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The purpose of this article is to carry out the thermal buckling analysis of power and sigmoid functionally graded material Sandwich plate (P-FGM and S-FGM) under uniform, linear, nonlinear and sinusoidal temperature rise.

Thermal buckling of FGM Sandwich plates namely, FGM face with ceramic core (Type-A) and homogeneous face layers with FGM core (Type-B), incorporated with nonpolynomial shear deformation theories are considered for an analytical solution in this investigation. Effective material properties and thermal expansion coefficients of FGM Sandwich plates are evaluated based on Voigt's micromechanical model considering power and sigmoid law. The governing equilibrium and stability equations for the thermal buckling analysis are derived based on sinusoidal shear deformation theory (SSDT) and inverse trigonometric shear deformation theory (ITSDT) along with Von Karman nonlinearity. Analytical solutions for thermal buckling are carried out using the principle of minimum potential energy and Navier's solution technique.

Critical buckling temperature of P-FGM and S-FGM Sandwich plates Type-A and B under uniform, linear, non-linear, and sinusoidal temperature rise are obtained and analyzed based on SSDT and ITSDT. Influence of power law, sigmoid law, span to thickness ratio, aspect ratio, volume fraction index, different types of thermal loadings and Sandwich plate types over critical buckling temperature are investigated. An analytical method of solution for thermal buckling of power and sigmoid FGM Sandwich plates with efficient shear deformation theories has been successfully analyzed and validated.

The temperature distribution across FGM plate under a high thermal environment may be uniform, linear, nonlinear, etc. In practice, temperature variation is an unpredictable phenomenon; therefore, it is essential to have a temperature distribution model which can address a sinusoidal temperature variation too. In the present work, a new sinusoidal temperature rise is proposed to describe the effect of sinusoidal temperature variation over critical buckling temperature for P-FGM and S-FGM Sandwich plates. For the first time, the FGM Sandwich plate is modeled using the sigmoid function to investigate the thermal buckling behavior under the uniform, linear, nonlinear and sinusoidal temperature rise. Nonpolynomial shear deformation theories are utilized to obtain the equilibrium and stability equations for thermal buckling analysis of P-FGM and S-FGM Sandwich plates.

The purpose of this paper is to carry out free vibration and buckling analysis of functionally graded material (FGM) plate.

Equilibrium and stability equations of FGM rectangular plate under different boundary conditions are derived using finite element method-based inverse trigonometric shear deformation theory (ITSDT). Eight-noded rectangular plate element with seven degrees of freedom at each node is used for the present analysis. The power-law distribution method has been considered for the continuously graded variation in composition of the ceramic and metal phases across the thickness of a functionally graded plate.

The finite element formulation incorporated with ITSDT and provisions of the constitutive model of FGM plate has been implemented in a numerical code to obtain the natural frequency and critical buckling load under uniaxial and biaxial compressive load. The influence of material gradation, volume fraction index, span to thickness ratio and boundary constraints over free vibration and buckling response has been studied.

Development and validation of finite element methodology using ITSDT to predict the structural response of the FGM plates under different loading, geometric and boundary conditions.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The purpose of this paper is to formulate an algorithm for a novel damage‐coupled material law for crystalline polyethylene at finite inelastic strains followed by investigation of the influence of the aggregate representation and material parameters on the material response.

The constitutive equations are developed within the framework of continuum damage mechanics to describe crystal fragmentation caused by atomic debonding of the crystallographic planes. The material is assumed initially isotropic and homogeneous and is represented as an aggregate of randomly oriented crystals with an orthorhombic lattice. For the velocity gradient, an additive decomposition into symmetric and skew‐symmetric components is applied, where the skew‐symmetric part (spin) is decoupled from the lattice shear by means of a damage variable. Structural features such as lattice parameters and orientations, slip systems, and kinematic constraints are incorpo‐rated.

The proposed model is implemented to predict stress‐strain behaviour under uniaxial tension and damage accumulation and texture development at the different stages of deformation. In the numerical examples, the effects of the aggregate size, crystal orientations, and material parameters on the model estimates are analyzed.

The model used herein is a first attempt to analyze the influence of crystal fragmentation caused by the debonding of the crystallographic planes on the predicted mechanical behaviour and texture development of polyethylene prior to failure.

The purpose of this paper is to analyse the nonlinear flexural behaviour of laminated curved panel under uniformly distributed load. The study has been extended to analyse different types of shell panels by employing the newly developed nonlinear mathematical model.

The authors have developed a novel nonlinear mathematical model based on the higher order shear deformation theory for laminated curved panel by taking the geometric nonlinearity in Green-Lagrange sense. In addition to that all the nonlinear higher order terms are considered in the present formulation for more accurate prediction of the flexural behaviour of laminated panels. The sets of nonlinear governing equations are obtained using variational principle and discretised using nonlinear finite element steps. Finally, the nonlinear responses are computed through the direct iterative method for shell panels of various geometries (spherical/cylindrical/hyperboloid/elliptical).

The importance of the present numerical model for small strain large deformation problems has been demonstrated through the convergence and the comparison studies. The results give insight into the laminated composite panel behaviour under mechanical loading and their deformation behaviour. The effects of different design parameters and the shell geometries on the flexural responses of the laminated curved structures are analysed in detailed. It is also observed that the present numerical model are realistic in nature as compared to other available mathematical model for the nonlinear analysis of the laminated structure.

A novel nonlinear mathematical model is developed first time to address the severe geometrical nonlinearity for curved laminated structures. The outcome from this paper can be utilized for the design of the laminated structures under real life circumstances.

Aims to analyse unique deformation properties of textile materials in terms of basic mechanical properties. Models fabric deformation as a nonlinear dynamical system so that a fabric can be completely specified in terms of its mechanical behaviour under general boundary conditions. Fabric deformation is dynamically analogous to waves travelling in a fluid. A localized two‐dimensional deformation evolves through the fabric to form a three‐dimensional drape or fold configuration. The nonlinear differential equations arising in the analysis of fabric deformation belong to the Klein‐Gordon family of equations which becomes the sine‐Gordon equation in three dimensions. The sine‐Gordon equation has its origins in the study of Bäcklund Transformations in differential geometry. Describes fabric deformation as a series of transformations of surfaces, defined in terms of curvature parameters using Gaussian representation of surfaces. By considering a deformed fabric as a two‐dimensional surface, algebraically constructs analytical solutions of fabric deformation by solving the sine‐Gordon Equation. The theory of Bäcklund Transformations is used to transform a trivial solution into a series of solitary wave solutions. These analytical expressions describing the curvature parameters of a surface represent actual solutions of fabric dynamical systems.

The purpose of this paper is to study the static buckling and free vibration of continuously graded ceramic-metal beams by employing a refined higher-order shear deformation, which is also the primary goal of this paper.

The proposed model is able to catch both the microstructural and shear deformation impacts without employing any shear correction factors, due to the realistic distribution of transverse shear stresses. The material properties are supposed to vary across the thickness direction in a graded form and are estimated by a power-law model. The equations of motion and related boundary conditions are extracted using Hamilton’s principle and then resolved by analytical solutions for calculating the critical buckling loads and natural frequencies.

The obtained results are checked and compared with those of other theories that exist in the literature. At last, a parametric study is provided to exhibit the influence of different parameters such as the power-law index, beam geometrical parameters, modulus ratio and axial load on the dynamic and buckling characteristics of FG beams.

Searching in the literature and to the best of the authors’ knowledge, there are limited works that consider the coupled effect between the vibration and the axial load of FG beams based on new four-variable refined beam theory. In comparison with a beam model, the number of unknown variables resulting is only four in the general cases, as against five in the case of other shear deformation theories. The actual model represents a real distribution of transverse shear effects besides a parabolic arrangement of the transverse shear strains over the thickness of the beam, so it is needless to use of any shear correction factors.

This paper aims to study the attenuation and dispersion phenomena of shear waves in anelastic and elastic porous strips. Numerical investigations are performed for the phase and damped velocity profiles of the wave. For numerical computation purposes, water-saturated limestone and kerosene oil saturated sandstone for the first and second porous strips, respectively. Some other peculiarities have been observed and discussed.

Dispersion and attenuation characteristic of the shear wave propagations have been studied in an inhomogeneous poro-anelastic strip of finite thickness, which is clamped between an inhomogeneous poroelastic strip of finite thickness and an elastic half-space. Both the strips are initially stressed and the half-space is self-weighted. Analytical methods are used to calculate the interior deformations of the model with the involvement of special functions. The determination of the frequency equation, which includes the Bessel’s and Whittaker functions, has been obtained using the prescribed boundary conditions.

Impacts of attenuation coefficient, dissipation factor, inhomogeneities, initial stresses, Biot’s gravity, porosity and thickness ratio parameters on the velocity profile of the wave have been demonstrated through the graphical visuals. These parameters are playing an important role and working as a catalyst in affecting the propagation behaviour of the wave.

Inclusion of the concept of doubly layered initially stressed inhomogeneous porous structure of elastic and anelastic medium bedded over a self-weighted half-space medium brings a novelty to the existing literature related to the study of shear wave. It may be helpful to geologists, seismologists and structural engineers in the development of theoretical and practical studies.

There exists a clear paucity of models for curved bi-directional functionally graded (BDFG) beams wherein the material properties vary along the axis and thickness of the beam simultaneously; such structures may help fulfil practical design requirements of the future and improve structural efficiency. In this context, the purpose of this paper is to extend the analytical model developed earlier to thick BDFG circular beams by using first-order shear deformation theory which allows for a non-zero shear strain distribution through the thickness of the beam.

Smooth functional variations of the material properties have been assumed along the axis and thickness of the beam simultaneously. The governing equations developed have been solved analytically for some representative determinate circular beams. In order to ascertain the effects of shear deformation in these structures, the total strain energy has been decomposed into its bending and shear components and the effects of the beam thickness and the arch angle on the shear energy component have been studied.

Closed-form exact solutions involving through-the-thickness integrals carried out numerically are presented for the bending of circular beams under the action of a variety of concentrated/distributed loads.

The results clearly indicate the importance of capturing shear deformation in thick BDFG beams and demonstrate the capability of tuning the response of these beams to fit a wide variety of structural requirements.

The paper is devoted to presenting a systematic investigation on the mechanical model and nonlinear dynamic characteristics of spur gear system with and without input shaft crack.

Considering the backlash, load-distribution, time-varying meshing stiffness and sliding friction, the modelling of a 5DOF gear system is proposed. Likewise, stiffness and damping models under elastohydrodynamic lubrication are developed, and sliding friction between gear pair is also outlined. In particular, a cracked input shaft which affects the support stiffness is presented, and breathing crack in keyway is adopted. On this basis, the dynamic responses of a gear system with and without input shaft crack are examined using numerical method, and some classical response diagrams are given, illustrating the effect of the important parameters on the gear system.

Dynamic simulation demonstrates that there exist periodic, quasi-periodic and chaotic motions in the gear system, and rational speed of the gear pair has noteworthy effects on vibration characteristic. Besides, comparison between healthy and cracked condition of input shaft indicates that occurring of crack convert periodic motion to quasi-periodic or chaotic motion.

The results give an understanding of the operating conditions under which undesirable dynamic behavior occurs, and provide some useful information to design and diagnose such gear system with crack fault.