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The purpose of this paper is to propose an approach based on Convolution quadrature (CQ) for the modeling and the numerical treatment of impedance boundary condition.

The model is derived from a general setting. Its discretization is discussed in details by providing pseudo-codes and by performing their complexity analysis. The model is validated through several numerical experiments.

CQ provides an efficient and accurate treatment of impedance boundary conditions.

The paper suggests a new effective treatment of impedance boundary conditions.

The Convolution Quadrature Method (CQM) has been widely applied to solve transient elastodynamic problems because of its stability and generality. However, the CQM suffers from the problems of huge memory requirement in case of direct implementation in time domain or CPU time in case of its reformulation in Laplace domain. The purpose of this paper is to combine the CQM with the pseudo-initial condition method (PICM) to achieve a good balance between memory requirement and CPU time.

The combined methods first subdivide the whole analysis into a few sub-analyses, which is dealt with the PICM, namely, the results obtained by previous sub-analysis are used as the initial conditions for the next sub-analysis. In each sub-analysis, the time interval is further discretized into a number of sub-steps and dealt with the CQM. For non-zero initial conditions, the pseudo-force method is used to transform them into equivalent body forces. The boundary face method is employed in the numerical implementation. Three examples are analyzed. Results are compared with analytical solutions or FEM results and the results of reformulated CQM.

Results demonstrate that the computation time and the storage requirement can be reduced significantly as compared to the CQM, by using the combined approach.

The combined methods can be successfully applied to the problems of long-time dynamic response, which requires a large amount of computer memory when CQM is applied, while preserving the CQM stability. If the number of time steps is high, then the accuracy of the proposed approach can be deteriorated because of the pseudo-force method.

The space fractional PDEs (SFPDEs) play an important role in the fractional calculus field. Proposing a high-order, stable and flexible numerical procedure for solving SFPDEs is the main aim of most researchers. This paper devotes to developing a novel spectral algorithm to solve the FitzHugh–Nagumo models with space fractional derivatives.

The fractional derivative is defined based upon the Riesz derivative. First, a second-order finite difference formulation is used to approximate the time derivative. Then, the Jacobi spectral collocation method is employed to discrete the spatial variables. On the other hand, authors assume that the approximate solution is a linear combination of special polynomials which are obtained from the Jacobi polynomials, and also there exists Riesz fractional derivative based on the Jacobi polynomials. Also, a reduced order plan, such as proper orthogonal decomposition (POD) method, has been utilized.

A fast high-order numerical method to decrease the elapsed CPU time has been constructed for solving systems of space fractional PDEs.

The spectral collocation method is combined with the POD idea to solve the system of space-fractional PDEs. The numerical results are acceptable and efficient for the main mathematical model.

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 investigate the linear and non-linear free vibration of a functionally graded material (FGM) rotating cantilever plate in the thermal environment. The study employs the development of a non-linear mathematical model using the higher order shear deformation theory in which the traction free condition is applied to derive the simplified displacement model with seven field variables instead of nine.

A mathematical model is developed based on the higher order shear deformation theory using von-Karman type non-linearity. The rotating plate domain has been discretized into C0 eight-noded quadratic serendipity elements with node wise 7 degrees of freedom. The material properties are considered temperature dependent and graded along the thickness direction obeying a simple power law distribution in terms of the volume fraction of constituents, based on Voigt’s micromechanical method. The governing equations are derived using Hamilton’s principle and are solved using the direct iterative method.

The importance of the present mathematical model developed for numerical analysis has been stated through the comparison studies. The results provide an insight into the vibration response of FGM rotating plate under thermal environment. The influence of various parameters like setting angle, volume fraction index, hub radius, rotation speed parameter, aspect ratio, side-thickness ratio and temperature gradient on linear and non-linear frequency parameters is discussed in detail.

A non-linear mathematical model is newly developed based on C0 continuity for the functionally graded rotating plate considering the 1D Fourier equation of heat conduction. The present findings can be utilized for the design of rotating plates made up of a FGM in the thermal environment under real-life situations.

Analyses a split production system which has a single station in the first stage followed by two parallel stations in the second stage, in connection with the efficiency of the system. Develops a mathematical model using semi‐regenerative processes to study the transient behaviour of the system. Obtains systems of convolution integral equations satisfied by various state probabilities and uses an iterative numerical technique to solve these systems of convolution integral equations to evaluate various measures of system performance.

The purpose of this paper is to present a general formulation of the quadrature element method (QEM). The method is then used to investigate the free vibration of functionally graded (FG) beams with general boundary conditions and different variations of material properties.

The quadrature elements with arbitrary number of nodes and nodal distributions are established on the basis of two types of FG Timoshenko beam theories. One called TBT-1 takes the cross-sectional rotation as the unknown function and the other called TBT-2 uses the transverse shear strain as the unknown function. Explicit formulas are provided via the help of the differential quadrature (DQ) rule and thus the elements can be implemented adaptively with ease.

The suitability and computational efficiency of the proposed quadrature elements for the vibration analysis of FG beams are demonstrated. The convergence rate of the proposed method is high. The elements are shear-locking free and can yield accurate solutions with a small number of nodes for both thin and moderately thick beams. The performance of the element based on TBT-1 is better than the one based on TBT-2.

The present QEM is different from the existing one which exclusively uses Gauss–Lobatto–Legendre (GLL) nodes and GLL quadrature and thus is more general. The element nodes can be either the same or different from the integration points, making the selection of element nodes more flexible. Presented data are accurate and may be a reference for other researchers to develop new numerical methods. The QEM may be also useful in multi-scale modeling and in the analysis of civil infrastructures.

The purpose of this study is the formulation of an efficient method to compute and analyse the scattering characteristics of cracks or grooves in a conducting object, where the size of the crack is significantly larger than the wavelength of an incident plane wave.

A hybrid finite element-boundary element procedure is formulated for the computation of the scattering properties of the object, where the fast multipole method is used in the boundary integral formulation. The basic fast multipole procedure is enhanced by utilising a fast Fourier transform-based convolution algorithm for the computation of the interactions between groups of source and field elements.

The algorithm accelerates the evaluation of the group interactions and enables the reduction of the memory requirements without introducing an additional approximation into the procedure.

The fast multipole method with convolution algorithm shows to be more efficient for the computation of scattering problems with a large number of unknowns than the conventional procedure.

This study aims to demonstrate the numerical application of differential quadrature (DQ) methods and show the experimental application of free vibration analysis of fiber-metal laminated composite (FML) plates with various boundary conditions.

The FMLs are hybrid structures consisting of fiber-reinforced polymer matrix composites such as carbon, glass, aramid and different metal sheets, and are currently widely used in the automobile, aircraft and aerospace industries. Thus, free vibration analysis of these hybrid materials is necessary for the design process. The governing equations of motion are derived based on the classical plate theory. The DQ, generalized DQ (GDQ) and harmonic DQ (HDQ) differential quadrature methods have been used to solve the governing equations of an FML composite plate numerically. The accuracy and convergence of the numerical model have been verified by comparing the results available in the published literature with the results obtained from these methods. Moreover, an experimental procedure has been performed in order to compare the results against those of the numerical methods.

It is noteworthy that a high degree of similarity and accuracy was observed between the numerical results obtained by the DQ methods and the experimental results. Thus, the present study validates the applicability of the DQ methods for designing the FML composite plates.

In this study, the advantages of the DQ methods have been demonstrated differently from previous studies on the vibration analysis of the FML plates.

The main objective is to develop an efficient BEM scheme for the numerical solution of two‐dimensional heat problems. Our scheme will be of the re‐initialization type, in which the domain integrals are computed by a recursion relation which depends only on the boundary temperature and flux at previous time step. To obtain the re‐initialization approach, we will use in the integral representation formula a Green function corresponding to zero temperature in a box containing the original domain, instead of using the classical free space fundamental solution. This Green function is given in terms of the original fundamental solution plus a regular solution of the heat equation inside the domain under consideration. It can therefore be used in the integral representation formula of the heat equation (direct formulation) to obtain the solution of a heat problem in such a domain. The Green function mentioned can be obtained by the images method, and the resulting source series can also be rewritten in terms of a double Fourier series, that we will use in the domain integral of the integral representation formula to transform such integral into equivalent surface integrals.