Nonlinear Engineering Problems Research Articles

A general analytical approach to study solute dispersion in non-Newtonian fluid flow

Abstract The homotopy analysis method (HAM), a general analytic technique for non-linear problems, is applied to analyze the solute dispersion process in non-Newtonian Carreau-Yasuda and Carreau fluids flow in a straight tube with the effect of wall absorption/reaction. Unlike the other analytical methods such as perturbation method, the HAM provides a simple way to get the convergent series solution. Any assumptions of small or high physical quantities are not required for the HAM. It provides us a great freedom to choose the so-called convergence control parameter which is used to guarantee the convergence of series solution. The convergent series solution is obtained by choosing the optimal value of convergence control parameter for which the series converges fastest. The optimal value of convergence control parameter is obtained by minimizing the square residual which also provides the convergence region for the series solution. The previous analytical studies on solute dispersion fail to justify the convergence of the series solution, whereas in this investigation, our results are convergent and valid for all physical parameters. In addition, present results are validated by the numerical and some existing results. This study explains elaborately about the advantage of the homotopy analysis method over perturbation and eigenfunction expansion methods for nonlinear problems. Owing to the great potential and flexibility of the homotopy analysis method, it is a more suitable analytical approach to solve the different types of non-linear problems in science and engineering. Besides, this study helps to gain some knowledge on the transportation process of drugs in the blood flow.

Structure of system solutions of ion sound and Langmuir dynamical models and their applications

The present study deals with the system of equations for the ion sound and Langmuir waves (SEISLWs) by employing the extended simple equation, modified F-expansion and exp $$(-\Psi (\xi ))$$ expansion methods for constructing novel exact travelling wave solutions. Graphical simulations of some solutions are helpful to study the behaviour of SEISLWs. Hence, this approach is practically effective and productive to better understand the nonlinear problems in mathematics, physics and engineering.

An analytic computation-driven algorithm for Decentralized Multicore Systems

In the modern era, increasing numbers of cores per chip are applied for decentralized systems, but there is not any appropriate symbolic computation approach to construct multicore analytic approximation. Thus, it is essential to develop an efficient, simple and unified way for decentralized Adomian decomposition method to increase the potential speed of the multicore systems. In our paper, we present an innovative parallel algorithm of constructing analytic solutions for nonlinear differential system, which based on the Adomian–Rach double decomposition method and Rach’s Adomian polynomials. Based on our algorithm, we further developed a user-friendly Python software package to construct analytic approximations of initial or boundary value problems. Finally, the scope of validity of our Python software package is illustrated by several different types of nonlinear examples. The obtained results demonstrate the effectiveness of our package by compared with exact solution and numeric method, the characteristics of each class of Adomian polynomials and the efficiency of parallel algorithm with multicore processors. We emphasis that the super-linear speedup may happens for the duration of constructing approximate solutions. So, it can be considered as a promising alternative algorithm of decentralized Adomian decomposition method for solving nonlinear problems in science and engineering.

An Automated Adaptive Finite Element Mesh Generation for Dynamics

Structural analysis remains as an essential part of any integrated civil engineering system in today’s rapidly changing computing environment. Even with enormous advancements in capabilities of computers and mobile tools, enhancing computational efficiency of algorithms is necessary to meet the changing demands for quick real time response systems. The finite element method is still the most widely used method of computational structural analysis; a robust, reliable and automated finite element structural analysis module is essential in a modern integrated structural engineering system. To be a part of an automated finite element structural analysis, an efficient adaptive mesh generation scheme based on R-H refinement for the mesh and error estimates from representative strain values at Gauss points is described. A coefficient that depends on the shape of element is used to correct overly distorted elements. Two simple case studies show the validity and computational efficiency. The scheme is appropriate for nonlinear and dynamic problems in earthquake engineering which generally require a huge number of iterative computations.

Solutions of Nonlinear Bending Problems of Plates with Complex Shapes

A high-order wavelet method is developed for general nonlinear boundary value problems with complex boundaries in mechanics. This method is established based on wavelet approximation of multiple integrals of interval bounded functions combined with an accurate and adjustable boundary extension technique. The convergence order of this approximation has been proven to be N as long as a typical family of wavelets named Coiflets with N-1 vanishing moment are adopted, which can be any positive even integers. Error analysis has proven that the proposed method is in accuracy of order N, and condition numbers of relevant matrices are almost independent of the number of collocation points. Examples of a wide range of strong nonlinear problems in engineering, especially in mechanics, including the extremely large deflection bending of plates with complex shapes, demonstrate that accuracy of the proposed method is even greater than the theoretical estimated order of N, and most interestingly, such accuracy is independent of the order of the differential equation of a problem to be solved. Comparison to existing numerical methods further justifies the accuracy and efficiency of the proposed method.

A hybridization of extended Kalman filter and Ant Colony Optimization for state estimation of nonlinear systems

In this paper, a new nonlinear heuristic filter based on the hybridization of an extended Kalman filter and an ant colony estimator is proposed to estimate the states of a nonlinear system. In this filter, a group of virtual ants searches the state space stochastically and dynamically to find and track the best state estimation while the position of each ant is updated at the measurement time using the extended Kalman filter. The performance of the proposed filter is compared with well-known heuristic filters using a nonlinear benchmark problem. The statistical results show that this algorithm is able to provide promising and competitive results. Then, the new filter is tested on a nonlinear engineering problem with more than one state. The problem is to estimate simultaneously the states of an unmanned aerial vehicle as well as the wind disturbances, applied to the system. In this case, a processor-in-the-loop experiment is also performed to verify the implementation capability of the proposed approach. This paper also investigates the real-time implementation capability of the proposed filter in the attitude estimation of a three degrees of freedom experimental setup of a quadrotor to further investigate its effectiveness in practice.

An optimal homotopy asymptotic method applied to the nonlinear thin film flow problems

Purpose This paper aims to discuss the approximate solution of the nonlinear thin film flow problems. A new analytic approximate technique for addressing nonlinear problems, namely, the optimal homotopy asymptotic method (OHAM), is proposed and used in an application to the nonlinear thin film flow problems. Design/methodology/approach This approach does not depend upon any small/large parameters. This method provides a convenient way to control the convergence of approximation series and to adjust convergence regions when necessary. Findings The obtained solutions show that the OHAM is more effective, simpler and easier than other methods. The results reveal that the method is explicit. By applying the method to nonlinear thin film flow problems, it was found to be simpler in applicability, and more convenient to control convergence. Therefore, the method shows its validity and great potential for the solution of nonlinear problems in science and engineering. Originality/value The proposed method is tested upon nonlinear thin film flow equation from the literature and the results are compared with the available approximate solutions including Adomian decomposition method (ADM), homotopy perturbation method, modified homotopy perturbation method and HAM. Moreover, the exact solution is compared with the available numerical solutions. The graphical representation of the solution is given by Maple and is physically interpreted.

On the multiscale simulation of squeezing nanofluid flow by a highprecision scheme

A novel, multiscale and precise method was used to discuss the heat and mass transfer analysis for an unsteady nanofluid flow which is squeezed between two parallel plates. Similarity solution was utilized to reduce the governing partial differential equations down to a set of ordinary differential equations (ODEs) and then the obtained nonlinear equations solved by a new multiscale method. An operational matrix of integral was established for the precise connection of function and its derivatives. The effect of parameters including nanoparticle concentration, Prandtl number, Eckert number and squeeze number on the non-dimensional velocity and temperature profiles were studied. Results of simulations showed that change in squeeze number can affect the temperature profiles remarkably and its effect is more noticeable than nano particle volume fraction. Four different kinds of nanoparticles were utilized and their influence on the temperature profile, Nusselt number and skin friction coefficient was investigated. Obtained results are illustrated graphically and compared with several numerical and semi-analytical methods from the literature. The simulations achieved by the new multiscale scheme were found to be in excellent agreement with the fourth order Runge–Kutta method and could be extended to solve other highly nonlinear engineering problems.

A novel automated MOALO algorithm aided RF low‐noise amplifier design for wireless applications

SummaryThis paper presents a Novel automated Multi Objective Ant Lion Optimization Algorithm (MOALO) aided Radio Frequency Low Noise Amplifier (RFLNA) design for wireless applications. This MO‐ALO algorithm has been used to resolve numerous nonlinear engineering problems with exceptional results. In regard of this, the MOALO algorithm is used to optimize the performance parameters of RF LNA. The RF LNA topology has a cascode structure with inductive source degeneration topology using 0.18 μm CMOS technology for wireless applications. This optimization using the MOALO algorithm is implemented using the Xilinx tool, which optimizes the active and passive parameters of RF LNA, and the optimized RF LNA is simulated using the Agilent ADS and Cadence OrCAD Capture 17.2 tools; the results are compared with the existing works. This optimized RF LNA provides high Gain, Low Noise Figure, and better Stability with less power and low circuit complexity.

An Alternate View of Dimensional Homogeneity, and Its Impact on Engineering Science

Aims:This article proposes an alternate view of dimensional homogeneity that greatly simplifies the solution of nonlinear engineering problems.Background:The conventional view of dimensional homogeneity is generally credited to Fourier (1822).Objectives:The objectives of this article are to describe the alternate view of dimensional homogeneity and to demonstrate its application to practical engineering problems.Methods:By presenting the solution of several nonlinear engineering problems, this article compares solutions based on the alternate view of dimensional homogeneity with solutions based on the conventional view.Results:Example problems demonstrate that nonlinear engineering problems are much easier to solve if the solutions are based on the alternate view of dimensional homogeneity rather than the conventional view. The relative simplicity results because the alternate view of dimensional homogeneity reduces the number of variables in nonlinear problems.Conclusion:The widely accepted view of dimensional homogeneity should be replaced by the alternate view because the solution of nonlinear engineering problems is greatly simplified.

Prediction of Excavation and Settlement of Shallow-buried Tunnel Based on Radial Basis Function Neural Network of Human Brain

Artificial neural network technology is to simulate the neural network structure of the human brain so as to solve the nonlinear engineering problem information processing system by establishing artificial neurons and sensors. The ground surface settlement caused by the excavation of shallow-buried tunnels is a research hotspot in the field of tunnels and underground engineering. By analyzing the influence factors that cause ground surface settlement, this study selects seven factors such as the cohesion and internal friction angle of surrounding rock as input and takes the measured value as the output to establish a ground surface settlement prediction model based on radial basis function neural network (RBFNN). A genetic algorithm is introduced to eliminate the slow convergence speed and local optimum of RBFNN. RBFNN prediction model can predict the ground surface settlement caused by the excavation of shallow-buried tunnels. The relative error of prediction is controlled within ±9%, and the prediction results meet the actual needs of the project. This study can provide reference for the expansion and application of RBFNN of human brain cortex in the engineering field.

Slope Stability Analysis Based on the Radial Basis Function Neural Network of the Cerebral Cortex

The artificial neural network technology simulates the neural network structure of the cerebral cortex by establishing artificial neurons and sensors to solve nonlinear engineering problems, and establishes the prediction model for solving such problems. Rock slope stability is a hot research topic in the field of geotechnical engineering, especially for those slopes affected by the cyclic changes of water level. This paper establishes a slope stability prediction model based on the radial basis function neural network (RBFNN) of the cerebral cortex and introduces the genetic algorithm to eliminate the drawbacks of the cerebral cortex RBFNN, that is, slow convergence and local optimisation. The cerebral cortex RBFNN prediction model can predict the slope safety factor, with the relative error controlled between -5.16% and 6.02%. According to the cerebral cortex RBFNN prediction results, as the water level in the tailing pond changes cyclically, the rock mechanics parameters of the slope gradually weaken, which leads to the continuous decrease of the slope safety factor. The results can provide reference for the extension and application of the cerebral cortex RBFNN in the engineering field, and serve as guidance for the specific project safety maintenance.

Nonlinear vibration of oscillatory systems using semi-analytical approach

In this paper, He\'s Variational Approach (VA) is used to solve high nonlinear vibration equations. The proposed approach leads us to high accurate solution compared with other numerical methods. It has been established that this method works very well for whole range of initial amplitudes. The method is sufficient for both linear and nonlinear engineering problems. The accuracy of this method is shown graphically and the results tabulated and results compared with numerical solutions.

Multi-Objective Optimization of EDM Process Parameters by Using Passing Vehicle Search (PVS) Algorithm

Electro-Discharge Machining (EDM) is very popular for machining high-strength conductive materials for aerospace and automotive application. These machining involve a range of processing parameters. In order to optimize these for the best performance, a trade-off has to be decided for the responses achieved through machining. Conventional algorithms have long been replaced by advanced optimization algorithms. Performance of meta-heuristic algorithms in relation to traditional deterministic approaches for multi-modal, non-linear engineering problems is very promising in recent days. In this paper, a multi-objective optimization approach is applied using a population-based meta-heuristic algorithm called Passing Vehicle Search (PVS) for optimizing process parameters of various mathematical models formulated by different authors. Different approaches depending on case have been adopted for formulating the multi-objective PVS algorithm and pareto front is obtained for each case to extract the desired results. The performance of multi-objective PVS is compared with different intelligent computing models employed in prior studies and better results are shown in case of former. This approach can be extended to various mathematical models besides those covered in the paper to obtain better optimization results.

Enriched self-adjusted performance measure approach for reliability-based design optimization of complex engineering problems

• Enriched self-adjusted PMA is developed to improve drawbacks of nonlinear engineering RBDO. • A novel merit function is proposed to adjust the modified search direction of ESMV using PMA. • The convergence performances of proposed PMA are illustrated with particular complex engineering aircraft stiffened panel. • Enriched self-adjusted mean value improves the convergence performances of the RBDO-based PMA. For reliability-based design optimization (RBDO) of practical structural/mechanical problems under highly nonlinear constraints, it is an important characteristic of the performance measure approach (PMA) to show robustness and high convergence rate. In this study, self-adjusted mean value is used in the PMA iterative formula to improve the robustness and efficiency of the RBDO-based PMA for nonlinear engineering problems based on dynamic search direction. A novel merit function is applied to adjust the modified search direction in the enriched self-adjusted mean value (ESMV) method, which can control the instability and value of the step size for highly nonlinear probabilistic constraints in RBDO problems. The convergence performance of the enriched self-adjusted PMA is illustrated using four nonlinear engineering problems. In particular, a complex engineering example of aircraft stiffened panel is used to compare the RBDO results of different reliability methods. The results demonstrate that the proposed self-adjusted steepest descent search direction can improve the computational efficiency and robustness of the PMA compared to existing modified reliability methods for nonlinear RBDO problems.

Comparison and assessment of time integration algorithms for nonlinear vibration systems

A corrected explicit method of double time steps (CEMDTS) was introduced to accurately simulate nonlinear vibration problems in engineering. The CEMDTS, the leapfrog central difference method, the Newmark method, the generalized-α method and the precise integration method were implemented in typical nonlinear examples for the purpose of comparison. Both conservative and non-conservative systems were examined. The results show that it isn’t unconditionally stable for the precise integration method, the Newmark method and the generalized-α method in nonlinear systems. The stable interval of the three methods is less than that of the CEMDTS. When a small time step (Δt≤T min/20) is employed, the precise integration method is endowed with the highest accuracy while the CEMDTS possesses the smallest computation effort. However, the CEMDTS becomes the most accurate one when the time step is large (Δt≥0.3T min) or the system is strongly nonlinear. Therefore, the CEMDTS is more applicable to the nonlinear vibration systems.

Accurate semi-analytical solution for nonlinear vibration of conservative mechanical problems

In this paper, it has been tried to propose a new semi analytical approach for solving nonlinear vibration of conservative systems. Hamiltonian approach is presented and applied to high nonlinear vibration systems. Hamiltonian approach leads us to high accurate solution using only one iteration. The method doesn\'t need any small perturbation and sufficiently accurate to both linear and nonlinear problems in engineering. The results are compared with numerical solution using Runge-Kutta-algorithm. The procedure of numerical solution are presented in detail. Hamiltonian approach could be simply apply to other powerfully non-natural oscillations and it could be found widely feasible in engineering and science.

A numerical analysis of a convective straight fin with temperature-dependent thermal conductivity

In this paper, heat transfer characteristics of a straight fin having temperature-dependent thermal conductivity were computed by using 3-D CFD analysis and MATLAB differential equation solver. The computations were performed with two different cases having both constant and linear function for thermal conductivity property. The CFD and MATLAB results were in good agreement with the data available in the literature. With the help of using these numerical techniques, fin efficiency can be improved and heat transfer rate of fins can be augmented by changing fin materials with variable thermal properties and air-flow conditions. Application of the proposed method can be effectively extended to solve the class of similar non-linear fin problems in engineering and sciences.

Local lagged adapted generalized method of moments and applications

ABSTRACTIn this work, an attempt is made for developing the local lagged adapted generalized method of moments (LLGMM). This proposed method is composed of: 1) development of the stochastic model for continuous-time dynamic process; 2) development of the discrete-time interconnected dynamic model for statistic process; 3) utilization of Euler-type discretized scheme for nonlinear and nonstationary system of stochastic differential equations; 4) development of generalized method of moment/observation equations by employing lagged adaptive expectation process; 5) introduction of the conceptual and computational parameter estimation problem; 6) formulation of the conceptual and computational state estimation scheme; and 7) definition of the conditional mean square ε-best sub-optimal procedure. The development of LLGMM is motivated by parameter and state estimation problems in continuous-time nonlinear and nonstationary stochastic dynamic model validation problems in biological, chemical, engineering, financial, medical, physical, and social sciences. The byproducts of LLGMM are the balance between model specification and model prescription of continuous-time dynamic process and the development of discrete-time interconnected dynamic model of local sample mean and variance statistic process (DTIDMLSMVSP). DTIDMLSMVSP is the generalization of statistic (sample mean and variance) drawn from the static dynamic population problems. Moreover, it is also an alternative approach to the GARCH (1,1) model and its many related variant models (e.g., EGARCH model, GJR GARCH model). It provides an iterative scheme for updating statistic coefficients in a system of generalized method of moment/observation equations. Furthermore, application of the LLGMM method to stochastic differential dynamic models for energy commodity price, U.S. Treasury bill yield interest rate U.S.–U.K. foreign exchange rate exhibits its unique role and scope.

A new model order reduction strategy adapted to nonlinear problems in earthquake engineering.

SummaryEarthquake dynamic response analysis of large complex structures, especially in the presence of nonlinearities, usually turns out to be computationally expensive. In this paper, the methodical developments of a new model order reduction strategy (MOR) based on the proper orthogonal decomposition (POD) method as well as its practical applicability to a realistic building structure are presented. The seismic performance of the building structure, a medical complex, is to be improved by means of base isolation realized by frictional pendulum bearings. According to the new introduced MOR strategy, a set of deterministic POD modes (transformation matrix) is assembled, which is derived based on the information of parts of the response history, so‐called snapshots, of the structure under a representative earthquake excitation. Subsequently, this transformation matrix is utilized to create reduced‐order models of the structure subjected to different earthquake excitations. These sets of nonlinear low‐order representations are now solved in a fractional amount of time in comparison with the computations of the full (non‐reduced) systems. The results demonstrate accurate approximations of the physical (full) responses by means of this new MOR strategy if the probable behavior of the structure has already been captured in the POD snapshots. Copyright © 2016 The Authors. Earthquake Engineering & Structural Dynamics Published by John Wiley & Sons Ltd.