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The present study employs the non-polynomial shear deformation theory within the framework of isogeometric analysis to study the vibration and buckling behavior of carbon nanotubes reinforced composite plates. Owing to the higher aspect ratio of carbon nanotubes, they are prone to agglomeration in matrix. Therefore, to analyze the effect of carbon nanotubes agglomeration in composite plates, a two-parameter micromechanics model is used to determine the effective mechanical properties of the composite plate. Current study opts isogeometric analysis as numerical method, as it can represents the complex shape geometries, and provides higher-order element continuity. Higher-order element continuity is desirable for implementation of non-polynomial shear deformation theory. By the virtue of non-uniform rational B-splines, isogeometric analysis turns out to be better analysis numerical method for complex and shell structures. Governing isogeometric element equations are derived using Hamilton's principle. A detailed parametric study is also performed to investigate the effect of degree of agglomeration, thickness to length/radius ratio, different boundary conditions, and complex shape cutouts in a composite plate. The presented formulation is validated across analytical and finite element method solutions with available literature. • Implemented isogeometric framework to achieve higher-order element continuity, desirable for implementing IHSDT. • Employed the inverse hyperbolic shear deformation theory for the real displacement and stress distribution. • Considered the effect of CNT agglomeration in composite's effective properties using a two-parameter micromechanics model. • Carried out vibration and buckling analysis of carbon nanotube reinforced composite plates with complex shape cutouts. [ABSTRACT FROM AUTHOR]

In this study, the buckling and free vibration characteristics of three-phase randomly distributed carbon nanotube (CNT) reinforced fiber composite (RD-CNTRFC) beams subjected to in-plane compressive loadings and thermal environment are discussed in-depth through a semi-analytical approach. Displacement-based governing equations of motion are derived using Lagrange equation considering higher-order shear deformation theory (HSDT). The effective material properties of RD-CNTRFC are determined in two stages; firstly, effective properties of hybrid matrix (CNTs + Polymer) are evaluated using the Eshelbhy-Mori-Tanaka approach. Finally, overall effective properties of CNTRFC are estimated by implementing different homogenization techniques. The influences of temperature-dependent material properties and CNT-agglomeration are included in the derived formulation. The buckling loads and natural frequencies of RD-CNTRFC beams are computed using a typical eigenvalue solution. The influence of various boundary conditions, CNT mass fraction, CNT-agglomeration, length-to-thickness ratio, and various ply sequences are also addressed. • Semi-analytical higher order formulation of three-phase RD-CNTRFC beams is presented. • Buckling and vibration characteristics are elucidated for different boundary conditions. • Influences of CNT-agglomeration and temperature-dependent properties of materials are included. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the free vibration and buckling of laminated homogeneous and non-homogeneous orthotropic truncated conical shells under lateral and hydrostatic pressures are studied. At first, the basic relations, the modified Donnell type dynamic stability and compatibility equations have been obtained for laminated orthotropic truncated conical shells, the Young''s moduli and density of which vary piecewise continuously in the thickness direction. Applying superposition and Galerkin methods to the foregoing equations, the buckling pressures and dimensionless frequency parameter of laminated homogeneous and non-homogeneous orthotropic conical shells are obtained. The appropriate formulas for single-layer and laminated cylindrical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Finally, the effects of the number and ordering of layers, the variations of conical shell characteristics, together and separately variations of the Young''s moduli and densities of the materials of layers on the critical lateral and hydrostatic pressures, and frequency parameter are found for different mode numbers. The results are compared with other works. [Copyright &y& Elsevier]

Abstract: The vibration and buckling characteristics of sandwich plates having laminated stiff layers are studied for different degrees of imperfections at the layer interfaces using a refined plate theory. With this plate theory, the through thickness variation of transverse shear stresses is represented by piece-wise parabolic functions where the continuity of these stresses is satisfied at the layer interfaces by taking jumps in the transverse shear strains at the interfaces. The transverse shear stresses free condition at the plate top and bottom surfaces is also satisfied. The inter-laminar imperfections are represented by in-plane displacement jumps at the layer interfaces and characterized by a linear spring layer model. It is quite interesting to note that this plate model having all these refined features requires unknowns only at the reference plane. To have generality in the analysis, finite element technique is adopted and it is carried out with a new triangular element developed for this purpose, as any existing element cannot model this plate model. As there is no published result on imperfect sandwich plates, the problems of perfect sandwich plates and imperfect ordinary laminates are used for validation. [Copyright &y& Elsevier]

This paper presents a comprehensive study on bending, vibration and buckling behaviours of the zigzag and armchair nanobeams. Based on a third order shear deformation beam theory and the doublet mechanics, a finite element model is proposed and employed to solve the problems of zigzag and armchair nanobeams with various boundary conditions for the first time. The verification is performed by comparing the numerical results with those from the previous studies with respect to various boundary conditions. A number of numerical examples on zigzag and armchair nanobeams with four boundary conditions have been carried out. The effects of material length scale parameters, aspect ratio, nanobeam model and boundary conditions on the displacements, natural frequencies and buckling loads of nanobeams are investigated in details. Some new results, which are not available in open literature, are provided as references for the future studies. [Display omitted] • The structural behaviors of the zigzag and armchair nanobeams are presented. • Doublet mechanics and finite element formulation are used. • S–S, C–S, C–C and C–F boundary conditions are analyzed for the first time. [ABSTRACT FROM AUTHOR]

In this paper, we present a deep autoencoder based energy method (DAEM) for the bending, vibration and buckling analysis of Kirchhoff plates. The DAEM exploits the higher order continuity of the DAEM and integrates a deep autoencoder and the minimum total potential principle in one framework yielding an unsupervised feature learning method. The DAEM is a specific type of feedforward deep neural network (DNN) and can also serve as function approximator. With robust feature extraction capacity, the DAEM can more efficiently identify patterns behind the whole energy system, such as the field variables, natural frequency and critical buckling load factor studied in this paper. The objective function is to minimize the total potential energy. The DAEM performs unsupervised learning based on generated collocation points inside the physical domain so that the total potential energy is minimized at all points. For the vibration and buckling analysis, the loss function is constructed based on Rayleigh's principle and the fundamental frequency and the critical buckling load is extracted. A scaled hyperbolic tangent activation function for the underlying mechanical model is presented which meets the continuity requirement and alleviates the gradient vanishing/explosive problems under bending. The DAEM is implemented using Pytorch and the LBFGS optimizer. To further improve the computational efficiency and enhance the generality of this machine learning method, we employ transfer learning. A comprehensive study of the DAEM configuration is performed for several numerical examples with various geometries, load conditions, and boundary conditions. • Deep autoencoder based energy method (DAEM) with tailored activation function. • Stable and accurate results without gradient vanishing/exploding problems. • Unsupervised DAEM applied to Kirchhoff plates. [ABSTRACT FROM AUTHOR]

A micro-nano-scale Timoshenko-Ehrenfest beam model is investigated using doublet mechanics theory in the present study. The governing equations and all possible boundary conditions are obtained based on doublet mechanics model. The static bending, buckling and vibration problems of Timoshenko microbeams are examined in detail. Deflection, rotation, critical buckling loads and natural frequencies predicted by the present doublet mechanics model are obtained for simply supported micro-scale Timoshenko beams by the Navier solution method. The obtained results are compared to other classical and non-classical continuum theories. To illustrate the present doublet mechanics model, the influences of thickness to length scale parameter ratio of the considered material and slenderness ratio on static bending, buckling and vibration problems are investigated. It is shown that there are two frequency spectrums in the vibration of nanobeams similar to macro Timoshenko beams. It is interesting to note that acceptable physical frequencies (mode numbers) have an upper bound due to Van Hove singularity depending on geometrical and material properties of the beam. That fact is observed first time in the open literature by using scale dependent theories. • Statics and dynamics of Timoshenko-Ehrenfest beam model have been studied via doublet mechanics theory. • A Timoshenko-Ehrenfest beam model has been derived based on doublet mechanics theory. • Softening material behaviour occurs in doublet mechanics according to classical Timoshenko beam theory. [ABSTRACT FROM AUTHOR]

This paper investigates the thermal vibration and buckling of the functionally graded carbon nanotube reinforced composite (FG-CNTRC) quadrilateral plate using the meshless method. Four distributions of the reinforcements along the thickness direction are considered, which are the uniform distributions (UD), FG-V, FG-O and FG-X. The corresponding effective material properties including Young's modulus, mass density, Poisson's ratio and thermal expansion coefficients are estimated by the rule of mixture with the CNT efficiency parameters accounting for the size-dependence. The first-order shear deformation theory (FSDT) with the consideration of thermal effects is employed. Based on Hamilton's principle and the moving least square (MLS) approximation, the discrete governing equations for the vibration of the FG-CNTRC plate are derived. The free vibration of the regular and irregular plates with and without the temperature effect are considered respectively, and the corresponding natural frequencies and mode shapes are obtained by the eigenvalue problem. The stability analysis of the uniaxial and biaxial mechanical and thermal buckling are also conducted subsequently. The effects of the volume fraction, distribution pattern, geometrical characteristics and temperature on the buckling behaviors of the CNTRC quadrilateral plate are discussed in detail. • Thermal vibration and buckling of FG-CNTRC quadrilateral plate are investigated. • Four distributions of reinforcements along thickness direction are considered. • First-order shear deformation theory is employed to derive governing equations. • The free vibrations of the regular and irregular plates are considered. • Natural frequencies and mode shapes are obtained. [ABSTRACT FROM AUTHOR]