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The purpose of this paper is to develop a general mathematical model for the evaluation of the bending and vibration responses of the skew sandwich composite plate using higher-order shear deformation theory. The sandwich structural components are highly preferable in modern engineering application because of their desirable structural advantages despite the manufacturing and analysis complexities. The present model is developed to solve the bending and vibration problem of the skew sandwich composite plate with adequate accuracy numerically in the absence of the experimental analysis.

The skew sandwich composite plate structure is modelled in the present analysis by considering laminated face sheet in conjunction with isotropic and/or orthotropic core numerically with the help of the higher-order mathematical model. Further, the responses are computed numerically with the help of in-house computer code developed in matrix laboratory (MATLAB) environment in conjunction with finite element (FE) steps. The system governing equations are derived via variational technique for the computation of the static and the frequency responses.

The skew sandwich composite plate is investigated using the higher-order kinematic model where the transverse displacement through the thickness is considered to be linear. The convergence and the validation study of the bending and the frequency values of the sandwich structure indicate the necessary accuracy. Further, the current model has been used to highlight the applicability of the higher-order kinematics for the evaluation of the sandwich structural responses (frequency and static deflections) for different design parameters.

In the present paper, the bending and the vibration responses of the skew sandwich composite plate are analysed numerically using the equivalent single-layer higher-order kinematic theory for the isotropic and the orthotropic core numerically with the help of isoparametric FE steps. Finally, it is understood that the present model is capable of solving the sandwich structural responses with less computation cost and adequate accuracy.

The purpose of this paper is to investigate the first three stochastic natural frequencies of skewed sandwich plates, considering uncertain system parameters. To conduct the sensitivity analysis for checking the criticality of input parameters.

The theoretical formulation is developed based on higher-order-zigzag theory in accordance with the radial basis function (RBF) and stochastic finite element (FE) model. A cubic function is considered for in-plane displacement over thickness while a quadratic function is considered for transverse displacement within the core and remains constant in the facesheet. RBF is used as a surrogate model to achieve computational efficiency and accuracy. In the present study, the individual and combined effect of ply-orientation angle, skew angle, number of lamina, core thickness and material properties are considered for natural frequency analysis of sandwich plates.

Results presented in this paper illustrates that the skewness in the sandwich plate significantly affects the global dynamic behaviour of the structure. RBF surrogate model coupled with stochastic FE approach significantly reduced the computational time (more than 1/18 times) compared to direct Monte Carlo simulation approach.

The stochastic results for dynamic stability of sandwich plates show that the inevitable source uncertainties present in the input parameters result in significant variation from the deterministic value demonstrates the need for inclusive design paradigm considering stochastic effects. The present paper comprehensively establishes a generalized new RBF-based FE approach for efficient stochastic analysis, which can be applicable to other complex structures too.

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.

The purpose of this paper is to study the nonlinear forced vibration responses of delaminated composite shells in hygrothermal environments.

Finite element method using an eight-noded C0 continuity, isoparametric quadrilateral element is employed. The theoretical formulations are based on the first order shear deformation theory and von Kármán type nonlinear kinematics. For modeling the delamination, multipoint constraint algorithm is incorporated in the finite element code.

The effect of delaminations on the nonlinear transient response of delaminated composite shells is dependent not only on the size but also on the location of the delaminations and hygrothermal environments.

The present study is limited to cylindrical and spherical shells having rectangular planform containing single delamination. Studies on different shell forms having non rectangular planforms containing multiple delaminations can be taken up for future research.

Nonlinear transient response of delaminated shells in hygrothermal environments is studied for the first time. It will assist researchers of nonlinear dynamic behavior of elastic systems.

The purpose of this paper is to study the nonlinear forced vibration response of delaminated composite shells in hygrothermal environments.

Finite element method using an eight‐noded C⁰ continuity, isoparametric quadrilateral element is employed. The theoretical formulations are based on the first‐order shear deformation theory and von Kármán type nonlinear kinematics. For modeling the delamination, multipoint constraint algorithm is incorporated in the finite element code.

The paper finds that the effect of presence of delaminations on the nonlinear transient response of composite shells is dependent not only on the size, but also on the location of the delaminations and the hygrothermal environments.

The present study is limited to cylindrical and spherical shells having rectangular planform containing single delamination. Studies on different shell forms having non‐rectangular planforms containing multiple delaminations can be taken up for future research.

The value in this paper lies in that nonlinear transient response of delaminated shells in hygrothermal environments is studied for the first time. It will assist researchers of nonlinear dynamic behavior of elastic systems.

The purpose of the study is to present a frequency domain spectral finite element model (SFEM) based on fast Fourier transform (FFT) for wave propagation analysis of smart laminated composite beams with embedded delamination. For generating and sensing high-frequency elastic waves in composite beams, piezoelectric materials such as lead zirconate titanate (PZT) are used because they can act as both actuators and sensors. The present model is used to investigate the effects of parametric variation of delamination configuration on the propagation of fundamental anti-symmetric wave mode in piezoelectric composite beams.

The spectral element is derived from the exact solution of the governing equation of motion in frequency domain, obtained through fast Fourier transformation of the time domain equation. The beam is divided into two sublaminates (delamination region) and two base laminates (integral regions). The delamination region is modeled by assuming constant and continuous cross-sectional rotation at the interfaces between the base laminate and sublaminates. The governing differential equation of motion for delaminated composite beam with piezoelectric lamina is obtained using Hamilton’s principle by introducing an electrical potential function.

A detailed study of the wave response at the sensor shows that the A0 mode can be used for delamination detection in a wide region and is more suitable for detecting small delamination. It is observed that the amplitude and time of arrival of the reflected A0 wave from a delamination are strongly dependent on the size, position of the delamination and the stacking sequence. The degraded material properties because of the loss of stiffness and density in damaged area differently alter the S0 and A0 wave response and the group speed. The present method provides a potential technique for researchers to accurately model delaminations in piezoelectric composite beam structures. The delamination position can be identified if the time of flight of a reflected wave from delamination and the wave propagation speed of A0 (or S0) mode is known.

Spectral finite element modeling of delaminated composite beams with piezoelectric layers has not been reported in the literature yet. The spectral element developed is validated by comparing the present results with those available in the literature. The spectral element developed is then used to investigate the wave propagation characteristics and interaction with delamination in the piezoelectric composite beam.

Double-beam/column systems have drawn much attention in many engineering fields. This work aims to present the free and forced vibrations of a novel and complex double-column system with concentrated masses, axial loads and discrete viscoelastic supports subjected to the excitation of ground acceleration are solved by the extended Laplace transform method (ELTM).

In this work, the authors proposed an extended Laplace transform method (ELTM), which is an exact and explicit analytical method. Firstly, the mathematical model simulating the vibrations of the double-column system is reformulated with Dirac's delta function. Secondly, the exact and explicit mode shape solutions are obtained, based on which the natural frequencies and dynamic responses are obtained. An illustrating example is presented to show the validity of the proposed method. A parametric study is carried out to investigate the influences of the non-dimensional column stiffness ratio and the support stiffness ratio on the peak dynamic displacement and velocity.

It is shown that the proposed method can give exact and explicit solutions of the mode shapes and natural frequencies. It is found that the asynchronous vibrations of the proposed double-column systems can be implemented to efficiently dissipate seismic energy, as shown in the time-histories of displacement and velocity.

This research systematically studied the free and forced vibrations of the complex double-column system. The proposed extended ELTM is a general method. Its application to studying the energy dissipation capability implicates that the double-column system can be utilized to reduce responses in structures under earthquake attacks.

The proposed extended ELTM is original and powerful. Its application to study the complex double-columns system with discrete supports, concentrated masses and axial loads is novel.

The purpose of this paper is to extend the meshless local exponential basis functions (MLEBF) method to the case of nonlinear and linear, variable coefficient partial differential equations (PDEs).

The original version of MLEBF method is limited to linear, constant coefficient PDEs. The reason is that exponential bases which satisfy the homogeneous operator can only be determined for this class of problems. To extend this method to the general case of linear PDEs, the variable coefficients along with all involved derivatives are first expanded. This expanded form is evaluated at the center of each cloud, and is assumed to be constant over the entire cloud. The solution procedure is followed as in the former version. Nonlinear problems are first converted to a succession of linear, variable coefficient PDEs using the Newton-Kantorovich scheme and are subsequently solved using the aforementioned approach until convergence is achieved.

The results obtained show good performance of the method as solution to a wide range of problems. The results are compared with the well-known methods in the literature such as the finite element method, high-order finite difference method or variants of the boundary element method.

The MLEBF method is a simple yet effective tool for analyzing various kinds of problems. It is easy to implement with high parallelization potential. The proposed method addresses the biggest limitation of the method, and extends it to linear, variable coefficient PDEs as well as nonlinear ones.