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This paper deals with the vibration and buckling behaviour of orthotropic double -layered graphene sheets with various boundary conditions in a hygrothermal environment. Two graphene sheets are coupled by an elastic media and also limited to the external Pasternak elastic foundations. The governing equations of motion and equilibrium are derived using Hamilton's principle and then solved using Galerkin's method. The general equations for transverse vibration and buckling of orthotropic double-layered graphene sheets subjected to in-plane edge hygrothemal loadings are formulated on the basis of Eringen's differential nonlocal elastic law and the new first order shear deformation theory. The accuracy of the present solutions is demonstrated by comparison with solutions available in the literature. Numerical results are presented to show variations of the frequency and critical buckling load corresponding to various values of the nonlocal parameter, temperature rise, moisture rise, elastic foundation parameter, and aspect ratio. Also, seven different boundary conditions are discussed in the paper. [ABSTRACT FROM AUTHOR]

Buckling behaviors of shear deformable grid-stiffened functionally graded cylindrical shells are investigated under the combined compressive and thermal loads. The governing equations are established on the basis of Reddy's higher-order shear deformation theory. For the perfect grid-stiffened cylindrical shells, separation of variables is employed to obtain the accurate buckling solutions. Then, according to the derived mode functions, Galerkin's solving procedure is conducted for shells including the initial geometric imperfection. The effects of geometric parameters, properties of FGMs and temperature fields on the anti-buckling performances of grid-stiffened shells are concerned under the clamped boundary condition. Besides, imperfection sensitivities for various reinforced grids are discussed in detail. [ABSTRACT FROM AUTHOR]

Buckling of laminated composite beams is studied by the finite element method. A multilayered beam element presented here consists of N -layers, and includes totally 3 N + 7 degrees of freedom (DOFs). Delamination and slip between the layers are avoided. Effect of shear deformation is considered according to the first-order shear deformation theory (FSDT). Numerical results for buckling loads of laminated beams with different boundary conditions and lamina stacking are presented. Comparisons show that results obtained agree well with those of previous works available in the literature. [ABSTRACT FROM AUTHOR]

Abstract: In present study, a refined nth-order shear deformation theory is proposed, formulated and validated for a variety of numerical examples of functionally graded (FG) plates resting on elastic foundation for the mechanical and thermal buckling responses. The present refined nth-order shear deformation theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a parabolic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Governing equations are derived from the principle of minimum total potential energy. A Navier type closed form solution methodology is also proposed for simply supported FG plates resting on elastic foundation which provides accurate solution. The accuracy of the present theory is verified by comparing the obtained results with those predicted by classical plate theory (CPT), first-order shear deformation theory (FSDT), higher-order shear deformation theory (HSDT) and refined plate theory (RPT). Moreover, results show that the present theory can achieve the same accuracy of the existing higher-order shear deformation theories which have more number of unknowns. [Copyright &y& Elsevier]

Abstract: The work presented here concerns the ultimate strength predictions of simply supported, square plates of laminated composite material subjected to uniaxial in-plane compressive load. Plates having a range of thicknesses and initial geometric imperfections have been investigated. Several models are established, each based on first order shear deformation theory and assumption of small deflections. The approaches give reasonable but somewhat conservative estimates for the thicker plates considered, while for the thinner plates, neglect of the post-buckling behaviour makes the results very conservative. It will be necessary to use a large deflection plate theory for some of the models to realise their full potential. [Copyright &y& Elsevier]

This paper presents a finite element model based on the first-order shear deformation theory for free vibration and buckling of functionally graded beams. The present element has five nodes and ten degrees-of-freedom. Material properties vary continuously through the beam thickness according to the power-law form. Governing equations are derived with the aid of Lagrange's equations. Natural frequencies and buckling loads are calculated numerically for different end conditions, power-law indices, and span-to-depth ratios. Accuracy of the present element is demonstrated by comparisons with the available results. [ABSTRACT FROM AUTHOR]

Abstract: The buckling of heated functionally graded material (FGM) annular plates on an elastic foundation is studied analytically. A conventional Pasternak-type elastic foundation is assumed to be in contact with plate during deformation, which acts in both compression and tension. The equilibrium equations of an annular-shaped plate are obtained based on the classical plate theory. Each thermo-mechanical property of the plate is assumed to be graded across the thickness direction of plate based on the power law form, while Poisson’s ratio is kept constant. Among all combinations of free, simply-supported, and clamped boundary conditions, existence of bifurcation buckling for various edge supports is examined and stability equations are obtained by means of the adjacent equilibrium criterion. An exact analytical solution is presented to calculate the thermal buckling load by obtaining the eigenvalues of the stability equation. Three types of thermal loading, namely; uniform temperature rise, transversely linear temperature distribution and heat conduction across the thickness type are studied. Effects of thickness to outer radii, inner to outer radii, power law index, elastic foundation coefficient, and thermal loading type on critical buckling temperature of FG plates are presented. [Copyright &y& Elsevier]

Abstract: In this work, the buckling behavior of the cross-ply laminated non-homogeneous orthotropic truncated conical shells in the large deformation under the uniform axial load is studied. Firstly, the basic relations of the cross-ply laminated non-homogeneous orthotropic truncated conical shells are derived using the large deformation theory. Then modified Donnell type non-linear stability and compatibility equations are obtained and solved. A computer program called Maple 14 has been used in the numerical solution. Finally, the influences of the degree of non-homogeneity, the number and ordering of layers and the variations of the conical shell characteristics on the non-linear axial buckling load are investigated. The comparison with available results is satisfactorily good. [Copyright &y& Elsevier]

Abstract: A mechanical model capable of taking into account the contribution of shear deformation on the lateral buckling behavior of open cross-sections pultruded FRP beams is presented. The total torsional rotation is divided into two parts: the first one, associated with axial warping and negligible shearing strains, the second one, associated entirely with shear strains. Through this approach it is therefore possible to consider with good approximation the shear strains, which are neglected by the classical Vlasov theory. The procedure is validated by comparing the results obtained via FEM with some numerical results available in literature. The effect of the normal to shear modulus ratio on the lateral buckling load is also investigated. [Copyright &y& Elsevier]

Abstract: Columns with non-uniform distribution of geometrical or material parameters i.e. functionally graded material distribution, varying cross-sectional area and flexural stiffness provide an economical solution to carry the desired higher compressive loads in engineering structures. In this paper, a low-dimensional mathematical model is presented, which is capable of computing the buckling loads of uniform and non-uniform functionally graded columns in the axial direction. The columns with spatial variation of flexural stiffness, due to material grading and/or non-uniform shape, are approximated by an equivalent column with piecewise constant geometrical and material properties. Such a formulation leads to certain transcendental eigenvalue problems where the matrix elements are transcendental functions. This model is further extended in analyzing some uniform and non-uniform elastically restrained or braced axially graded columns with equal or unequal spans. The mathematical modeling, closed-form transcendental functions and numerical solution technique are described and several examples of estimating buckling loads for various boundary configurations are presented. Some of the results are also validated against available solutions, representing the convergence, effectiveness, accuracy and versatility of the proposed modeling and numerical method. Formulation of such low-dimensional eigenvalue problems can also be extended for analyzing, designing and optimizing the static and dynamic behavior of structural components that are made of functionally graded materials. [Copyright &y& Elsevier]

Abstract: In this study, the effects of hole diameter and hole location on the lateral buckling behaviour of woven fabric laminated composite cantilever beams have been investigated. In the experimental studies, two different groups of samples were used; samples with a single circular hole and samples with no hole. The critical buckling load for each sample was then determined experimentally. For the numerical analyses, ANSYS 10.0 finite element program was utilized. It has been noted that there is a good agreement between experimental results and those of finite element analyses. On the basis of this harmony, the numerical analyses of some models having different dimensions and fiber orientations have been done by changing length and width of the beam, diameter and location of the hole. It has been concluded that the effects of the hole diameter and hole location on the lateral buckling behaviours is very important, especially for the short beams. [Copyright &y& Elsevier]

Abstract: Laminated carbon fiber reinforced polymer (CFRP) composites have widespread applications in aerospace structures, and thus optimization of the stacking sequences in these composites is indispensable. Here, a fractal branch and bound method (FBB) is proposed for optimizing the stacking sequences. This method requires only low computational costs, and an optimal result can be obtained rapidly by means of the deterministic process. For practical stacking sequence optimizations, more than two laminates have to be optimized, because a practical aerospace structural component usually comprises a panel and stiffeners made from composite laminates. Since the stacking sequences of the skin panel and stiffeners affect the buckling load of the stiffened panel, the optimization of both laminates must be performed simultaneously. In the present study, a new method to implement a strength constraint for the FBB method is proposed for the simultaneous optimization of more than two laminates (such as a panel and stiffeners). Moreover, a quadratic polynomial objective function, which includes lamination parameter variables of the two laminates: the stiffeners and the panel, is adopted. The strength constraint is implemented by means of a response surface. The new method is applied to the buckling load maximization of a blade-stiffened composite panel, in which the strength constraint is demonstrated as a feasibility study. The method successfully obtained optimal stacking sequences with the strength constraint at low computational cost. [Copyright &y& Elsevier]

Abstract: A study has been made to determine the critical time parameters of truncated conical shells with functionally graded coatings (FGCs) and subjected to a time dependent axial load in the large deformation. The method of solution utilizes Superposition principle and Galerkin procedure. Donnell–Karman type non-linear differential equations for the truncated conical shell with FGCs are derived and reduced to ordinary differential equation with the time dependent coefficient. The Runge–Kutta method and modified Budiansky–Roth criterion are then used to solve this non-linear differential equation with the time dependent coefficient. Finally, effects of compositional profiles of coatings, variation of truncated conical shell parameters and loading speed on the dimensionless linear and non-linear critical time parameters have been studied. Comparing the results of this study with those in the literature validates the present analysis. [Copyright &y& Elsevier]

This paper proposes a new higher-order shear deformation theory for buckling and free vibration analysis of isotropic and functionally graded (FG) sandwich beams. The present theory accounts a new hyperbolic distribution of transverse shear stress and satisfies the traction free boundary conditions. Equations of motion are derived from Lagrange's equations. Analytical solutions are presented for the isotropic and FG sandwich beams with various boundary conditions. Numerical results for natural frequencies and critical buckling loads obtained using the present theory are compared with those obtained using the higher and first-order shear deformation beam theories. Effects of the boundary conditions, power-law index, span-to-depth ratio and skin-core-skin thickness ratios on the critical buckling loads and natural frequencies of the FG beams are discussed. [ABSTRACT FROM AUTHOR]

Abstract: In this paper the authors derive a higher-order shear deformation theory for modeling functionally graded plates accounting for extensibility in the thickness direction. The explicit governing equations and boundary conditions are obtained using the principle of virtual displacements under Carrera’s Unified Formulation. The static and eigenproblems are solved by collocation with radial basis functions. The efficiency of the present approach is assessed with numerical results including deflection, stresses, free vibration, and buckling of functionally graded isotropic plates and functionally graded sandwich plates. [Copyright &y& Elsevier]

This work investigates the interplay between viscoelasticity and instabilities in soft particulate composites undergoing finite deformation. The composite is subjected to in-plane deformation at various constant strain rates, and experiences microstructural buckling upon exceeding the critical strain level. We characterize the dependence of the critical strain and wavelength on the applied strain rate through our numerical analysis. In the simulations, we employ the single and multiple-branch visco-hyperelastic models. We find that the critical strain and wavelength – characterized by the single-branch model – show a non-monotonic dependence on the strain rate, reaching a maximum at a specific strain rate. Remarkably, different buckling patterns (with different critical wavelengths) can be activated by changing strain rates. The space of admissible buckling modes widens in composites with higher instantaneous shear modulus. In the composites characterized by the multiple-branch model, the critical strain function exhibit multiple local maxima following a superposition of the single-branch responses. Typically, the branch with a larger relaxation time has a more significant effect on the critical strain. Moreover, the local maximum (of the critical strain function) is amplified by increasing the strain–energy factor of the corresponding branch term. Finally, we perform the experiments on the 3D-printed particulate soft composite characterized by a broad spectrum of relaxation times. The comparison of the experimental and simulation results demonstrates the ability of the numerical model to predict the critical buckling characteristics. [ABSTRACT FROM AUTHOR]

Abstract: A study on buckling phenomena in pultruded Fiber Reinforced Polymer (FRP) beams, based on two mechanical models recently formulated by the authors with regard to composite thin-walled beams, is presented in this paper. Global buckling behavior is analyzed by means of a one-dimensional model in which cross-section torsional rotation is divided into two parts: the first one, associated with Vlasov’s axial warping, the second one, associated entirely with shear strains. The study of local behavior is based on the individual buckling analysis of the components of FRP profile, assumed as elastically restrained transversely isotropic plates. Both mechanical models take into account, within the field of small strains and moderate rotations, the contribution of shear deformation in the kinematic hypotheses. Design charts suitable to evaluate the buckling load of FRP “I” beams with either narrow or wide flanges are obtained and presented in this paper. [Copyright &y& Elsevier]

This paper presents buckling analysis of a two-dimensional functionally graded cylindrical shell reinforced by axial stiffeners (stringer) under combined compressive axial and transverse uniform distributive load. The shell material properties are graded in the direction of thickness and length according to a simple power law distribution in terms of the volume fractions of the constituents. Primarily, the third order shear deformation theory (TSDT) is used to derive the equilibrium and stability equations. Since there is no closed form solution, the numerical differential quadrature method, (DQM), is applied for solving the stability equations. Initially, the obtained results for an isotropic shell using DQM were verified against those given in the literature for simply supported boundary conditions. The effects of load, geometrical and stringer parameters along with FG power index in the various boundary conditions on the critical buckling load have been studied. The study of results confirms that, stringers have significant effects on critical buckling load. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the buckling and vibration analysis of isotropic and laminated plates by a first-order shear deformation theory. The numerical approach is based on collocation with radial basis functions. The model allows the analysis of arbitrary boundary conditions and irregular geometries. It is shown that the present method, based on a first-order shear deformation theory produces highly accurate natural frequencies and modes of vibration, as well as critical loads and modes. [Copyright &y& Elsevier]

In this paper, thermal buckling of double-layered graphene sheets (GSs) with various boundary conditions is analyzed. The new first-order shear deformation theory (NFSDT) is reformulated using nonlocal differential constitutive relations of Eringen. Unlike the conventional first-order shear deformation (FSDT), NFSDT contains only two unknowns. It is assumed that two GSs are bonded by an internal elastic medium and surrounded by external elastic foundations. The equations of equilibrium of the nonlocal model have been derived by using the virtual displacement method. Analytical solutions for the thermal buckling of double-layered GSs under various boundary conditions are presented. The analytical expression is given for the three types of temperature distribution as uniform, linear, and nonlinear temperatures rise through the thickness of the plate. Two comparison studies are carried out to demonstrate the high accuracy of the presented nonlocal NFSDT. The influences of nonlocal parameter, plate aspect ratio, elastic foundation parameters, boundary conditions on critical buckling temperature, and critical temperature ratio are investigated. [ABSTRACT FROM AUTHOR]

The buckling behavior of functionally graded carbon nanotube (FG-CNT) reinforced composite thick skew plates is studied. The CNTs are reinforced uniaxially aligned in the axial direction. Material properties of the nanocomposites are assumed to be graded in the thickness direction. The element-free IMLS-Ritz method is employed for the numerical analysis. The theoretical formulation has incorporated the effects of transverse shear deformation and rotary inertia through employing the first-order shear deformation theory (FSDT). A few numerical examples are chosen to demonstrate the numerical stability and accuracy of the IMLS-Ritz method. The validity of the IMLS-Ritz results is examined by comparing them with those of the known data in the literature. Parametric studies are conducted for various types of CNTs distributions, CNT ratios, skew plates, aspect ratios and thickness-to-height ratios under different boundary conditions. Some conclusions are drawn on the parametric studies with respect to the buckling characteristics. [ABSTRACT FROM AUTHOR]

Abstract: Electro-thermo-torsional buckling response of a double-walled boron nitride nanotube (DWBNNT) has been investigated based on nonlocal elasticity and piezoelasticity theories. The effects of surrounding elastic medium such as the spring constant of the Winkler-type and the shear constant of the Pasternak-type are taken into account. The van der Waals (vdW) forces are considered between inner and outer layers of nanotube. According to the relationship between the piezoelectric coefficient of armchair boron nitride nanotubes (BNNTs) and stresses, the first order shear deformation theory (FSDT) is used. Energy method and Hamilton’s principle are employed to obtain coupled differential equations containing displacements, rotations and electric potential terms. The detailed parameter study is conducted to investigate the effects of nonlocal parameter, elastic foundation modulus, temperature change, piezoelectric and dielectric constants on the critical torsional buckling load. Results indicate that the critical buckling load decreases when piezoelectric effect is considered. [Copyright &y& Elsevier]

A high order shear deformation theory is used to develop a discrete model for the structural and sensitivity analyses allowing for the material distribution and sizing optimization of functionally graded material (FGM) structures. The finite element formulation for general FGM plate-shell type structures is presented, and a non-conforming triangular flat plate/shell element with 24° of freedom for the generalized displacements is used. The formulation accounts for geometric and material nonlinear behaviour, free vibrations and linear buckling analyses, and their analytical gradient based sensitivities. The p-index of the power–law material distribution and the thickness are the design variables. Mass, displacement, fundamental frequency and critical load are the objective functions or constraints. The optimization solutions, obtained by a Feasible Arc Interior Point gradient-based algorithm, for some plate-shell examples are presented for benchmarking purposes. [ABSTRACT FROM AUTHOR]

Abstract: The objective of this paper is to study the interaction curves along with buckling and postbuckling responses of a quasi-isotropic laminate with a centrally placed circular cutout of various sizes under uni-axial compression combined with in-plane shear loads (positive and negative). The present study is carried out using finite element method. The finite element formulation is based on the first order shear deformation theory and von Karman’s assumptions to incorporate geometric nonlinearity. The resulting nonlinear algebraic equations are solved by Newton–Raphson method. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. It is observed that pure compression- buckling, -first-ply failure and -ultimate failure strengths of the quasi-isotropic laminate with and without circular cutout decreases with increasing accompanying shear load. In addition, it is also noted that for a given uni-axial compression load, a quasi-isotropic laminate with and without a cutout can sustain higher negative shear load in comparison to the positive shear load. [Copyright &y& Elsevier]

Abstract: This paper presents a postbuckling analysis of functionally graded cylindrical shells under axial compression and thermal loads using the element-free kp-Ritz method. The formulation is developed to handle problems of small strains and moderate rotations, based on the first-order shear deformation shell theory and von Kármán strains. The effective material properties of the shells are assumed to be continuous along their thickness direction, and are obtained using a power-law distribution of the volume fractions of the constituents. The approximations of the two-dimensional displacement fields are expressed in terms of a set of mesh-free kernel particle functions. The system bending stiffness is evaluated using a stabilized conforming nodal integration method and the membrane and shear terms are estimated using direct nodal integration to eliminate shear locking. The postbuckling path is traced using a combination of the arc-length and mesh-free kp-Ritz methods. The proposed formulation is validated by comparing the results of the proposed method with those in the literature. The postbuckling responses of two types of functionally graded conical shells, one composed of Al/ZrO2 and the other of SUS304/Si3N4, are investigated and the effects of volume fraction, boundary condition, and length-to-thickness ratio on postbuckling behavior are discussed in detail. [Copyright &y& Elsevier]

Abstract: An investigation into the progression of damage in pin-loaded fibre metal laminate (FML) joints is presented. A parametric study was carried out on the commercially available FML, GLARE®, in which edge distance to hole diameter (e/d) and width to hole diameter (w/d) ratios were varied and corresponding failure modes and loads identified. It was found that bearing failure was the dominant failure mode, and obtaining shear-out and net-tension failures required very low e/d and w/d ratios, respectively. Even in specimens that failed by shear-out or net-tension, substantial bearing damage was present. The catastrophic nature of the bearing failure mode under load control was demonstrated. Damage progression was examined using microscopy on specimens loaded to ultimate failure and to percentages of their ultimate failure load. Initial non-linearity in all types of specimens was found to be primarily due to plastic deformation of the aluminium plies and micro-buckling of fibres in the 0° layers at the bearing plane. For specimens loaded to percentages of failure, the glass layers were found to recover some of their strain after removal of the pin, while the aluminium layers did not recover. At higher loads, the rate of stiffness loss in both shear-out and net-tension specimens slowed due to the activation of tensile loading of fibres, until just prior to failure when the fibres started to break. In the bearing specimens, final failure involved complete separation of the outer aluminium plies from the glass layers, which under load control was found to be an unstable process. The study provides supporting information for the development and validation of numerical damage models for FML joints. [Copyright &y& Elsevier]

Abstract: The buckling behaviour of straight sandwich beams joined with curved sandwich beams loaded in pure bending is investigated using two different models. One is based on a high order sandwich beam theory and the other model is based on finite element analysis. The analyses are applied to a numerical example and the results are compared with experimental results. [Copyright &y& Elsevier]

Abstract: Considering the effects of interfacial damage, geometric nonlinearity and transverse shear deformation, thermal postbuckling of fiber–metal laminated plates including interfacial damage is analyzed in detail. Firstly, the Heaviside step function and higher order shear deformation functions are introduced into displacement field so that the damage degree can be characterized. Then, the shape functions can be determined by using the stress continuity conditions between interfaces and the stress boundaries on surfaces. By using the generalized variational principle, the thermal postbuckling equilibrium equations of fiber–metal laminated plates including interfacial damage are established. Finally, the thermal postbuckling problem is solved by adopting finite difference method and iteration method. In numerical examples, the effects of interfacial damage, width-to-thickness ratio and thermal load on the thermal postbuckling of fiber–metal laminated plates including interfacial damage are investigated. [Copyright &y& Elsevier]

The present study deals with the nonlinear postbuckling and free vibration of third-order shear deformable rectangular nanoplate with various edge supports in the pre- and post-buckling regimes incorporating the surface effects. The Gurtin–Murdoch surface stress elasticity theory in conjunction with the third-order shear deformation plate theory is used for the size-dependent mathematical modeling of the nanoplates. The von Kármán-type kinematic nonlinearity is used to consider the nonlinear behavior of the nanoplate subjected to the in-plane loadings. The normal stress is assumed to be changed cubically through the thickness direction of nanoplate to satisfy the equilibrium conditions between on the surfaces and bulk layers. The size-dependent coupled in-plane and out-of-plane governing differential equations of motion and corresponding boundary conditions are derived by means of an energy method based on Hamilton's principle. The generalized differential quadrature (GDQ) method and pseudo-arc length continuation are employed to obtain the postbuckling load-deflection curves of nanoplates with various edge supports. A time-dependent small disturbance around the buckled configuration is considered to analyze the free vibration of postbuckled nanoplates. The effects of thickness and surface parameters on the postbuckling path and free vibration characteristics of nanoplates in the pre- and post-buckling regimes are studied. Also, a comparison is made between the results based upon the surface stress elasticity and classical continuum theories so as to show the significance of surface effects. [ABSTRACT FROM AUTHOR]

In this paper, we develop a novel size-dependent plate model for the axisymmetric bending, buckling and free vibration analysis of functionally graded circular/annular microplates based on the strain gradient elasticity theory. The displacement field is chosen by using a refined third-order shear deformation theory which assumes that the in-plane and transverse displacements are partitioned into bending and shear components and satisfies the zero traction boundary conditions on the top and bottom surfaces of the microplate. Besides, the present model contains three material length scale parameters to capture the size effect. The material properties of the microplate are assumed to vary in the thickness direction and estimated through the classical rule of mixture. By using Hamilton's principle, the equations of motion and boundary conditions are obtained. Afterward, the differential quadrature method is adopted to discretise the governing differential equations along with various types of edge supports and therefore the deflection, critical buckling load and natural frequency can be determined. Convergence and comparison studies are carried out to establish the reliability and accuracy of the numerical results. Finally, a parametric study is conducted to investigate the influences of material length scale parameters, gradient index, thickness-to-outer radius ratio, outer-to-inner radius ratio and boundary conditions on the mechanical characteristics of the microplate. [ABSTRACT FROM AUTHOR]

A new inverse trigonometric shear deformation theory is proposed for the static, buckling and free vibration analyses of isotropic and functionally graded (FG) sandwich plates. It accounts for a inverse trigonometric distribution of transverse shear stress and satisfies the traction free boundary conditions. Equations of motion obtained here are solved for three types of FG plates: FG plates, sandwich plates with FG core and sandwich plates with FG faces. Closed-form solutions are obtained to predict the deflections, stresses, critical buckling loads and natural frequencies of simply supported plates. A good agreement between the obtained predictions and the available solutions of existing shear deformation theories is found to demonstrate the accuracy of the proposed theory. [ABSTRACT FROM AUTHOR]

Abstract: Cellular solids such as honeycombs and foams are widely used as structural materials for their low density and high specific stiffness. Under compression or shear loading buckling may occur in cells, and complex deformation modes can result in sudden variations in the strength characteristics of the cellular material. In this paper, the behaviour of regular hexagonal honeycombs under general in-plane loading (compression, traction and shear) is examined by experimental tests and numerical evaluation. In addition, the influence of geometrical imperfections on the failure process is considered. A set of uniform deformation fields is imposed on several honeycomb models with different imperfections in order to determine the overall strength properties, the principal buckling modes and the post-buckling behaviour. Experimental tests are properly designed in order to obtain a complete nonlinear in-plane mechanical characterisation of an Al 3033 honeycomb. Moreover, all the numerical analyses are performed by means of an in-house developed FE code. [Copyright &y& Elsevier]

Abstract: We present in this paper a simple and effective formulation based on a fifth-order shear deformation theory (FiSDT) in combination with isogeometric finite element analysis (IGA) for composite sandwich plates. The FiSDT yields non-linear distribution of the transverse shear stresses through the plate thickness and ensures a prior tangential stress-free boundary condition. The IGA uses same basis functions, namely B-splines or non-uniform rational B-splines (NURBS), for preserving the precisely geometric representation and providing the numerical solution. It enables to achieve easily the smoothness with arbitrary continuity order and in the present method the C 1-continuity requirement of higher order shear deformation models is fulfilled. The static, dynamic and buckling analysis of rectangular and circular plates is investigated for different boundary conditions. Numerical examples are given to show high accuracy of the proposed method. [Copyright &y& Elsevier]

Abstract: The first-order shear deformation beam theory for static and free vibration of axially loaded rectangular functionally graded beams is developed. In this theory, the improved transverse shear stiffness is derived from the in-plane stress and equilibrium equation and thus, associated shear correction factor is then obtained analytically. Equations of motion are derived from the Hamilton’s principle. Analytical solutions are presented for simply-supported functionally graded beams. The obtained results are compared with the existing solutions to verify the validity of the developed theory. Effects of the power-law index, material contrast and Poisson’s ratio on the displacements, natural frequencies, buckling loads and load–frequency curves as well as corresponding mode shapes are investigated. [Copyright &y& Elsevier]

Abstract: This paper presents a novel and effective formulation based on isogeometric approach (IGA) and higher-order deformation plate theory (HSDT) to study the behavior of functionally graded material (FGM) plates. HSDT model using C 1 continuous element is able to improve the accuracy of solution and describe exactly the shear stress distribution without shear correction factors. IGA utilizes the non-uniform rational B-spline (NURBS) functions which allow us to achieve easily the smoothness with arbitrary continuity order. The present method hence fulfills the C 1 – requirement of HSDT model. The effective material properties of the FGM plates, which property varies only through the thickness of plate, are calculated using the rule of mixture and the Mori–Tanaka homogenization technique. The static, dynamic and buckling analysis of rectangular and circular plates is investigated for different boundary conditions. Numerical results show high effectiveness of the present formulation. [Copyright &y& Elsevier]

A new hyperbolic shear and normal deformation plate theory, presented in this paper, is used to study the static, free vibration and buckling analysis of the simply supported functionally graded sandwich plates on elastic foundation. This theory accounts for the realistic variations of the displacements through the thickness. In the analysis, two common types of FGM sandwich plates, namely, homogeneous face sheets with FGM core and FGM face sheets with homogeneous core are considered. The elastic foundation is described by the Pasternak model. The equations of motion are derived from Hamilton's principle. The closed form solutions are obtained by using Navier technique. Numerical results of present theory are compared with three-dimensional elasticity solutions and other higher-order theories reported in the literature. It can be concluded that the proposed theory is simple and efficient in predicting the mechanical behavior of functionally graded sandwich plates. [ABSTRACT FROM AUTHOR]

The major goal of this research was to obtain a closed form of the solution for critical combined loads (combined effects of the axial load and l lateral pressure or the axial load and hydrostatic pressure) of functionally graded (FG) truncated conical shell in the framework of the shear deformation theory (SDT). The basic equations of FG truncated conical shell shells subjected to the combined loads are derived in the framework of the SDT. By using the Galerkin method to basic equations are obtained the expressions for critical combined loads of FG truncated conical shell in the framework of the SDT. In particular, similar expressions in the framework of the classical shell theory (CST) are obtained, also. Our numerical experiments reveal that the proposed solution may offer accurate critical combined loads for the FGM shells as compared with reference solutions available in the literature. Finally, the calculation and presentation of the effects of many parameters included in the analysis conclude the goals to be reached in the study. [ABSTRACT FROM AUTHOR]

Abstract: A linear finite strip plate element based on the first order shear deformation theory is considered for the analysis of viscoelastic plates. The plate end conditions are considered to be simply supported and the polynomial shape functions are used to evaluate the deflection of plates in transverse direction. The mechanical properties of the material are considered to be linear viscoelastic by expressing the relaxation modulus in terms of Prony series. The time history of maximum deflection of viscoelastic plates subjected to loading and unloading is calculated. In addition, a nonlinear procedure is used to calculate the changing of in-plane critical load of plate with time. Moreover, the effect of thickness and the interaction of biaxial loading on critical load of plate are studied. [Copyright &y& Elsevier]

Abstract: The large displacement response of tapered cantilever beams made of axially functionally graded material is investigated by the finite element method. A co-rotational beam element taking the effects of the material inhomogeneity, shear deformation and nonuniform cross section into account is formulated and employed in computing the response of the beams. The numerical results show that the large displacement response of the beam is governed by the material distribution, the taper ratio and taper type. The axial displacement at the free end of the beam is most sensitive to the taper ratio, and the transverse displacement at the point is least affected by this parameter. The influence of the length to height ratio is also investigated and highlighted. [Copyright &y& Elsevier]

Numerical investigation of buckling and free vibration of functionally graded plates considering in-plane material inhomogeneity is presented in this paper. A novel and effective approach based on isogeometric analysis (IGA) and higher-order shear deformation theory (HSDT) is developed for fulfilling that purpose, analyzing the critical buckling parameter and natural eigenvalues of functionally graded plates involving the in-plane material inhomogeneity. The HSDT allows us to account for shear deformation effect without requiring any shear correction factors. Non-uniform rational B-spline is used as basis functions, resulting in both exact geometric representation and high order approximations, enabling to easily achieve the C 1 -continuity requirement of the HSDT without any additional variables. The material properties of functionally graded plates are assumed to vary along in-plane direction. Numerical examples are presented and discussed, in which the effects of material inhomogeneity, length to thickness ratio and boundary conditions on natural frequencies and critical buckling loads are investigated. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a C° four node flat facetted shell element with drilling rotational degrees of freedom based on a first order shear deformation shell theory is developed to study the transient response of initially stressed composite sandwich folded plates. The new shell element contains three translations, two rotations of the normals about the shell mid-plane, and one drilling rotational degree of freedom per node. A consistent mass matrix formulation is employed to evaluate the total kinetic energy of the system. A generic validation study is carried out to evaluate the performance of the present finite element formulation. New results are presented for the transient analysis of initially stressed composite sandwich folded plate structures. [Copyright &y& Elsevier]

Meso-scale finite element modeling is a powerful tool to analyze the deformation of textile composite reinforcements. At the meso-scale, the yarns of the reinforcement are considered to be solids made of a continuous material in contact with their neighbors. These yarns are generally under tension, but some loadings of the reinforcement lead to a longitudinal compression state. The yarns, made up of a large number of fibers, present a specific behavior when under longitudinal compression. Local buckling of the fibers causes the compressive stiffness of the continuous material representing the yarn to be much weaker than when under tension. In addition, longitudinal compression causes an important transverse expansion. It is shown in the present work that the transverse expansion could be depicted by a Poisson ratio that remained roughly constant when the yarn length and the compression strain varied. Buckling of the fibers significantly increases the transverse dimensions of the yarn which leads to a large Poisson ratio (up to 12 for a yarn analyzed in the present study). The longitudinal compression and transverse expansion were integrated in a mechanical model of the yarn. Meso-scale finite element simulations of reinforcements with binder yarns submitted to longitudinal compression showed that these improvements led to results in good agreement with micro-CT analyses. [ABSTRACT FROM AUTHOR]

Abstract: This paper evaluates the humidity effect on the elastic properties and failure mechanism of two types of layered corrugated paperboard structures composed of entirely recycled material and virgin radiata pine (Pinus radiata D. Don) kraft and mixed fibre linerboards and fluting medium. Board samples and their component paper sheets were tested at 50% and 90% constant relative humidity (RH) under compression load and images of failure zones were obtained by serial sectioning and confocal microscopy. The compressive strength and modulus of elasticity of all components were found to be highest in the machine direction at 50% RH and lowest in the cross-machine direction at 90% RH. Virgin paper sheet components performed better in compressive performance than recycled components in both directions and at both relative humidities. In both types of corrugated board microscopic examination showed that failure under compression at 50% and 90% RH occurred along the adhesive line as well as by failure of inter-fibre bonds within the components. The combination of failure mechanisms resulted in local buckling of the boards. The elastic performance of recycled corrugated board was found to be inferior to that of virgin corrugated board at both RH conditions. [Copyright &y& Elsevier]

Abstract: The super convergent finite beam elements are newly presented for the spatially coupled stability analysis of composite beams. For this, the theoretical model applicable to the thin-walled laminated composite I-beams subjected to the axial force is developed. The present element includes the transverse shear and the warping induced shear deformation by using the first-order shear deformation beam theory. The stability equations and force–displacement relationships are derived from the principle of minimum total potential energy. The explicit expressions for the seven displacement parameters are then presented by applying the power series expansions of displacement components to simultaneous ordinary differential equations. Finally, the element stiffness matrix is determined using the force–displacement relationships. In order to demonstrate the accuracy and the superiority of the beam element developed by this study, the numerical solutions are presented and compared with the results obtained from other researchers, the isoparametric beam elements based on the Lagrangian interpolation polynomial, and the detailed three-dimensional analysis results using the shell elements of ABAQUS. The effects of shear deformation, boundary condition, fiber angle change, and modulus ratios on buckling loads are investigated in the analysis. [Copyright &y& Elsevier]

Abstract Tuning the piezoresistive behavior of conductive polymeric composites requires an in-depth understanding of the structure-property relationships and deformation mechanisms at the polymer/conductive filler interface. In this paper, the unknown sources of nonlinearity (as frequently observed for specific material systems) are identified for the flexible and stretchable chopped carbon fiber (CCF)/polydimethylsiloxane (PDMS) conductive yarns. It is found that under cyclic loading the resistance initially reduces (negative piezoresistivity) up to a specific transition strain, beyond which positive piezoresistivity is observed until the onset of unloading. Apart from the opposing effects of fiber separation and Poisson's effect, the results suggest that such nonlinearity stems from carbon fiber (CF) buckling induced by CCF/PDMS interfacial friction upon unloading. Nevertheless, a low percolation threshold (1.41 wt%) was attained along with high sensitivity (gauge factors as high as ∼60 in cyclic loading) and stretchability (up to 25%). These characteristics make the CCF/PDMS sensors suitable for 3D-printable inks and stain sensing applications. For the latter, the sensors were integrated with a picture frame shear test setup to monitor the strain along the yarns in fiberglass/polypropylene fabrics subjected to Picture Frame test. Also, the capability of the sensors was demonstrated while used as wearable devices for detecting human joint motion. Graphical abstract Image 1 Highlights • Chopped carbon fiber (CCF)/PDMS sensors fabricated by mechanical blending. • First-cycle maximum gauge factor of 700 was obtained for the 1.4 wt% CCF content. • Nonlinear piezoresistivity with negative to positive transition was observed. • Interfacial friction, CCF separation and Poisson's effect govern resistance changes. • Yarn sensors are suitable for motion detection and structural health monitoring. [ABSTRACT FROM AUTHOR]

Abstract This experimental investigation addresses the use of transversely placed composite ropes made of basalt as external standalone confining reinforcement in cases of reinforced concrete columns with square section or combined with already applied FRP sheets. Non bonded, non impregnated basalt fiber rope is wrapped around the columns by hand in 1 or 2 layers or is pre-tensioned with special mechanical devices. The efficiency of wrapped columns is compared with identical columns confined with polypropylene fiber ropes. Further, the columns are wrapped with externally bonded GFRP sheets and then with non bonded basalt fiber ropes in a hybrid scheme. The columns are subjected to multiple cycles of increasing compressive deformation to simulate seismic actions. The columns wrapped with two layers of basalt composite ropes (pre-tensioned or not) present an ever increasing stress-strain response for concrete axial strains higher than 5.6%, even for very high rope pretension level, without rope fracture. Both the polypropylene and basalt ropes reveal a high potential for strain redistribution around the variably damaged concrete core. In the cases of hybrid FRP – basalt rope confinement the strain redistribution potential of the rope is similarly remarkable, controlling the dilation of the column even after the multiple fracture of the GFRP sheet. The rope could increase the axial strain sustained by the concrete from 2.21% to beyond 5.1%, without rope fracture. [ABSTRACT FROM AUTHOR]

We investigate elastic instabilities and pattern formations in 3D-printed deformable fiber composites. We experimentally realize the instability induced patterns in the deformable 3D systems of periodically distributed fibers embedded in soft matrix. We observe that the fiber composites exhibit significant softening upon achieving the critical strain at which the stiff fibers cooperatively buckle into wavy patterns. For periodically distributed fiber composites with square in-plane periodicity, we observe the transition of the instability induced patterns from small wavelength wavy pattern to long wave mode with an increase in fiber volume fraction. Both experimental results and rigorous Bloch-Floquet numerical analysis show that the critical wavenumber and critical strain decrease with an increase in fiber volume fraction. For composites with rectangular in-plane periodicity of fibers, we observe that the cooperative buckling mode develops in the direction, where the fibers are close to each other; and an increase in the periodicity aspect ratio leads to a decrease in critical wavenumber and critical strain. In addition, we present our theoretical, numerical, and experimental results for single fiber in soft matrix system. For the single fiber system, we observe that the critical wavelength has a linear dependence on fiber diameter. An explicit formula is derived to estimate the dependence of critical wavelength on shear modulus contrast, and further verified by experimental data and numerical simulations. [ABSTRACT FROM AUTHOR]

Smart structures based on shape memory polymer composites (SMPCs) are gradually applied to the aerospace field hosting an ideal combination of properties. The damage behavior of SMPC-based smart structures with large deformations requires mechanism research to satisfy their reliability. In this study, a programmable SMPC-based locking laminate was investigated, which is expected to replace initiating explosives. Firstly, based on fiber buckling theory, fiber-reinforced SMPC locking laminate was designed and analyzed, and the safe allowable area and damage modes were determined. Additionally, the deformation test of the locking laminate based on fiber fabric reinforced SMPC showed that there is two typical damage behavior: matrix cracking and interlayer delamination. For this reason, theoretical analysis was performed to reveal the damage mechanism and initial damage location. The results indicated that the fiber bundle width, arc radius, and thickness were the influencing factors of matrix cracking, while the center angle was the influencing factor of delamination. Finally, finite element analysis shows the validity of the theoretical analysis. This research has potent inspiration and reference significance for the design of SMPC-based smart structures. [ABSTRACT FROM AUTHOR]

The paper presents an effective plate formulation based on isogeometric analysis (IGA) and a novel simple quasi-3D hyperbolic shear deformation theory (S-Q3HSDT) to study static bending, free vibration, and buckling behaviors of functionally graded plates. In S-Q3HSDT fashion, five unknowns per node are included; both shear deformation and thickness-stretching effects across the thickness are taken into account; and the awkward shear locking phenomenon is avoided. The requirement for C 1 -continuity in terms of the S-Q3DHSDT is straightforwardly possessed with the aid of inherent high-order continuity of non-uniform rational B-spline (NURBS), which serve as basis functions in our IGA formulation. The superior performance and accuracy of the proposed method is demonstrated through numerous numerical examples. The calculated results are then compared with reference solutions, investigating the effects of boundary conditions, gradient index, and other aspect ratios on mechanical responses of functionally graded plates. [ABSTRACT FROM AUTHOR]

The 3D auxetic buckling pattern in the compression process is used to design auxetic structures. However, obtaining this pattern is time consuming and unintentional. In this paper, three auxetic structures, namely, globally deformed cross-frustum (GC) structure, partially deformed cross-frustum (PC) structure, and core deformed cross-frustum (CC) structure are proposed on the basis of the 3D auxetic deformation equation. The GC structure and PC structure can stably realize the 3D auxetic property through finite element analysis and experimental verification of structures. The structural strength of the latter structure is 2–5 times greater than that of the former structure. The CC structure exhibits a 3D auxetic property during the entire compression process and has excellent structural strength, which is greater than that of the first two structures. The rotational pattern can be also realized by the CC structure within the specified parameter range. A soft crawling robot with a motion module and perception module is designed by using the proposed auxetic structures. The motion module of the soft robot is designed by using the GC structure, and the perception module is realized by using the CC structure. The combination of modules can realize different functions, including advancement and rotation. The robot can be rapidly fabricated by digital light processing and has potential application value in medical treatment and other fields. [Display omitted] [ABSTRACT FROM AUTHOR]