonlinear vibration of imperfect functionally graded nanocomposite (FG-CNTRC) double curved shallow shells on elastic foundations subjected to mechanical load in thermal environments are introduced in this paper. The double curved shallow shells are reinforced by single-walled carbon nanotubes (SWCNTs) which are assumed to be graded through the thickness direction according to the different types of linear functions. Motion and compatibility equations are derived using Reddy's higher order shear deformation shell theory and taking into account the effects of initial geometrical imperfection and temperature – dependent properties. The deflection – time curve and the natural frequency are determined by using Galerkin method and fourth – order Runge – Kutta method. The effects geometrical parameters, elastic foundations, initial imperfection, temperature increment, mechanical loads and nanotube volume fraction on the nonlinear thermal vibration of the nanocomposite double curved shallow shells are discussed in numerical results. The accuracy of present approach and theoretical results is verified by some comparisons with the known data in the literature.

This paper presents the nonlinear vibration of porous functionally graded sandwich plate on elastic foundations subjected to blast loading by the analytical approach. The sandwich plate consists of two FGM face sheets and a homogeneous core which is made from metal or ceramic. Two types of porosity distribution, including evenly and unevenly distributed porosity have been considered for sandwich plate. The material properties of sandwich plate are assumed to vary in the thickness direction according to simple power law distribution with a volume fraction index and a porosity coefficient. The blast loading is assumed to be uniformly distributed on the surface of the sandwich plate and modeled by an exponential function. The Reddy’s higher order shear deformation theory with von Karman type nonlinearity is used to establish governing equations for the vibration of sandwich plate. By applying Galerkin and fourth-order Runge–Kutta methods, the numerical results show the effects of volume fraction index, porosity coefficient, type of porosity distribution, geometrical parameters, elastic foundations and parameters of blast loading on the nonlinear vibration of the sandwich plate. Comparisons are conducted to evaluate the reliability of the obtained results.

Mathematic modeling and analytical approach are presented for nonlinear vibration analysis of laminated plate with auxetic honeycomb core and magneto-electro-elastic face sheets supported by Pasternak-type elastic foundations. The laminated plate is subjected to the simultaneous action of blast, thermal, electric and magnetic loadings. The mechanical properties of auxetic core including negative Poisson’s ratio are assumed to depend on the geometrical parameters of the unit cells and elastic modulus of original material. The volume fraction of two components of each magneto-electro-elastic face sheet is chosen equally. The nonlinear motion equations and the geometrical compatibility equation are established by using Reddy’s higher order shear deformation plate theory taking into account the coupling between elastic, electric and magnetic fields. The analytical vibration solutions for the auxetic laminated plate can be obtained by using Galerkin and fourth-order Runge – Kutta methods . The numerical results are conducted to investigate the effect of geometrical and material parameters, elastic foundations, temperature increment, magnetic and electric potentials on the vibration characteristics of the auxetic laminated plate.

In the recent years, organic solar cell (OSC) has attracted much interest of the research community due to its great promise as renewable sources. This paper presents the first analytical approach to investigate the nonlinear dynamic response and vibration of imperfect rectangular nanocompsite multilayer organic solar cell subjected to mechanical loads using the classical plate theory . Nanocompsite organic solar cell consists of five layers of Al, P3HT:PCBM, PEDOT:PSS, IOT and glass. Motion and compatibility equations are derived using the classical plate theory and taking into account the effects of initial geometrical imperfection and geometrical nonlinearity in Von Karman – Donnell sense. The Galerkin method and fourth – order Runge – Kutta method are used to give explicit expressions of natural frequencies, nonlinear frequency – amplitude relation and nonlinear dynamic responses of nanocompsite organic solar cell. The numerical results show the influences of geometrical parameters, the thickness of layers, imperfections, and mechanical loads on the nonlinear dynamic response and nonlinear vibration of nanocompsite organic solar cell.

The analytical investigation for the nonlinear thermal dynamic buckling of smart sandwich plate subjected to mechanical, thermal and electric loadings is presented. The sandwich plate is composed of a porous homogeneous core, two carbon nanotube reinforced composite (CNTRC) layers and two piezoelectric face sheets. Basic equations are derived based on the Reddy's higher order shear deformation plate theory and Hamilton's principle in which the initial imperfection and Pasternak-type elastic foundations are included. The external pressure is assumed to be uniformly distributed on the surface of the sandwich plate and depend on time according to the linear functions. The nonlinear dynamic response, the frequency – amplitude relation are obtained by using the Galerkin and Runge – Kutta methods and the critical dynamic buckling load is determined by using Budiansky – Roth criterion. Bees Algorithm is used to determine the maximum value of natural frequency of smart sandwich plate and the corresponding optimum values of geometrical and material parameters. The effects of geometrical parameters, CNT volume fraction, elastic foundations, temperature increment, initial imperfection and porosity coefficient on the nonlinear vibration and dynamic buckling of the smart sandwich plate are considered specifically. The numerical results are also compared with existing results using different theories.

This study follows an analytical approach to investigate the nonlinear dynamic response and vibration of eccentrically stiffened sandwich functionally graded material (FGM) cylindrical panels with metal–ceramic layers on elastic foundations in thermal environments. It is assumed that the FGM cylindrical panel is reinforced by the eccentrically longitudinal and transversal stiffeners and subjected to mechanical and thermal loads. The material properties are assumed to be temperature dependent and graded in the thickness direction according to a simple power law distribution. Based on the Reddy’s third-order shear deformation shell theory, the motion and compatibility equations are derived taking into account geometrical nonlinearity and Pasternak-type elastic foundations. The outstanding feature of this study is that both FGM cylindrical panel and stiffeners are assumed to be deformed in the presence of temperature. Explicit relation of deflection–time curves and frequencies of FGM cylindrical panel are determined by applying stress function, Galerkin method and fourth-order Runge-Kutta method. The influences of material and geometrical parameters, elastic foundations and stiffeners on the nonlinear dynamic and vibration of the sandwich FGM panels are discussed in detail. The obtained results are validated by comparing with other results in the literature.

Recently, auxetic cellular solids in the forms of honeycombs and carbon nanotube reinforced composite (CNTRC) have great potential in a diverse range of applications. This paper studies the nonlinear free and forced vibration of sandwich cylindrical panel on visco-Pasternak foundations in thermal environment subjected to blast load The sandwich cylindrical panel consists of auxetic honeycombs core layer and two CNTRC face sheets. The Poisson’ ratio of the auxetic core is negative and the material properties of CNTRC face sheets are assumed to continuously vary in the thickness direction according to four different types of linear functions. The blast load is determined from the distance of the center of blast to center of the structure and the mass of explosive materials. The fundamental equations are established based on Reddy’s higher order shear deformation shell theory taking into account the effect of initial imperfection and visco-Pasternak foundations. The Galerkin and Runge–Kutta methods are used to obtain the nonlinear dynamic response and the natural frequency of the sandwich cylindrical panel. The numerical results show the effect of geometrical parameters, visco foundations, initial imperfection, temperature increment, nanotube volume fraction and blast load on the nonlinear vibration characteristics of the sandwich cylindrical panel. The accuracy of present approach and theoretical results is verified by some comparisons with the known data in the literature.

This article presents analytical solutions for the nonlinear static and dynamic stability of imperfect eccentrically stiffened functionally graded material (FGM) higher order shear deformable double curved shallow shell on elastic foundations in thermal environments. It is assumed that the shell’s properties depend on temperature and change according to the power functions of the shell thickness. The shell is reinforced by the eccentrically longitudinal and transversal stiffeners made of full metal. Equilibrium, motion, and compatibility equations are derived using Reddy’s higher order shear deformation shell theory and taking into account the effects of initial geometric imperfection and the thermal stress in both the shells and stiffeners. The Galerkin method is applied to determine load–deflection and deflection–time curves. For the dynamical response, motion equations are numerically solved using Runge–Kutta method. The nonlinear dynamic critical buckling loads are found according to the crite...

In this article, nonlinear vibration and dynamic response of imperfect functionally graded materials (FGM) thick double-curved shallow shells resting on elastic foundations are investigated using Reddy's third-order shear deformation shell theory in thermal environments. Material properties are assumed to be temperature dependent and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The FGM shells are subjected to mechanical, damping, and thermal loads. The Galerkin method and fourth-order \hboxRunge–Kutta method are used to calculate natural frequencies, nonlinear frequency–amplitude relation, and dynamic response of the shells. In numerical results, the effects of geometrical parameters, material properties, imperfections, shear deformation, the elastic foundations, mechanical, thermal and damping loads on the nonlinear dynamic response, and nonlinear vibration of FGM double-curved shallow shells are investigated....

This paper presents an analytical approach on the nonlinear vibration of nanocomposite multilayer organic solar cell (NMOSC) subjected to the combination of wind load and uniform temperature change. The NMOSC comprises of five layers, which are made of Al, P3HT:PCBM, PEDOT:PSS, Graphene and Glass. Compared to common models of the NMOSC, ITO is replaced by graphene to control the output colors of NMOSC. The nonlinear motion equations and the compatibility equation are deriving by taking into account the effect of viscous damping, von Karman nonlinearity terms, elastic foundations and initial imperfection. The formula of the wind load is improved for consideration in the general case that the direction of the wind load is not just perpendicular to the structure. Four edges of the NMOSC are assumed to be simply supported and immovable in the transverse plane. The Galerkin and Runge – Kutta methods are applied to obtain the dynamic response and the natural frequency of the NMOSC. Four optimization algorithms (Bees Algorithm, Basic differential evolution algorithm, enhanced colliding bodies optimization algorithm, social group optimization algorithm) are used to determine the maximum value of natural frequency of the NMOCS, which depends on nine variables including the geometrical parameters, elastic foundations stiffness and temperature increment. In the numerical results, the effects of elastic foundations, initial imperfection, viscous damping ratio, temperature increment, wind load and the length to width ratio on the dynamic response and natural frequency are considered in details. The maximum values of the natural frequency of the NMOSC with four algorithms are obtained and compared. The results show that the optimal value obtained by four algorithms is close to each other. However, the calculation time with enhanced colliding bodies optimization algorithm is the fastest and with Bees Algorithm is the longest of all.

This paper deals with the nonlinear forced vibration of imperfect penta – graphene plates integrated with piezoelectric actuator layers. The plate is subjected to combination of mechanical, thermal, and electrical loadings. Based on the first order shear deformation plate theory, the governing equations are established taken into account the effect of the von Karman type of geometrical nonlinearity, the Pasternak type elastic foundations, the damping and the piezoelectric – thermal effects. Four edges of the hybrid plate are assumed to be simply supported and immovable in the in-plane directions. The solution forms that satisfy the boundary conditions are assumed to be trigonometric. The closed form expressions of natural frequency, the frequency ratio – amplitude and the deflection amplitude – time curves are obtained by using the Galerkin and Runge – Kutta methods. The numerical results show positive effects of elastic foundations, negative effect of temperature increment and initial imperfection, considerable effect of geometrical parameters as well as small effect of applied voltage on the nonlinear forced vibration of piezoelectric penta – graphene plate.

This paper presents an analytical approach on the nonlinear magneto-electro-elastic vibration of smart sandwich plate. The sandwich plate consists of a carbon nanotube reinforced nanocomposite (CNTRC) core integrated with two magneto-electro-elastic face sheets. For core layer, three types of carbon nanotube (CNT) distribution such as FG-O, FG-V, FG-X are considered while the volume fraction of BaTiO3 − CoFe2O4 in each face sheet is chosen to be 0.5. It is assumed that the smart sandwich plate is rested on Pasternak-type elastic foundations and subjected to the combination of external pressure, thermal, electric and magnetic loads. The coupled constitutive relations are derived based on the Hamilton's principle in which the kinematic nonlinearity is defined using Reddy's higher order shear deformation theory. The analytical solutions which satisfy the boundary conditions are assumed to have the trigonometric form. The Galerkin method is used to obtain the closed form expressions of natural frequency, the relation between the frequency ratio and dimensionless amplitude and the dynamic response of the sandwich plate. The numerical results are conducted to illustrate the effect of geometrical parameters, CNT volume fraction, temperature and moisture increment, electric and magnetic potentials on the nonlinear vibration of smart sandwich plate. The reliability of present results is evaluated by comparing with the previous results based on different approach.

This paper carries out the nonlinear stability of nanocomposite multilayer organic solar cell (NMOSC) subjected to axial compressive loads. The model of organic solar cell is assumed to consist five layers: Al, P3HT:PCBM, PEDOT:PSS, IOT and Glass. Based on the classical plate theory, the basic equations are established taking into account the effect of elastic foundations and initial imperfection. The approximation solutions are selected based on the boundary conditions of the four edges of NMOSC. The equation which indicates the relationship between axial compressive loads and deflection amplitude of NMOSC is obtained by using the Galerkin method. Bees Algorithm is applied to maximize the value of critical buckling load with nine variables including the thickness of five layers, the length and the width of NMOSC and two stiffness coefficients of elastic foundations. The numerical results show the effect of geometrical and material parameters, initial imperfection and elastic foundations on the nonlinear static stability and the critical buckling load of NMOSC. Optimal values of nine geometrical parameters of NMOSC are also determined.

ispartof: Proc. CMWR2018: Computational Methods in Water Resources XXII “Bridging the gaps between data, models, and predictions” ispartof: CMWR2018: Computational Methods in Water Resources XXII “Bridging the gaps between data, models, and predictions” location:Saint-Malo, France date:3 Jun - 7 Jun 2018 status: Published online

This paper presents an analytical approach to investigate the nonlinear stability analysis of eccentrically stiffened thin FGM cylindrical panels on elastic foundations subjected to mechanical loads, thermal loads and the combination of these loads. The material properties are assumed to be temperature-dependent and graded in the thickness direction according to a simple power law distribution. Governing equations are derived basing on the classical shell theory incorporating von Karman–Donnell type nonlinearity, initial geometrical imperfection, the Lekhnitsky smeared stiffeners technique and Pasternak type elastic foundations. Explicit relations of load–deflection curves for FGM cylindrical panels are determined by applying stress function and Galerkin method. The effects of material and geometrical properties, imperfection, elastic foundations and stiffeners on the buckling and postbuckling of the FGM panels are discussed in detail. The obtained results are validated by comparing with those in the literature..

Based on first-order shear deformation, this paper investigates the nonlinear dynamic analysis and vibration of shear deformable imperfect eccentrically stiffened functionally graded thick cylindrical panels, taking into account the damping when subjected to mechanical loads. The volume fractions of metal and ceramic are applied by Sigmoid-law distribution for functional graded material (S-FGM) with metal–ceramic–metal layers. The panels are assumed to be resting on elastic foundations and are reinforced by eccentric longitudinal and transversal stiffeners made of full metal. The nonlinear equations are solved by the Galerkin method and fourth-order Runge–Kutta method. The influences of inhomogeneous parameters, dimensional parameters, stiffeners, elastic foundations, boundary conditions and mechanical loads on the nonlinear dynamic analysis and nonlinear vibration of thick S-FGM cylindrical panels are examined in detail. The results are compared with known results in the literature.

Nonlinear dynamic analysis and vibration of imperfect functionally graded materials (FGM) thick double curved shallow shells with piezoelectric actuators on elastic foundations subjected to the combination of electrical, thermal, mechanical and damping loading are investigated in this paper. Material properties of FGM shells are assumed to be temperature dependent and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations are established based on Reddy’s higher order shear deformation theory that includes thermo-piezoelectric effects and are solved by the stress function, the Galerkin method and fourth-order Runge–Kutta method. In numerical results, the effects of geometrical parameters; the material properties; imperfections; elastic foundations; electrical, mechanical, thermal and damping loads on the nonlinear dynamic analysis and nonlinear vibration of the FGM hybrid double curved shallow shells are discussed.

Based on Reddy's third order shear deformation shell theory and Galerkin method, this paper introduces analytical solutions to study nonlinear buckling behaviors of imperfect carbon nanotube reinforced composite cylindrical panels on elastic foundations in thermal environments. The panels are reinforced by single-walled carbon nanotubes and the eccentrically longitudinal and transversal stiffeners. The effects of geometrical parameters, eccentrically stiffeners, elastic foundations, initial imperfection, temperature increment and nanotube volume fraction on the mechanical behaviors of the nanocomposite cylindrical panels are also examined in numerical results. Some comparisons with results of other authors show the accuracy of the present theory and approach.

An analytical approach is presented to investigate the nonlinear dynamic response and vibration of imperfect eccentrically stiffened FGM double curved thin shallow shells on elastic foundation using a simple power-law distribution (P-FGM) in thermal environment. The formulations are based on the classical shell theory taking into account geometrical nonlinearity, initial geometrical imperfection, temperature-dependent properties and the Lekhnitsky smeared stiffeners technique with Pasternak type elastic foundation. By applying Galerkin method and using stress function, explicit relations of thermal load-deflection curves for simply supported curved eccentrically stiffened FGM shells are determined. Effects of material and geometrical properties, temperature, elastic foundation and eccentrically stiffeners on the dynamic response and vibration of the imperfect eccentrically stiffened P-FGM double curved shallow shells in thermal environments are analyzed and discussed. The numerical results in this paper are compared with results reported in other publications.

In the present paper, the nonlinear response of eccentrically stiffened FGM cylindrical panels on elastic foundation subjected to mechanical loads is presented. Material properties are graded in the thickness direction of the FGM panel according to a simple power law distribution. By applying Bubnov-Galerkin method, the Lekhnitsky smeared stiffeners technique with Pasternak type elastic foundation and stress function, explicit relations of load-deflection curves for simply supported eccentrically stiffened FGM panels are determined. Numerical results are given for evaluate effects of material and geometrical properties, elastic foundation and eccentrically outside stiffeners on the buckling and postbuckling of the FGM panels. The obtained results are validated by comparing with those in the literature.

This paper presents an analytical approach to investigate the nonlinear dynamic response and vibration of imperfect eccentrically stiffened FGM thick double curved shallow shells on elastic foundation using both the first order shear deformation theory and stress function with full motion equations (not using Volmir's assumptions). The FGM shells are assumed to rest on elastic foundation and subjected to mechanical and damping loads. Numerical results for dynamic response of the FGM shells are obtained by Runge–Kutta method. The results show the influences of geometrical parameters, the material properties, imperfections, the elastic foundations, eccentrically stiffeners and mechanical loads on the nonlinear dynamic response and nonlinear vibration of functionally graded double curved shallow shells. The numerical results in this paper are compared with results reported in other publications.

The novelty of this study is using the analytical approach to investigate the nonlinear dynamic response and vibration of shear deformable functionally graded truncated conical panel with piezoelectric actuators, resting on Pasternak type elastic foundations in thermal environments. Material properties are graded in the thickness direction according to a simple power law distribution in terms of the fractions of constituents. The governing equations are derived based on the first order shear deformation shell theory with a von Karman – Donnell type of kinematic nonlinearity in which the Hamilton's principle is used to derive the equations of motion of piezoelectric functionally graded truncated conical panel. The those equations are solved by the Galerkin method and Runge – Kutta method to determine the nonlinear deflection amplitude – time curves and natural frequency of the functionally graded panel. In numerical results, the effects of applied actuator voltage, temperature increment, dimensional parameters, semi – vertex angle, material properties and elastic foundations on the nonlinear dynamic response and vibration of the piezoelectric functionally graded truncated conical panel are discussed in details. The approach are verified with the known results in the literature.

This paper first time presents an analytical investigation on the nonlinear postbuckling for imperfect eccentrically stiffened FGM double curved thin shallow shells on elastic foundation using a simple power-law distribution (P-FGM) in thermal environments. The formulations are based on the classical shell theory taking into account geometrical nonlinearity, initial geometrical imperfection, temperature-dependent properties and the Lekhnitsky smeared stiffeners technique with Pasternak type elastic foundation. By applying Galerkin method and using stress function, explicit relations of thermal load–deflection curves for simply supported curved eccentrically stiffened FGM shells are determined. Effects of material and geometrical properties, temperature, elastic foundation and eccentrically stiffeners on the buckling and postbuckling loading capacity of the imperfect eccentrically stiffened P-FGM double curved shallow shells in thermal environments are analyzed and discussed.

The nonlinear response of buckling and posbuckling of imperfect thin functionally graded doubly curved thin shallow shells resting on elastic foundations and subjected to some mechanical loads is investigated analytically. The elastic moduli of materials, Young’s modulus, and Poisson ratio are all graded in the shell thickness direction according to a simple power-law in terms of volume fractions of constituents. All formulations are based on the classical theory of shells with account of geometrical nonlinearity, an initial geometrical imperfection, and a Pasternak-type elastic foundation. By employing the Galerkin method, explicit relations for the load–deflection curves of simply supported doubly curved shallow FGM shells are determined. The effects of material and geometrical properties, foundation stiffness, and imperfection of shells on the buckling and postbuckling loadcarrying capacity of spherical and cylindrical shallow FGM shells are analyzed and discussed.

An analytical investigation into the nonlinear response of a thin imperfect laminated three-phase polymer composite plate consisting of a matrix and reinforcing fibers and particles and subjected to mechanical loads is presented. All formulations are based on the classical theory of plates with account of interaction between the matrix and reinforcement, the geometrical nonlinearity, and an initial geometrical imperfection. By using the Galerkin method, explicit relations for the load–deflection relationships are determined. The effects of reinforcing fibers and particles, material and geometrical properties, and imperfections on the buckling and postbuckling load-carrying capacities of a 3-phase composite plate are analyzed and discussed.

This paper presents an analytical investigation on the nonlinear dynamic analysis of functionally graded double curved thin shallow shells using a simple power-law distribution (P-FGM) with temperature-dependent properties on an elastic foundation and subjected to mechanical load and temperature. The formulations are based on the classical shell theory, taking into account geometrical nonlinearity, initial geometrical imperfection, temperature-dependent properties and unlike other publications, Poisson ratio is assumed to be varied smoothly along the thickness [Formula: see text]. The nonlinear equations are solved by the Bubnov-Galerkin and Runge-Kutta methods. The obtained results show the effects of temperature, material and geometrical properties, imperfection and elastic foundation on the nonlinear vibration and nonlinear dynamical response of double curved FGM shallow shells. Some results were compared with those of other authors.

An analytical investigation into the nonlinear response of thick functionally graded double-curved shallow panels resting on elastic foundations and subjected to thermal and thermomechanical loads is presented. Young’s modulus and Poisson’s ratio are both graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of constituents. All formulations are based on the classical shell theory with account of geometrical nonlinearity and initial geometrical imperfection in the cases of Pasternak-type elastic foundations. By applying the Galerkin method, explicit relations for the thermal load–deflection curves of simply supported curved panels are found. The effects of material and geometrical properties and foundation stiffness on the buckling and postbuckling load-carrying capacity of the panels in thermal environments are analyzed and discussed.

An investigation on the nonlinear dynamic response and vibration of the imperfect laminated three-phase polymer nanocomposite panel resting on elastic foundations and subjected to hydrodynamic loads is presented in this paper. The formulations are based on the classical shell theory and stress function taking into account geometrical nonlinearity, initial geometrical imperfection and Pasternak type elastic foundation. Numerical results for dynamic response and vibration of the three-phase polymer composite panel are obtained by Runge–Kutta method. The influences of fibers and particles, material and geometrical properties, foundation stiffness, imperfection and hydrodynamic loads on the nonlinear dynamic response and nonlinear vibration of the three-phase composite panel are discussed in detail.