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Computing the Electric and Magnetic Green’s Functions in General Electrically Gyrotropic Media
Get PDFA method for an approximate computation of the electric and magnetic Green’s functions for the time-harmonic Maxwell’s equations in the general electrically gyrotropic materials is proposed. This method is based on the Fourier transform meta-approach: the equations for electric and magnetic fields are written in terms of images of the Fourier transform with respect to space variables and as a result of it the linear algebraic systems for finding Fourier images of the columns of the Green’s functions are obtained. The explicit formulas for the solutions of the obtained systems have been found. Finally, elements of the Green’s functions are determined by the inverse Fourier transform in the space of tempered distributions. The approximate computation of the inverse Fourier transform has been implemented by MATLAB tools. The computational experiments confirm the robustness of the method
Bending, Free Vibration and Buckling Analysis of Functionally Graded Plates via Wavelet Finite Element Method
Get PDFFollowing previous work, a wavelet finite element method is developed for bending, free vibration and buckling analysis of functionally graded (FG) plates based on Mindlin plate theory. The functionally graded material (FGM) properties are assumed to vary smoothly and continuously throughout the thickness of plate according to power law distribution of volume fraction of constituents. This article adopts scaling functions of two-dimensional tensor product BSWI to form shape functions. Then two-dimensional FGM BSWI element is constructed based on Mindlin plate theory by means of two-dimensional tensor product BSWI. The proposed two-dimensional FGM BSWI element possesses the advantages of high convergence, high accuracy and reliability with fewer degrees of freedoms on account of the excellent approximation property of BSWI. Numerical examples concerning various length-to-thickness ratios, volume fraction indexes, aspect ratios and boundary conditions are carried out for bending, free vibration and buckling problems of FG plates. These comparison examples demonstrate the accuracy and reliability of the proposed WFEM method comparing with the exact and referential solutions available in literatures
Normal Stresses in an Ifnitite Elastic Body with a Locally Curved and Hollow Nanofiber
Get PDFIn the framework of the piecewise homogeneous body model with the use of the three-dimensional geometrically nonlinear exact equations of the theory of elasticity, the method developed for the determination of the stress distribution in the nanocomposites with unidirectional locally curved and hollow nanofibers is used to investigate the normal stresses acting along the nanofibers. Furthermore, it is assumed that the body is loaded at infinity by uniformly distributed normal forces which act along the nanofibers and the crosssection of the nanofibers and normal to its axial line, is a circle of constant radius along the entire nanofiber length. For the solution of considered boundary value problem, an approximate analitical method is developed by using the boundary form perturbation method. The numerical results related to stress distribution in considered body and the influence of geometrical nonlinearity to this distribution are presented and interpreted
Structural Performance of Precast and Cast-in-situ Ultra High Strength Concrete Sandwich Panel
Get PDFThis paper investigates the flexural performance of a sandwich panel made up of ultra high strength concrete (UHSC) as top and bottom skin and cold formed steel as sandwich. A novel sandwich panel has been designed such a way that bottom skin of UHSC is of precast in nature and top skin of UHSC is cast-insitu and cold formed steel (profiled sheet) as sandwich. The connection between top skin of UHSC and cold formed steel is made with self tapping screws. Flexural performance of UHSC sandwich panel has been tested under flexural loading and it is found that the post peak response of the panel is significant in terms of more energy absorption. It is observed that the final failure of the specimen is occurred by forming a dominant crack on the bottom face of the skin apart formation of many multiple cracks with increase of load. Numerical investigations have been carried out by simulating the experimental conditions and found that the response obtained through simulation is in good agreement with the corresponding experimental values. From the studies, it can be concluded that UHSC steel sandwich panels can be employed for structural and non structural applications
Inclined Plane Jet Impinging a Moving Heated Wall
Get PDFThe present work is devoted to the numerical study of the interaction of an inclined plane turbulent jet with a moving horizontal isothermal hot wall. The inclination of the jet allows the control of the stagnation point location. Numerical predictions based on statistical modeling are obtained using a second order Reynolds stress turbulence model coupled to an enhanced wall treatment. For a given impinging distance H (H =8e), the considered problem parameters are: (a) jet exit Reynolds number (Re, based on the thickness "e" of the nozzle) in the range from 10000 to 25000, (b) surface-to-jet velocity ratio Rsj from left to right; ranging between 0 and 1.75 and (c) optimal inclination angle of the jet between 0° to 25°. The calculations are in good agreement with the available data. The numerical results show that the heat transfer is greatly influenced by the velocities of the jet and the moving wall. In particular, the local Nusselt number decreases with increasing surface-to-jet velocity ratios (until Rsj=1). Optimal inclination of the jet can be used to enhance heat transfer and modify the stagnation point location. The distribution of average Nusselt number is correlated with typical problem parameters
A Fully Discrete SCNFVE Formulation for the Non-stationary Navier-Stokes Equations
Get PDFA semi-discrete Crank-Nicolson (CN) formulation about time and a fully discrete stabilized CN finite volume element (SCNFVE) formulation based on two local Gauss integrals and parameter-free with the second-order time accuracy are established for the non-stationary Navier-Stokes equations. The error estimates of the semi-discrete and fully discrete SCNFVE solutions are derived. Some numerical experiments are presented to illustrate that the fully discrete SCNFVE formulation possesses more advantages than its stabilized finite volume element formulation with the first-order time accuracy, thus validating that the fully discrete SCNFVE formulation is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes equations
On Solving Linear and Nonlinear Sixth-Order Two Point Boundary Value Problems Via an Elegant Harmonic Numbers Operational Matrix of Derivatives
Get PDFThis paper is concerned with developing two new algorithms for direct solutions of linear and nonlinear sixth-order two point boundary value problems. These algorithms are based on the application of the two spectral methods namely, collocation and Petrov-Galerkin methods. The suggested algorithms are completely new and they depend on introducing a novel operational matrix of derivatives which is expressed in terms of the well-known harmonic numbers. The basic idea for the suggested algorithms rely on reducing the linear or nonlinear sixth-order boundary value problem governed by its boundary conditions to a system of linear or nonlinear algebraic equations which can be efficiently solved by a suitable solver. The algorithms are supported by investigating the convergence and the error analysis of the used expansion. Some illustrative examples are considered aiming to ascertain the wide applicability, and the high efficiency of the suggested algorithms. The obtained numerical results are convincing and the proposed approximate solutions are very close to the analytical ones
Generalized Finite Difference Method for Numerical Solutions of Density-driven Groundwater Flows
Get PDFA combination of the generalized finite difference method (GFDM), the implicit Euler method and the Newton-Raphson method is proposed to efficiently and accurately analyze the density-driven groundwater flows. In groundwater hydraulics, the problems of density-driven groundwater flows are usually difficult to be solved, since the mathematical descriptions are a system of time- and space-dependent nonlinear partial differential equations. In the proposed numerical scheme, the GFDM and the implicit Euler method were adopted for spatial and temporal discretizations of governing equations. The GFDM is a newly-developed meshless method and is truly free from time-consuming mesh generation and numerical quadrature. Based on the concept of star in the GFDM and the movingleast- squares method, the derivatives with respect to space coordinates at every node are expressed by linear combinations of nearby function values with different weighting coefficients. After discretizations of the GFDM and the implicit Euler method, a system of nonlinear algebraic equations at every time step is yielded and then can be efficiently solved by the Newton-Raphson method. Two numerical tests including the Henry and the Elder problems were adopted to verify the accuracy and the stability of the proposed meshless numerical scheme. Besides, the numerical results were compared with other numerical and semi-analytical solutions
Nonlinear Dynamics of Duffing Oscillator with Time Delayed Term
No full textThe improved constrained optimization harmonic balance method(COHBM) is presented to solve the Duffing oscillator with time delayed term. Within the framework of the proposed method, the analytical gradients of the objective function and nonlinear quality constraints with respect to optimization variables are formulated and the sensitivity information of the Fourier coefficients can also obtained. The general formulas of the geometrically nonlinear and time delayed terms are analytically derived, which makes the calculations of nonlinear differential equations in the frequency domain easily. A stability analysis method based on the analytical formulation of the nonlinear equality constraints is presented for the nonlinear systems with time delayed. A hybrid method which combines the improved COHBM and the continuation technique is also presented to investigate the global dynamics of nonlinear delayed systems. Numerical results indicate that the Duffing system displays a wide variety of rich and interesting dynamical behaviors. It is found that the proposed method yields accurate prediction on the global dynamics of time-delayed systems than the traditional method of multiple scales
Vibration Control and Separation of a Device Scanning an Elastic Plate
Get PDFThe control and separation of a scanning device moving along an arbitrary trajectory on an elastic plate is investigated. The system is a moving mass problem and is difficult to analyze directly. A semi-analytical method for the movingmass model is presented here. Without vibration control, the separation of a vehicle from a plate is likely to happen. The mechanism of separation of a vehicle from a plate is studied. Moreover, the effects of several parameters on vibration separation and the critical speed of system are studied. An effective control methodology is proposed for suppressing vibration and separation This model is applied to simulate a system containing a device scanning a plate. Due to the complexity of the moving-mass model, it is usually approximated by the moving-load model in most literature. The analytical solution of the moving-load model is also derived here and compared to the proposed models