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Sensitivity of Dynamic Response of a Simply Supported Functionally Graded Magneto-electro-elastic Plate to its Elastic Parameters
Get PDFDynamic response sensitivity of a simply supported functionally graded magneto-electro-elastic plates have been studied by combining analytical method with finite element method. The functionally graded material parameters are assumed to obey exponential law in the thickness direction. A series solution of double trigonometric function agreed with the simply supported boundary condition is adopted in the plane of the plate and finite element method is used across the thickness of the plate. The finite element model is established based on energy variational principle. The coupled electromagnetic dynamic characteristics of a simply supported functionally graded magneto- electro-elastic plate are decided by its dynamics differential equation into which displacement components, electric potential and magnetic potential as nodal degree of freedom are incorporated. Dynamic response sensitivity is defined as a partial differential of dynamic response with respect to material parameter. Sensitivity of dynamic response of a simply supported functionally graded magneto-electro-elastic plate to its elastic parameters has been studied. The influence of the different exponential factor on dynamic response sensitivity has also been investigated
Heat Transfer in FHD Boundary Layer Flow with Temperature Dependent Viscosity over a Rotating Disk
Get PDFThe present study is carried out to examine the effects of temperature dependent variable viscosity on the three dimensional steady axi-symmetric Ferrohydrodynamic (FHD) boundary layer flow of an incompressible electrically nonconducting magnetic fluid in the presence of a rotating disk. The disk is subjected to an externally applied magnetic field and is maintained at a uniform temperature. The nonlinear coupled partial differential equations governing the boundary layer flow are non dimensionalized using similarity transformations and are reduced to a system of coupled ordinary differential equations. To study the effects of temperature dependent viscosity on velocity profiles and temperature distribution within the generated boundary layer, solution of the problem is obtained by employing Finite Difference and Shooting methods, subsequently. Beside the flow profiles, skin friction coefficients, rate of heat transfer at the wall and the boundary layer displacement thickness are also calculated. All of the obtained results are validated, and discussed quantitatively and through graphs giving their physical interpretations
The JEREMI-Project on Thermocapillary Convection in Liquid Bridges. Part B: Overview on Impact of Co-axial Gas Flow.
Get PDFPure surface-tension-driven flow is a unique type of flow that can be controlled through external manipulation of thermal and/or mechanical boundary conditions at the free liquid surface where the entire driving force for the convection is generated. This unique feature has been exploited in recent studies for the active control of the flow instability. The use of forced coaxial gas streams has been proposed as a way to stabilize the Marangoni convection in liquid bridges in the planned space experiment JEREMI (Japanese and European Research Experiment on Marangoni Instabilities). It is aimed at understanding the mechanism of the instability and the role of the surface heat transfer and surface shear stresses. This overview presents corresponding preparatory experimental and numerical studies
Contribution to Improving the Performance of a Wind Turbine Using Natural Convection
Get PDFNatural Convection in a vertical channel with internal objects is encountered in several technological applications, among them particular interest of heat dissipation from electronic circuits, refrigerators, heat exchangers, nuclear reactors fuel elements, dry cooling towers, home ventilation, etc. This numerical study deals with the study of natural convection in a vertical convergent channel with a circular block. The considered parameters are 104 ≤ Ra ≤ 106, Prandtl number Pr = 0.71, channel height 10 ≤ A ≤ 30, inclination angle of the channel φ = 0,2.86°,5.74°. The size block conductivity and the block radius are assumed to be constant Λ = 100, R = 0,1 respectively. The Nusselt number and the mass flow rate are correlated with Rayleigh number. Further, the maximum kinetic energy (∆Vmax) is also evaluated
Boundary Layer Effect in Regularized Meshless Method for Laplace Equation
Get PDFThis paper presents an efficient strategy for the accurate evaluation of near-boundary solutions in the regularized meshless method (RMM), also known as the boundary layer effect associated with the boundary element method. The RMM uses the double layer potentials as its interpolation basis function. When the field point is close to the boundary, the basis function will present nearly strongand hyper-singularities, respectively, for potentials and its derivative. This paper represents the first attempt to apply a nonlinear transformation, based on sinh function, to the accurate evaluation of nearly singular kernels associated with the RMM. The accuracy and efficiency of the proposed strategy are demonstrated through several numerical examples, where the solutions at as close as 1.0E–6 distance to the boundary are accurately evaluated
Prediction of Fracture Parameters of High Strength and Ultra-high Strength Concrete Beam using Gaussian Process Regression and Least Squares
Get PDFThis paper studies the applicability of Gaussian Process Regression (GPR) and Least Squares Support Vector Machines (LSSVM) to predict fracture parameters and failure load (Pmax) of high strength and ultra-high strength concrete beams. Fracture characteristics include fracture energy (GF), critical stress intensity factor (KIC) and critical crack tip opening displacement (CTODC) Mathematical models have been developed in the form of relation between several input variables such as beam dimensions, water cement ratio, compressive strength, split tensile strength, notch depth, modulus of elasticity and output fracture parameters. Four GPR and four LSSVM models have been developed using MATLAB software for training and prediction of fracture parameters. A total of 87 data sets (input-output pairs) are used, 61 of which are used to train the model and 26 are used to test the models. The data-sets used in this study are derived from experimental results. The developed models have also been compared with the Artificial Neural Networks (ANN), Support Vector Regression (SVR) and Multivariate Adaptive Regression Splines (MARS). From the overall study, it is observed that the concept of GPR and LSSVM can be successfully applied to predict fracture parameters of high strength and ultra high strength concrete
Time-Domain BEM Analysis for Three-dimensional Elastodynamic Problems with Initial Conditions
Get PDFIn this paper, a time-domain boundary element method formulation for the analysis of three-dimensional elastodynamic problems with arbitrary, non-null initial conditions is presented. The formulation is based on the convolution quadrature method, by which the numerical stability is improved significantly. In order to take into account the non-null initial conditions in this formulation, a general method is developed to replace the initial conditions by equivalent pseudo-forces based on the pseudo-force method. The original governing equation is transformed into a new one subjected to null initial conditions. In the numerical examples, longitudinal vibrations of a free beam and a cantilevered beam are considered as the illustrative problems to evaluate the new formulation. Results are shown to be in good agreement with the analytical solutions or the finite element method solutions
A Hybrid Variational Formulation for Strain Gradient Elasticity Part I: Finite Element Implementation
Get PDFThe present paper starts with Mindlin’s theory of the strain gradient elasticity, based on three additional constants for homogeneous materials (besides the Lamé’s constants), to arrive at a proposition made by Aifantis with just one additional parameter. Aifantis’characteristic material length g2, as it multiplies the Laplacian of the Cauchy stresses, may be seen as a penalty parameter to enforce interelement displacement gradient compatibility also in the case of a material in which the microstructure peculiarities are in principle not too relevant, but where high stress gradients occur. It is shown that the hybrid finite element formulation – as proposed by Pian and generalized by Dumont for finite and boundary elements – provides a natural conceptual framework to properly deal with the interelement compatibility of the normal displacement gradients, in which “corner nodes” are not an issue. Nonsingular fundamental solutions – domain interpolation functions – are presented for two-dimensional (2D) and three-dimensional (3D) problems, with the generation of families of finite elements that may be implemented in a straightforward way. Since the experimental data available in the technical literature are still scarce and the numerical results are in part questionable, consistency is assessed by means of patch tests and by investigating the spectral properties of the matrices derived for some 2D plane strain elements. The present developments, although of academical relevance, involve too many degrees of freedom to be considered for practical applications and are actually intended as a step toward a boundary-only implementation in terms of singular fundamental solutions
Using Eulerlets to Give a Boundary Integral Formulation in Euler Flow and Discussion on Applications
Get PDFBoundary element models in inviscid (Euler) flow dynamics for a manoeuvring body are difficult to formulate even for the steady case; Although the potential satisfies the Laplace equation, it has a jump discontinuity in twodimensional flow relating to the point vortex solution (from the 2π jump in the polar angle), and a singular discontinuity region in three-dimensional flow relating to the trailing vortex wake. So, instead models are usually constructed bottom up from distributions of these fundamental solutions giving point vortex thin body methods in two-dimensional flow, and panel methods and vortex lattice methods in three-dimensional flow amongst others. Instead, the idea here is to present initially a boundary integral formulation in Euler flow that can then produce a true top down boundary element formulation. This is done for the steady two-dimensional case by matching the Euler flow to a far-field Oseen flow to determine the appropriate description for the Green’s function Eulerlets. It is then shown how this reduces to the standard point vortex representations. Finally, two applications are outlined that can be used to test this approach, that of steady flow past a semi-infinite flat plate and steady flow past circular cylinder
Approximate Analytical Solution of Time-fractional order Cauchy-Reaction Diffusion equation
Get PDFThe objective of this article is to carry out an approximate analytical solution of the time fractional order Cauchy-reaction diffusion equation by using a semi analytical method referred as the fractional-order reduced differential transform method (FRDTM). The fractional derivative is illustrated in the Caputo sense. The FRDTM is very efficient and effective powerful mathematical tool for solving wide range of real world physical problems by providing an exact or a closed approximate solution of any differential equation arising in engineering and allied sciences. Four test numerical examples are provided to validate and illustrate the efficiency of FRDTM