Thermoelasticity of Cylindrically Anisotropic Generally Laminated Cylinders

1976 ◽  
Vol 43 (1) ◽  
pp. 124-130 ◽  
Author(s):  
J. Padovan
Keyword(s):  
Numerical Experiments ◽  
Differential Operators ◽  
Integral Transforms ◽  
Fourier Integral ◽  
Material Anisotropy ◽  
Complex Power ◽  
Different Types ◽  
Power Series Expansions ◽  
Cylindrically Anisotropic ◽  
Stated Problem

The effects of cylindrically curvilinear mechanical and thermal material anisotropy on the stationary thermoelastic fields of generally laminated cylinders are studied. To model the stated problem, each individual ply of the cylinder is considered to be composed of both mechanically and thermally cylindrically anisotropic media whose governing fields satisfy the 3-D elasticity and conduction equations. Based on finite and infinite Fourier integral transforms together with the use of complex adjoint differential operators and complex power series expansions, a nonhomogeneous pseudo-stiffness procedure is used to develop the general solution form for the stated problem. Through the use of the model and its solution, several numerical experiments are presented which emphasize the significant effects of cylindrical material anisotropy on the governing fields of several different types of laminate configuration.

Thermoelasticity of Anisotropic Generally Laminated Slabs Subject to Spatially Periodic Thermal Loads

1975 ◽  
Vol 42 (2) ◽  
pp. 341-346 ◽  
Author(s):  
J. Padovan
Keyword(s):  
Numerical Experiments ◽  
Differential Forms ◽  
Laminated Plates ◽  
Series Expansions ◽  
Thermal Loads ◽  
Material Anisotropy ◽  
Spatially Periodic ◽  
Conduction Theory ◽  
The Given ◽  
Stated Problem

Based on 3-D thermoelasticity theory, the effects of mechanical and thermal material anisotropy on the local stationary fields of generally laminated plates are investigated. In particular, to model the stated problem, each individual lamina of the slab is considered to be composed of mechanically and thermally possibly fully anisotropic materials whose fields satisfy 3-D elasticity and conduction theory. Using complex series expansions, together with the properties of complex adjoint differential forms, a 3-D solution of the given model is obtained. Its generality is such that plates consisting of any number of distinct fully anisotropic lamina subject to arbitrary spatially periodic external and internal mechanical and thermal loads can be handled. In terms of the model and its solution, the results of several numerical experiments which emphasize the effects of material anisotropy on the governing fields of symmetric, alternating, and shingle-type laminates are reported.

COMPUTING AN ADAPTIVE MESH IN FLUID PROBLEMS USING NEURAL NETWORK AND GENETIC ALGORITHM WITH ADAPTIVE RELAXATION

2008 ◽  
Vol 17 (06) ◽  
pp. 1089-1108 ◽  
Author(s):  
NAMEER N. EL. EMAM ◽  
RASHEED ABDUL SHAHEED
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Numerical Experiments ◽  
Back Propagation ◽  
Adaptive Mesh ◽  
Learning System ◽  
Back Propagation Algorithm ◽  
Adaptive Smoothing ◽  
Different Types ◽  
Optimal Values

A method based on neural network with Back-Propagation Algorithm (BPA) and Adaptive Smoothing Errors (ASE), and a Genetic Algorithm (GA) employing a new concept named Adaptive Relaxation (GAAR) is presented in this paper to construct learning system that can find an Adaptive Mesh points (AM) in fluid problems. AM based on reallocation scheme is implemented on different types of two steps channels by using a three layer neural network with GA. Results of numerical experiments using Finite Element Method (FEM) are discussed. Such discussion is intended to validate the process and to demonstrate the performance of the proposed learning system on three types of two steps channels. It appears that training is fast enough and accurate due to the optimal values of weights by using a few numbers of patterns. Results confirm that the presented neural network with the proposed GA consistently finds better solutions than the conventional neural network.

scholarly journals -BOUNDS FOR PSEUDO-DIFFERENTIAL OPERATORS ON COMPACT LIE GROUPS

2017 ◽  
Vol 18 (3) ◽  
pp. 531-559 ◽  
Author(s):  
Julio Delgado ◽  
Michael Ruzhansky
Keyword(s):  
Phase Space ◽  
Vector Fields ◽  
Differential Operators ◽  
Compact Lie Group ◽  
Compact Lie Groups ◽  
Pseudo Differential Operators ◽  
Different Types ◽  
Unitary Dual ◽  
Laplacian Operators ◽  
Noncommutative Analogue

Given a compact Lie group$G$, in this paper we establish$L^{p}$-bounds for pseudo-differential operators in$L^{p}(G)$. The criteria here are given in terms of the concept of matrix symbols defined on the noncommutative analogue of the phase space$G\times \widehat{G}$, where$\widehat{G}$is the unitary dual of$G$. We obtain two different types of$L^{p}$bounds: first for finite regularity symbols and second for smooth symbols. The conditions for smooth symbols are formulated using$\mathscr{S}_{\unicode[STIX]{x1D70C},\unicode[STIX]{x1D6FF}}^{m}(G)$classes which are a suitable extension of the well-known$(\unicode[STIX]{x1D70C},\unicode[STIX]{x1D6FF})$ones on the Euclidean space. The results herein extend classical$L^{p}$bounds established by C. Fefferman on$\mathbb{R}^{n}$. While Fefferman’s results have immediate consequences on general manifolds for$\unicode[STIX]{x1D70C}>\max \{\unicode[STIX]{x1D6FF},1-\unicode[STIX]{x1D6FF}\}$, our results do not require the condition$\unicode[STIX]{x1D70C}>1-\unicode[STIX]{x1D6FF}$. Moreover, one of our results also does not require$\unicode[STIX]{x1D70C}>\unicode[STIX]{x1D6FF}$. Examples are given for the case of$\text{SU}(2)\cong \mathbb{S}^{3}$and vector fields/sub-Laplacian operators when operators in the classes$\mathscr{S}_{0,0}^{m}$and$\mathscr{S}_{\frac{1}{2},0}^{m}$naturally appear, and where conditions$\unicode[STIX]{x1D70C}>\unicode[STIX]{x1D6FF}$and$\unicode[STIX]{x1D70C}>1-\unicode[STIX]{x1D6FF}$fail, respectively.

scholarly journals The Bessel Expansion of Fourier Integral on Finite Interval

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 607
Author(s):  
Yongxiong Zhou ◽  
Zhenyu Zhao
Keyword(s):  
Bessel Function ◽  
Numerical Experiments ◽  
Complex Analysis ◽  
Finite Interval ◽  
Fourier Integral ◽  
Type Method ◽  
Function Expansion ◽  
Oscillation Frequencies

In this paper, we further extend the Filon-type method to the Bessel function expansion for calculating Fourier integral. By means of complex analysis, this expansion is effective for all the oscillation frequencies. Namely, the errors of the expansion not only decrease as the order of the derivative increases, but also decrease rapidly as the frequency increases. Some numerical experiments are also presented to verify the effectiveness of the method.

On Viscoelasticity and Standing Waves in Tires

1976 ◽  
Vol 4 (4) ◽  
pp. 233-246 ◽  
Author(s):  
J. Padovan
Keyword(s):  
Exact Solution ◽  
Standing Wave ◽  
Wave Phenomenon ◽  
Numerical Experiments ◽  
Standing Waves ◽  
Structural Damping ◽  
Resonance Response ◽  
Foundation Model ◽  
Stated Problem ◽  
Classical Ring

Abstract Based on the classical ring on foundation model for the tire, the effect which structural damping has on the development of the standing wave phenomenon is investigated. In particular, the model employed consists of a rotating ring on foundation where, in addition to including Coriolis effects, Kelvin-Voigt-type viscoelasticity is admitted in both the ring and foundation. Enforcing strict periodicity in space and time, the exact solution is obtained to the stated problem. Several parametric numerical experiments employing this solution are reported. These demonstrate that the standing wave phenomenon in tires is essentially a viscoelastic-type resonance response.

Local Clustering Organization (LCO) Solving a Large-Scale TSP

2005 ◽  
Vol 17 (5) ◽  
pp. 560-567 ◽  
Author(s):  
Masashi Furukawa ◽  
◽  
Michiko Watanabe ◽  
Yusuke Matsumura ◽  
◽  
...  
Keyword(s):  
Traveling Salesman Problem ◽  
Numerical Experiments ◽  
Large Scale ◽  
The Self ◽  
Traveling Salesman ◽  
Self Organizing Map ◽  
Two Cities ◽  
Local Clustering ◽  
Different Types ◽  
The Traveling Salesman Problem

The traveling salesman problem (TSP) is one of the most difficult problems that occur in different types of industrial scheduling situations. We propose a solution, involving local clustering organization (LCO), for a large-scale TSP based on the principle of the self-organizing map (SOM). Although the SOM can solve TSPs, it is not applicable to practical TSPs because the SOM references city coordinates and assigns synapses to coordinates. LCO indirectly uses the SOM principle and, instead of city coordinates, references costs between two cities, to determine the sequence of cities. We apply LCO to a large-scale TSP to determine its efficiency in numerical experiments. Results demonstrate that LCO obtains the desired solutions.

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