Implementing the Node Based Smoothed Finite Element Method as User Element in Abaqus for Linear and Nonlinear Elasticity

In this paper,the node based smoothed-strain Abaqus user element(UEL)in the framework of finite element method is introduced.The basic idea behind of the node based smoothed finite element(NSFEM)is that finite element cells are divided into subcells and subcells construct the smoothing domain associated with each node of a finite element cell[Liu,Dai and Nguyen-Thoi(2007)].Therefore,the numerical integration is globally performed over smoothing domains.It is demonstrated that the proposed UEL retains all the advantages of the NSFEM,i.e.,upper bound solution,overly soft stiffness and free from locking in compressible and nearly-incompressible media.In this work,the constant strain triangular(CST)elements are used to construct node based smoothing domains,since any complex two dimensional domains can be discretized using CST elements.This additional challenge is successfully addressed in this paper.The efficacy and robustness of the proposed work is obtained by several benchmark problems in both linear and nonlinear elasticity.The developed UEL and the associated files can be downloaded from https://github.com/nsundar/NSFEM.

Effect of Si δ-Doping on the Linear and Nonlinear Optical Absorptions and Refractive Index Changes in InAlN/GaN Single Quantum Wells

In the framework of effective mass approximation, we theoretically investigate the electronic structure of the Si δ-doped InAIN/GaN single quantum well by solving numerically the coupled equations Schrodinger-Poisson self-consistently. The linear, nonlinear optical absorption coefficients and relative refractive index changes are calculated as functions of the doping concentration and its thickness. The obtained results show that the position and the amplitude of the linear and total optical absorption coefficients and the refractive index changes can be modified by varying the doping concentration and its thickness. In addition, it is found that the maximum of the optical absorption can be red-shifted or blue-shifted by varying the doping concentration. The obtained results are important for the design of various electronic components such as high-power FETs and infrared photonic devices.

Effects of built-in electric field and donor impurity on linear and nonlinear optical properties of wurtzite InxGa1-xN/GaN nanostructures

The linear and nonlinear optical absorption coefficients(ACs)and refraction index changes(RICs)of 1s-1p,1p-1d,and 1f-1d transitions are investigated in a wurtzite InxGa1-xN/GaN core-shell quantum dot(CSQD)with donor impurity by using density matrix approach.The effects of built-in electric field(BEF),ternary mixed crystal(TMC),impurity,and CSQD size are studied in detail.The finite element method is used to calculate the ground and excited energy state energy and wave function.The results reveal that the BEF has a great influence on the linear,nonlinear,and total ACs and RICs.The presence of impurity leads the resonant peaks of the ACs and RICs to be blue-shifted for all transitions,especially for 1s-1p transition.It is also found that the resonant peaks of the ACs and RICs present a red shift with In-composition decreasing or core radius increasing.Moreover,the amplitudes of the ACs and RICs are strongly affected by the incident optical intensity.The absorption saturation is more sensitive without the impurity than with the impurity,and the appearance of absorption saturation requires a larger incident optical intensity when considering the BEF.

Effect of size and indium-composition on linear and nonlinear optical absorption of InGaN/GaN lens-shaped quantum dot

Based on the Schr ¨odinger equation for envelope function in the effective mass approximation, linear and nonlinear optical absorption coefficients in a multi-subband lens quantum dot are investigated. The effects of quantum dot size on the interband and intraband transitions energy are also analyzed. The finite element method is used to calculate the eigenvalues and eigenfunctions. Strain and In-mole-fraction effects are also studied, and the results reveal that with the decrease of the In-mole fraction, the amplitudes of linear and nonlinear absorption coefficients increase. The present computed results show that the absorption coefficients of transitions between the first excited states are stronger than those of the ground states. In addition, it has been found that the quantum dot size affects the amplitudes and peak positions of linear and nonlinear absorption coefficients while the incident optical intensity strongly affects the nonlinear absorption coefficients.

Comparison of linear and nonlinear extreme wave statistics

An extremely large（＂freak＂） wave is a typical though rare phenomenon observed in the sea. Special theories（for example, the modulation instability theory） were developed to explain mechanics and appearance of freak waves as a result of nonlinear wave-wave interactions. In this paper, it is demonstrated that the freak wave appearance can be also explained by superposition of linear modes with the realistic spectrum. The integral probability of trough-to-crest waves is calculated by two methods： the first one is based on the results of the numerical simulation of a wave field evolution performed with one-dimensional and two-dimensional nonlinear models.The second method is based on calculation of the same probability over the ensembles of wave fields constructed as a superposition of linear waves with random phases and the spectrum similar to that used in the nonlinear simulations. It is shown that the integral probabilities for nonlinear and linear cases are of the same order of values

The Relationship between Carbon Dioxide Emission Intensity and Economic Growth in China:Cointegration,Linear and Nonlinear Granger Causality

This study is to use cointegration, linear and non-linear Granger causality test to investigate the relationship between carbon dioxide （CO2） emissionand economic growth （GDP） in China for the period 1961-2010. Our analysis shows that CO2 emission and GDP are balanced in the long-run. The results suggest that there is evidence that economic development can improve environmental degradation in the long-run. Moreover, the result of linear and non-linear Granger causality test indicates a long-run unidirectional causality running from GDP to CO2 emissions. The study suggests that in the long run, economic growth may have an adverse effect on the CO2 emissions in China. Government should take into account the environment in their current policies, which may be of great importance for policy decision-makers to develop economic policies to preserve economic growth while curbing of carbon emissions.

linear and nonlinear fractional differential equation modified Riemann–Liouville derivatives exact solutions fractional auxiliary sub-equation expansion method Mittag–Leffler function method

In this paper, the fractional auxiliary sub-equation expansion method is proposed to solve nonlinear fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional Kd V equation, the space-time fractional RLW equation, the space-time fractional Boussinesq equation, and the（3＋1）-spacetime fractional ZK equation. The solutions are expressed in terms of fractional hyperbolic and fractional trigonometric functions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The analytical solution of homogenous linear FDEs with constant coefficients are obtained by using the series and the Mittag–Leffler function methods. The obtained results recover the well-know solutions when α = 1.

Exact investigation of the electronic structure and the linear and nonlinear optical properties of conical quantum dots

Intersubband linear and third-order nonlinear optical properties of conical quantum dots with infinite barrier potential are studied. The electronic structure of conical quantum dots through effective mass approximation is determined analytically. Linear, nonlinear, and total absorption coefficients, as well as the refractive indices of GaAs conical dots, are calculated. The effects of the size of the dots and of the incident electromagnetic field are investigated. Results show that the total absorption coefficient and the refractive index of the dots largely depend on the size of the dots and on the intensity and polarization of the incident electromaenetic field.

LINEAR AND NONLINEAR BAROTROPIC INSTABILITY

Based on a non-frictional and non-divergent nonlinear barotropic vorticity equation and its solutions of travelling waves,the criteria for linear and nonlinear barotropic instability are gained respectively at an equilibrium point of the equation on a phase plane.The linear and nonlinear analytical solutions to instability waves are also found.The computational results show that if their amplitudes are equal at the initial time,the amplitude increments of nonlinear instable barotropic wave are always less than those of linear instable barotropic wave. The nonlinear effects can slow down the exponential growth of linear instability.The time needed for making the amplitude double that of initial time by instabilities,is about 6h for linear instability and about 18h for nonlinear instability,the latter is in agreement with the observations in the real atmosphere.

COMPARISON OF LINEAR AND NONLINEAR WAVES ASSOCIATED WITH STEADY-STATE FORCING SOURCES

Low-frequency phenomena in the atmosphere are intimately related to stationary waves and, in a sense, the former may even be viewed as the time-varying part of the quasi-stationary waves themselves, Much attention has been focused on nonlinear interactions in the conceptual study on stationary waves. Linear and nonlinear primitive-equation baroclinic spectral models are adopted to investigate the response of stationary waves to large- scale mechanical forcing and steady-state thermal forcing, both idealized and realistic, followed by calculations of the EP fluxes and three-dimensional wave activity fluxes (Plumb, 1985) for both the linear and nonlinear solu- tions. Results show that when the forcing source grows intense enough to be comparable to the real one, non- linear interaction becomes very important, especially for the maintenance of tropical and polar stationary waves. Care should be taken, however, in using the EP flux and Plumb's 3-D flux for diagnostic analysis of observational data as they are highly sensitive to nonlinear interaction.

Numerical Treatment of Nonlinear Volterra-Fredholm Integral Equation with a Generalized Singular Kernel

In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM) was studied. This technique is a convergent series from easily computable components. Four examples are exhibited, when the kernel takes Carleman and logarithmic forms. Numerical results uncover that the method is efficient and high accurate.

Linear polarization holography

Polarization holography is a newly researched field,that has gained traction with the development of tensor theory.It primarily focuses on the interaction between polarization waves and photosensitive materials.The extraordinary capabil-ities in modulating the amplitude,phase,and polarization of light have resulted in several new applications,such as holo-graphic storage technology,multichannel polarization multiplexing,vector beams,and optical functional devices.In this paper,fundamental research on polarization holography with linear polarized wave,a component of the theory of polariz-ation holography,has been reviewed.Primarily,the effect of various polarization changes on the linear and nonlinear po-larization characteristics of reconstructed wave under continuous exposure and during holographic recording and recon-struction have been focused upon.The polarization modulation realized using these polarization characteristics exhibits unusual functionalities,rendering polarization holography as an attractive research topic in many fields of applications.This paper aims to provide readers with new insights and broaden the application of polarization holography in more sci-entific and technological research fields.

Vibrations of revolution shells in turning-point range and applications in loudspeakers

An overview of the research conducted in the area of linear and nonlinear vibrations of loudspeakers and revolution shells was given in the turning-point frequency range in Chapter 1. It shows that some problems concerning vibrations of shells in the turning-point range have to be further studied. The linear vibrations of truncated revolution shells with the first-order turningpoint were systematically investigated in the turningpoint range from Chapter 2 to Chapter 6, including the general solutions for the free vibration, the eigenvalues under various boundary conditions, the forced vibrations driven by an edge force or an edge displacement and some related special effects, and the applications in loudspeaker vibrations. The nonlinear autoparametric vibration was examined in Chapter 7. Main results are listed as follows.

Optical and electrical properties of InGaZnON thin films

The substrate temperature(Ts)and N2 partial pressure(PN2)dependent optical and electrical properties of sputtered InGaZnON thin films are studied.With the increased Ts and PN2,the thin film becomes more crystallized and nitrified.The Hall mobility,free carrier concentration(Ne),and electrical conductivity increase with the lowered interfacial potential barrier during crystal growing.The photoluminescence(PL)intensity decreases with the increased Ne.The band gap(Eg)narrows and the linear refractive index(n1)increases with the increasing concentration of N in the thin films.The Stokes shift between the PL peak and absorption edge decreases with Eg.The n1,dispersion energy,average oscillator wavelength,and oscillator length strength all increase with n1.The single oscillator energy decreases with n1.The nonlinear refractive index and third order optical susceptibility increase with n1.The Seebeck coefficient,electron effective mass,mean free path,scattering time,and plasma energy are all Ne dependent.

Large-scale edge waves generated by a moving atmospheric pressure

Long waves generated by a moving atmospheric pressure distribution, associated with a storm, in coastal region are investigated numerically. For simplicity the moving atmospheric pressure is assumed to be moving only in the alongshore direction and the beach slope is assumed to be a constant in the on-offshore direction. By solving the linear shallow water equations we obtain numerical solutions for a wide range of physical parameters, including storm size （2a）, storm speed （U）, and beach slope （a）. Based on the numerical results, it is determined that edge wave packets are generated if the storm speed is equal to or greater than the critical velocity, Ucr, which is defined as the phase speed of the fundamental edge wave mode whose wavelength is scaled by the width of the storm size. The length and the location of the positively moving edge wave packet is roughly Ut/2 〈 y 〈 Ut, where y is in the alongshore direction and t is the time. Once the edge wave packet is generated, the wavelength is the same as that of the fundamental edge wave mode corresponding to the storm speed and is independent of the storm size, which can, however, affect the wave amplitude. When the storm speed is less than the critical velocity, the primary surface signature is a depression directly correlated to the atmospheric pressure distribution.

Evaluation of forecasting methods from selected stock market returns

Forecasting stock market returns is one of the most effective tools for risk management and portfolio diversification.There are several forecasting techniques in the literature for obtaining accurate forecasts for investment decision making.Numerous empirical studies have employed such methods to investigate the returns of different individual stock indices.However,there have been very few studies of groups of stock markets or indices.The findings of previous studies indicate that there is no single method that can be applied uniformly to all markets.In this context,this study aimed to examine the predictive performance of linear,nonlinear,artificial intelligence,frequency domain,and hybrid models to find an appropriate model to forecast the stock returns of developed,emerging,and frontier markets.We considered the daily stock market returns of selected indices from developed,emerging,and frontier markets for the period 2000–2018 to evaluate the predictive performance of the above models.The results showed that no single model out of the five models could be applied uniformly to all markets.However,traditional linear and nonlinear models outperformed artificial intelligence and frequency domain models in providing accurate forecasts.

Numerical Solutions of a Generalized Nth Order Boundary Value Problems Using Power Series Approximation Method

In this paper, a new approach called Power Series Approximation Method (PSAM) is developed for the numerical solution of a generalized linear and non-linear higher order Boundary Value Problems (BVPs). The proposed method is efficient and effective on the experimentation on some selected thirteen-order, twelve-order and ten-order boundary value problems as compared with the analytic solutions and other existing methods such as the Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) available in the literature. A convergence analysis of PSAM is also provided.

A generalized approach for implicit time integration of piecewise linear/nonlinear systems

A generalized solution scheme using implicit time integrators for piecewise linear and nonlinear systems is developed.The piecewise linear characteristic has been well‐discussed in previous studies,in which the original problem has been transformed into linear complementarity problems(LCPs)and then solved via the Lemke algorithm for each time step.The proposed scheme,instead,uses the projection function to describe the discontinuity in the dynamics equations,and solves for each step the nonlinear equations obtained from the implicit integrator by the semismooth Newton iteration.Compared with the LCP‐based scheme,the new scheme offers a more general choice by allowing other nonlinearities in the governing equations.To assess its performances,several illustrative examples are solved.The numerical solutions demonstrate that the new scheme can not only predict satisfactory results for piecewise nonlinear systems,but also exhibits substantial efficiency advantages over the LCP‐based scheme when applied to piecewise linear systems.

A NEW GENERALIZED ASYNCHRONOUS PARALLELMULTISPLITTING ITERATION METHOD

For the large sparse systems of linear and nonlinear equations, a new class of generalized asynchronous parallel multisplitting iterative method is presented, and its convergence theory is established under suitable conditions. This method not only unifies the discussions of various existing asynchronous multisplitting iterations, but also affords new algorithmic and theoretical results for the parallel solution of large sparse system of linear equations. Besides its generality, this method is also much more suitable for implementing on the MIMD multiprocessor systems.

Discrete-time based sliding-mode control of robot manipulators

Purpose-The purpose of this paper is to develop sliding mode control with linear and nonlinear manifolds in discrete-time domain for robot manipulators.Design/methodology/approach–First,a discrete linear sliding mode controller is designed to an n-link robot based on Gao’s reaching law.In the second step,a discrete terminal sliding mode controller is developed to design a finite time and high precision controller.The stability analysis of both controllers is presented in the presence of model uncertainties and external disturbances.Finally,sampling time effects on the continuous-time system outputs and sliding surfaces are discussed.Findings–Computer simulations on a three-link SCARA robot show that the proposed controllers are robust against model uncertainties and external disturbance.It was also shown that the sampling time has important effects on the closed loop system stability and convergence.Practical implications-The proposed controllers are low cost and easily implemented in practice in comparison with continuous-time ones.Originality/value-The novelty associated with this paper is the development of an approach to finite time and robust control of n-link robot manipulators in discrete-time domain.Also,obtaining an upper bound for the sampling time is another contribution of this work.