The Experts below are selected from a list of 48156 Experts worldwide ranked by ideXlab platform
Vladimir Mazya - One of the best experts on this subject based on the ideXlab platform.
-
Boundary Characteristic point regularity for navier stokes equations blow up scaling and petrovskii type criterion a formal approach
Nonlinear Analysis-theory Methods & Applications, 2012Co-Authors: Victor A Galaktionov, Vladimir MazyaAbstract:The three-dimensional (3D) Navier-Stokes equations less thanbrgreater than less thanbrgreater thanu(t) + (u . del)u = -del p + Delta u, divu = 0 in Q(0), (0.1) less thanbrgreater than less thanbrgr ...
-
Boundary Characteristic point regularity for navier stokes equations blow up scaling and petrovskii type criterion a formal approach
arXiv: Analysis of PDEs, 2011Co-Authors: Victor A Galaktionov, Vladimir MazyaAbstract:It is shown that Wiener's regularity of the vertex of a backward paraboloid for 3D Navier-Stokes equations with zero Dirichlet conditions on the paraboloid Boundary is given by Petrovskii's criterion for the heat equation (1934), i.e., the nonlinear convection term does not affect the regularity result.
Egge D Reese - One of the best experts on this subject based on the ideXlab platform.
-
localized microstructural characterization of a dissimilar metal electron beam weld joint from an aerospace component
Materials & Design, 2016Co-Authors: Sathiskuma Jothi, Torste Sebald, Hele Davies, Egge D ReeseAbstract:Abstract Hydrogen induced cold cracking (HICC) and hydrogen embrittlement (HE) are influenced by the microstructural evolution, residual plastic strain (i.e. local misorientation), recrystallization of grains and the resultant grain Boundary Characteristic distribution (GBCD) brought about by welding processes. HICC and HE are known to cause failures in aerospace components and it is vitally important to quantify the microstructural evolution, degree of residual plastic strain and determine the GBCD across dissimilar weld joints in order to assess the susceptibility of the weld joint to these phenomena. In this investigation a full a microstructural characterization study was carried out at various locations within and around a dissimilar weld joint of pulse-plated nickel (PP-Ni) and Inconel 718 (IN718), taken from an aerospace component. Areas examined included the base metals, weld fusion zone and heat affected zones on both sides of the weld joint, formed via electron beam welding. Scanning electron microscopy (SEM) in combination with electron backscatter diffraction (EBSD) was employed to measure the residual plastic strain, grain structure, grain size distribution, crystal orientation distribution, grain Boundary misorientation distribution and GBCD of the dissimilar metal weld joint. Finally a metallurgical examination was carried out using SEM on the IN718 HAZ in order to investigate the secondary phase precipitation arising from the welding process. The results shows large variety of GBCD, crystallographic orientation distribution, local plastic strain distribution and grain size, shape and structure distribution across dissimilar weld joint. And these localized microstructural characterized data sets need to be carefully transferred using data-driven approach in order to develop predictive multiscale material modelling for hydrogen induced cracking and hydrogen embrittlement.
R Lal - One of the best experts on this subject based on the ideXlab platform.
-
Boundary Characteristic orthogonal polynomials in the study of transverse vibrations of nonhomogeneous rectangular plates with bilinear thickness variation
Shock and Vibration, 2012Co-Authors: R Lal, Y KumarAbstract:The free transverse vibrations of thin nonhomogeneous rectangular plates of variable thickness have been studied using Boundary Characteristic orthogonal polynomials in the Rayleigh-Ritz method. Gram-Schmidt process has been used to generate these orthogonal polynomials in two variables. The thickness variation is bidirectional and is the cartesian product of linear variations along two concurrent edges of the plate. The nonhomogeneity of the plate is assumed to arise due to linear variations in Young's modulus and density of the plate material with the in-plane coordinates. Numerical results have been computed for four different combinations of clamped, simply supported and free edges. Effect of the nonhomogeneity and thickness variation with varying values of aspect ratio on the natural frequencies of vibration is illustrated for the first three modes of vibration. Three dimensional mode shapes for all the four Boundary conditions have been presented. A comparison of results with those available in the literature has been made.
-
Characteristic orthogonal polynomials in the study of transverse vibrations of nonhomogeneous rectangular orthotropic plates of bilinearly varying thickness
Meccanica, 2012Co-Authors: R Lal, Kumar YajuvindraAbstract:Effect of nonhomogeneity on the vibrational Characteristics of thin orthotropic rectangular plates of bilinearly varying thickness has been studied using Boundary Characteristic orthogonal polynomials in the Rayleigh-Ritz method. The thickness variation is taken as the Cartesian product of linear variations along two concurrent edges of the plate. The orthogonal polynomials in two variables are generated using the Gram-Schmidt process. The nonhomogeneity of the plate material is assumed to arise due to linear variations in Young’s moduli, shear modulus and density of the plate with the in-plane coordinates. Numerical results have been computed for four different combinations of clamped, simply supported and free edges. Effect of thickness variation together with varying values of aspect ratio and nonhomogeneity on the natural frequencies is illustrated for the first three modes of vibration. Three dimensional mode shapes have been presented. Comparison has been made with the known results.
-
transverse vibrations of nonhomogeneous rectangular plates of uniform thickness using Boundary Characteristic orthogonal polynomials
2010Co-Authors: R Lal, Y KumarAbstract:Analysis and numerical results for the free transverse vibrations of uniform nonhomogeneous rectangular plates have been presented using Boundary Characteristic orthogonal polynomials in the Rayleigh-Ritz method on the basis of classical plate theory for four different combinations of clamped, simply supported and free edges. Gram-Schmidt process has been used to generate these orthogonal polynomials satisfying essential Boundary conditions. The nonhomogeneity of the plate is assumed to arise due to linear variations in Young’s modulus and density of the plate material with the space coordinates. Effect of the nonhomogeneity with varying values of aspect ratio on natural frequencies is illustrated for the first three modes of vibration. Three dimensional mode shapes have been presented for all the four Boundary conditions. A comparison of results with those available in the literature shows a close agreement.
S Chakraverty - One of the best experts on this subject based on the ideXlab platform.
-
Boundary Characteristic orthogonal polynomials based galerkin and least square methods for solving bagley torvik equations
2020Co-Authors: Rajarama Mohan Jena, S ChakravertyAbstract:In this paper, efficient numerical methods for solving Bagley–Torvik (B-T) equations with variable coefficients and three-point Boundary value conditions are considered. This model is considered as a viscoelastic behavior of geological strata, metal, and glasses using fractional differential equations. Many viscoelastic materials are proposed in which derivatives of fractional-order replace the usual time derivatives of integer order. An application of such a model is the prediction of the transient response of frequency-dependent materials. As such the titled problem is challenging to solve using the efficient method(s). The fractional derivative is described in the Caputo sense. First, a linearly independent set such as \( \left\{ {1,x,x^{2} ,x^{3} , \ldots } \right\} \) is converted to Boundary Characteristic Orthogonal Polynomials (BCOPS) by Gram–Schmidt Orthogonalization process then these are used in the Galerkin and Least Square methods to reduce B-T Equations to the linear or nonlinear system of algebraic equations. Example problems are addressed to show the powerfulness and efficacy of the method.
-
free vibration of euler and timoshenko nanobeams using Boundary Characteristic orthogonal polynomials
Applied Nanoscience, 2014Co-Authors: Laxmi Behera, S ChakravertyAbstract:Vibration analysis of nonlocal nanobeams based on Euler–Bernoulli and Timoshenko beam theories is considered. Nonlocal nanobeams are important in the bending, buckling and vibration analyses of beam-like elements in microelectromechanical or nanoelectromechanical devices. Expressions for free vibration of Euler–Bernoulli and Timoshenko nanobeams are established within the framework of Eringen’s nonlocal elasticity theory. The problem has been solved previously using finite element method, Chebyshev polynomials in Rayleigh–Ritz method and using other numerical methods. In this study, numerical results for free vibration of nanobeams have been presented using simple polynomials and orthonormal polynomials in the Rayleigh–Ritz method. The advantage of the method is that one can easily handle the specified Boundary conditions at the edges. To validate the present analysis, a comparison study is carried out with the results of the existing literature. The proposed method is also validated by convergence studies. Frequency parameters are found for different scaling effect parameters and Boundary conditions. The study highlights that small scale effects considerably influence the free vibration of nanobeams. Nonlocal frequency parameters of nanobeams are smaller when compared to the corresponding local ones. Deflection shapes of nonlocal clamped Euler–Bernoulli nanobeams are also incorporated for different scaling effect parameters, which are affected by the small scale effect. Obtained numerical solutions provide a better representation of the vibration behavior of short and stubby micro/nanobeams where the effects of small scale, transverse shear deformation and rotary inertia are significant.
-
recent research on vibration of structures using Boundary Characteristic orthogonal polynomials in the rayleigh ritz method
The Shock and Vibration Digest, 1999Co-Authors: S Chakraverty, R B Bhat, Ion StiharuAbstract:Vibration analysis of arbitrary shaped structures has been of interest to structural designers for several decades. Dynamic behavior of these structures is strongly dependent on Boundary conditions, geometrical shapes, material properties, different theories, and various complicating effects. Closed-form solutions are possible only for a limited set of simple Boundary conditions and geometries. For analysis of arbitrary shaped structures, several numerical methods, such as finite element method, finite difference method, Boundary element method, and so on, are usually applied. Although such discretization methods provide a general framework for general structures, they invariably result in problems with a large number of degrees of freedom. This deficiency is overcome by using the Rayleigh-Ritz method. Recently, a tremendous amount of work has been done by using the newly developed method of Boundary Characteristic orthogonal polynomials, first proposed in 1985, with the Rayleigh-Ritz method. This method provides better accuracy of results, is more efficient and simple, and is easier for computer implementation. This paper gives a survey of the research that has been done for the analysis of vibration of various structures with different effects using this method. More than a hundred papers have been reported and discussed that use this method over the past 12 years.
-
recurrence scheme for the generation of two dimensional Boundary Characteristic orthogonal polynomials to study vibration of plates
Journal of Sound and Vibration, 1998Co-Authors: R B Bhat, S Chakraverty, Ion StiharuAbstract:The recurrence scheme presented above is quite convenient for computer implementation. Two dimensional Boundary Characteristic orthogonal polynomials have been generated using the present scheme for a variety of geometries
-
Boundary Characteristic orthogonal polynomials in numerical approximation
Communications in Numerical Methods in Engineering, 1994Co-Authors: Bani Singh, S ChakravertyAbstract:The paper describes a procedure to generate Boundary Characteristic orthogonal polynomials (BCOPs) over a domain in Rn. The method is based upon the Gram-Schmidt process of orthogonalization. The orthogonal polynomial sequence (OPS) is generated from a set of linearly independent functions which satisfy the given Boundary conditions. The procedure is illustrated by taking several examples in R2, the most important case from the application point of view. Extensive numerical work has been carried out for simple domains like the circle, square and isosceles right-angled triangle. The following cases have been considered: (a) when the BCOPs vanish on the Boundary; (b) when they and their normal derivatives vanish on the Boundary; (c) when no conditions have been imposed on the Boundary. The results for other geometries such as an ellipse, a parallelogram and an arbitrary triangle follow by some simple transformations. The procedure is also applicable to one-dimensional problems and can be easily extended to R3.
Sathiskuma Jothi - One of the best experts on this subject based on the ideXlab platform.
-
localized microstructural characterization of a dissimilar metal electron beam weld joint from an aerospace component
Materials & Design, 2016Co-Authors: Sathiskuma Jothi, Torste Sebald, Hele Davies, Egge D ReeseAbstract:Abstract Hydrogen induced cold cracking (HICC) and hydrogen embrittlement (HE) are influenced by the microstructural evolution, residual plastic strain (i.e. local misorientation), recrystallization of grains and the resultant grain Boundary Characteristic distribution (GBCD) brought about by welding processes. HICC and HE are known to cause failures in aerospace components and it is vitally important to quantify the microstructural evolution, degree of residual plastic strain and determine the GBCD across dissimilar weld joints in order to assess the susceptibility of the weld joint to these phenomena. In this investigation a full a microstructural characterization study was carried out at various locations within and around a dissimilar weld joint of pulse-plated nickel (PP-Ni) and Inconel 718 (IN718), taken from an aerospace component. Areas examined included the base metals, weld fusion zone and heat affected zones on both sides of the weld joint, formed via electron beam welding. Scanning electron microscopy (SEM) in combination with electron backscatter diffraction (EBSD) was employed to measure the residual plastic strain, grain structure, grain size distribution, crystal orientation distribution, grain Boundary misorientation distribution and GBCD of the dissimilar metal weld joint. Finally a metallurgical examination was carried out using SEM on the IN718 HAZ in order to investigate the secondary phase precipitation arising from the welding process. The results shows large variety of GBCD, crystallographic orientation distribution, local plastic strain distribution and grain size, shape and structure distribution across dissimilar weld joint. And these localized microstructural characterized data sets need to be carefully transferred using data-driven approach in order to develop predictive multiscale material modelling for hydrogen induced cracking and hydrogen embrittlement.