Automatic two- and three-dimensional mesh generation based on fuzzy knowledge processing

This paper describes the development of a novel automatic FEM mesh generation algorithm based on the fuzzy knowledge processing technique.A number of local nodal patterns are stored in a nodal pattern database of the mesh generation system. These nodal patterns are determined a priori based on certain theories or past experience of experts of FEM analyses. For example, such human experts can determine certain nodal patterns suitable for stress concentration analyses of cracks, corners, holes and so on. Each nodal pattern possesses a membership function and a procedure of node placement according to this function. In the cases of the nodal patterns for stress concentration regions, the membership function which is utilized in the fuzzy knowledge processing has two meanings, i.e. the closeness of nodal location to each stress concentration field as well as nodal density. This is attributed to the fact that a denser nodal pattern is required near a stress concentration field. What a user has to do in a practical mesh generation process are to choose several local nodal patterns properly and to designate the maximum nodal density of each pattern. After those simple operations by the user, the system places the chosen nodal patterns automatically in an analysis domain and on its boundary, and connects them smoothly by the fuzzy knowledge processing technique. Then triangular or tetrahedral elements are generated by means of the advancing front method. The key issue of the present algorithm is an easy control of complex two- or three-dimensional nodal density distribution by means of the fuzzy knowledge processing technique.To demonstrate fundamental performances of the present algorithm, a prototype system was constructed with one of object-oriented languages, Smalltalk-80 on a 32-bit microcomputer, Macintosh II. The mesh generation of several two- and three-dimensional domains with cracks, holes and junctions was presented as examples.     

Fuzzy Reliability Analysis of the Washing System in a Paper Plant for Components with Different Membership Function

The washing system in paper plant is a complex engineering system that needs to develop effective maintenance programs for enhancing its performance via reliability analysis. The reliability analysis of these systems require precise numerical data which may be very difficult to obtain in desired crisp form due to uncertainty. In general, triangular fuzzy number are used to quantify data uncertainty and fuzzy arithmetic operations are employed which give vide range of prediction for each computed reliability index due to accumulating phenomenon of fuzziness. To reduce the range of prediction of system reliability and fasten the computation process, this paper presents \(T_\omega \) (weakest t-norm) based generalized fuzzy lambda–tau technique in which different fuzzy membership functions are used to quantify uncertainty while \(\alpha \)-cut and \(T_\omega \) based approximate fuzzy arithmetic operations are employed for computation. The advantage of this technique is that this technique uses different fuzzy numbers as input to quantify different types of uncertainties and gives fuzzy reliability indices of the system having shape preserving characteristic, fitter decision values with compressed range of prediction under vague environment which is better for strong decision making to improve system performance. To show the effectiveness of the presented approach, computed results have been compared with results obtained from four other existing approaches. Moreover, this paper uses extended Tanaka et al. (Komal in Ocean Eng 155:278–294, 2018b) approach to rank the critical components of the system. Sensitivity, long run reliability and availability analyses have also been conducted to analyse the impact of variation of different reliability indices and time respectively on system performance.     

Natural language estimates of nonlinear response structural sensitivity

In many cases attempts to employ numeric, or quantitative, methods to contruct adequate computer models of real engineering situations fall definitely short of expectations. It is believed that one of the reasons may be the computer inability to process imprecise, or fuzzy, terms like very low, about four to six, etc., which are typical of any judgements made by humans. The objective of the paper is to propose a computer-assisted algorithm for assessing nonlinear response structural sensitivity to imperfections. The fuzzy set theory is used to represent imperfections in terms of the natural language expressions. Both the theory and an illustrative example are meant to display the significance of such an approximate reasoning in getting realistic estimates for structural sensitivity.     

On the Laplace transform of a matrix of fundamental solutions for thermoelastic plates

The Laplace transform of a matrix D(x,t) of fundamental solutions for the partial differential operator describing the time-dependent bending of thermoelastic plates with transverse shear deformation is constructed, and its asymptotic behavior near the origin is investigated. The differential system is reduced to an algebraic one through the application of the Laplace and then Fourier transformations, and all possible cases of roots of the determinant of the latter system are considered. It is shown that in every case, the asymptotic expansion of near the origin has the same dominant term. This is an important step in the construction of boundary-element methods for the above time-dependent model because it determines the nature of the singularity of the kernel of the boundary-integral-equations associated with various initial-boundary-value problems for the governing system.     

Interpretation of the time axis from the standpoint of the theory of fuzzy sets

The time axis is interpreted from the standpoint of the theory of fuzzy sets. It is shown that a continuous, uniformly dense fragment of the time axis can be obtained from a sequence of fuzzy time intervals, each of which is constructed from two consecutive time marks.Translated from Izmeritel'naya Tekhnika, No. 8, pp. 32–34, August, 1993.     

An approximate analytical 2D-solution for the stresses and strains in eigenstrained cubic materials

Summary Continuous and discrete Fourier transforms (CFT and DFT, respectively) are used to derive a formal solution for the Fourier transforms of stresses and strains that develop in elastically homogeneous but arbitrarily eigenstrained linear-elastic bodies. The solution is then specialized to the case of a dilatorically eigenstrained cylindrical region in an infinite matrix, both of which are made of the same cubic material with the same orientation of principal axes. In the continuous case all integrations necessary for the inverse Fourier transformation can be carried out explicitly provided the material is slightly cubic. This results in an approximate but analytical expression for the stresses and strains in physical space. Moreover, the stress-strain fields inside of the inclusion prove to be of the Eshelby type, i.e., they are homogeneous and isotropic. The range of validity of the analytical solution is assessed numerically by means of discrete Fourier transforms (DFT). It is demonstrated that even for strongly cubic materials the stresses and strains are quite well represented by the aforementioned approximate solution. Moreover, the total elastic energy of two eigenstrained cylindrical inclusions in slightly cubic material with the same orientation of their principal axes is calculated analytically by means of CFT. The minimum of the energy is determined as a function of the relative position of the two inclusions with respect to the crystal axes and it is used to explain the formation of textures in cubic materials.     

Note on “A fuzzy approach to transport optimization problem”

In the article (Sudhagar and Ganesan in Optim Eng  10.1007/s11081-012-9202-6) Sudhagar and Ganesan presented an algorithm to solve a fuzzy transportation problem without converting it into a crisp transportation problem based upon score method of ranking fuzzy numbers. Using an example we show that their method will not always lead to a fuzzy optimal solution. Specially, we give a non negative fuzzy solution for the numerical example solved by them which has less total fuzzy transportation cost.     

Stokes flow for a stokeslet between two parallel flat plates

Summary Velocity and pressure fields for Stokes flow due to a force singularity of arbitrary orientation and arbitrary distance between two parallel plates are found, using the image technique and a Fourier transform. Two alternative expressions for the solution, one in terms of infinite integrals and the other in terms of infinite series, are given. The infinite series solution is especially suitable for computation purposes being an exponentially decreasing series. From the series the far field behaviour is extracted. It is found that a force singularity parallel to the two planes has a far field behaviour of source and image for the parallel components (a two dimensional source doublet of height-dependent strength) whereas the normal component, and all fields due to a force singularity normal to the planes, die out exponentially. Velocity fields are compared with those of the one plane case. An estimate of the influence of the second wall and when its effect can be disregarded is obtained.     

Fast Solution of 3D-Elasticity Problem of a Planar Crack of Arbitrary Shape

A planar crack of an arbitrary shape in a homogeneous elastic medium is considered. The problem is reduced to integral equation for the crack opening vector. Its numerical solution utilizes Gaussian approximating functions that drastically simplify construction of the matrix of a linear algebraic system of the discretized problem. For regular grids of approximating nodes, this matrix turns out to have the Teoplitz structure. It allows one to use the Fast Fourier Transform algorithms for calculation of the matrix-vector products in the process of iterative solution of the discretized problem. The method is applied to a crack bounded by the curve for 0.2 ≤ p ≤ 4. The contribution of a crack to the overall effective elastic constants is calculated.     

A note on “A fuzzy approach to transport optimization problem”

Sudhagar and Ganesan (Optim Eng, 2012, doi: 10.1007/s11081-012-9202-6) proposed an approach to find the fuzzy optimal solution of such fuzzy transportation problems in which all the parameters are represented by fuzzy numbers. In this note, it is pointed out that the authors have used some mathematical incorrect assumptions in their proposed method.     

Fuzzy Motion-Adaptive Interpolation With Picture Repetition Detection for Deinterlacing

A novel fuzzy motion-adaptive deinterlacing algorithm is presented in this paper. It uses fuzzy logic to interpolate between two processing modes, i.e., a spatial $(I_{S})$ and a temporal $(I_{T})$ interpolator. Furthermore, the temporal interpolator employs a very simple fuzzy inference system to implement a smart temporal interpolation that locally adapts to the features of the television (TV) material, such as possible picture repetition modes in the fields or in part of the fields (hybrid material). The combination of both systems provides effective results with a low cost in terms of computational resources.      

Strain analysis by mismatch moire method and grid method using Fourier transform

We have formerly presented a new method of the moire analysis of strain using the Fourier transform. It uses the phase information of the moire fringe brightness. By shifting the Fourier spectrum of the image of deformed grating lines, we obtain the complex moire pattern. Strain distribution is given as the derivatives of the phases of the complex moire fringes. The analysis is completely automated by digital image processing. All of the laborious and subjective procedures required in the conventional analysis such as fringe sign determination, fringe ordering and fringe interpolation are thus eliminated, and objective, fast and accurate analysis can be made.In this paper, we develop the method to a mismatch method and a grid method. We show some applications for analyzing strain distribution by using this method.     

Fuzzy computer-aided design of process manufacturing facilities

Preliminary design of process manufacturing facilities involves, among other things, the synthesis of detailed layout designs. In current practice, this spatial design process is very labor-intensive and expensive. This paper describes a prototype CAD system which models design decision-making, providing a computable framework for automation. The CAD system performs auto-elicitation of an expert's judgment in the form of fuzzy sets using interactive computer graphics. These fuzzy sets are then used in a heuristic search process employing multi-objective, non-linear optimization. Designs synthesized by this fuzzy CAD system are comparable to those generated by hand, and in some cases exceed a practitioner's design in quality. The CAD system, as presently constructed, provides multiple solutions. Conclusions and recommendations regarding processing speed and unrepresented heuristic content are made.     

Selection of Modeling Criteria in the Development of Systems for Excitation of the Active Medium for Gas‐Discharge Lasers

It is shown that an algorithm for selection of modeling criteria that lies in isolating the most general features of the objects studied can lead to such investigational methods as methods of dimensional theory and similarity theory. Similarity relations for electrodeless gas discharges are given that are obtained based on the above algorithm. A design technique is presented for a system for excitation of the active medium for CO₂ lasers with pumping by a nonselfmaintained discharge and preionization by an electrodeless pulsed discharge.     

The velocity field in quantum hydrodynamics

In the usual form of quantum hydrodynamics the velocity field is defined in terms of the inverse density operator ^–1(x). It is found that this inverse does not exist. An unambiguous velocity field can, however, be constructed without the use of ^–1(x) by requiring that its Fourier components be canonical conjugates to the corresponding Fourier components of the density operator when the system is in a box with periodic boundary conditions. This velocity field has at mostN nonzero Fourier components whereN is the number of particles in the system; it satisfiesj(x)=1/2[(x)v(x)+v(x)(x)]; it has the proper behavior under galilean transformations; and the corresponding classical field is uniquely determined at theN particle positions, where it is equal to the particle velocity, and is a smooth interpolating field between these points. The velocity is not defined uniquely at positions where there are no particles, but this is a reflection of the atomicity of the system—a field uniquely defined at each point in space would represent a continuum with an infinity of degrees of freedom. The commutation relations of the velocity field with itself and with the current density are derived and found to be similar but not identical to those given by Landau.Based on work performed under the auspices of the U.S. Atomic Energy Commission     

Statistical analysis of speckle fields in digital laser monitoring of the microstructure of paper

It has been shown that digital dynamic speckle photography is an effective method for quantitative diagnostics of changes in the structure of paper processed by pulsed discharge. A theory of the dynamic statistics of speckle fields and mathematical relations are given. In using optical magnification = 1, the software developed permits fast statistical processing of up to 250,000 microzones in a two-dimensional CCD image of size 20 × 30 mm. The results obtained point to a high spatial and temporal resolution of the method and the possibility of its real-time realization. It has been shown that noise filtering is an important part of speckle image processing. The software permits filtering both in direct calculation of the correlation function and in the Fourier plane with the use of the fast Fourier transform. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 4, pp. 127–137, July–August, 2007.     

Chemical solution method for fabrication of nanocrystalline iron(III) oxide thin films

A chemical solution technique for preparation of nanocrystalline iron(III) oxide thin films is developed. The deposition process is essentially based on the thermal decomposition of urea. The as-deposited and post-deposition heat-treated materials were characterized by X-ray analysis and Fourier transform infrared (FTIR) spectroscopy. Basic optical and electrical investigations were also performed. X-ray analysis confirmed that post-deposition heat-treated material is nontextured -iron(III) oxide, with an average crystal size of 22 nm. The optical investigations show that the absorption of films (as-deposited and post-deposition treated) gradually decreases with an increase of the wavelength in the 390–820 nm region. The optical band gap for the as-deposited and post-deposition heat-treated films was determined to be 3.2 eV and 2.0 eV, respectively. The obtained -Fe₂O₃ thin films exhibit a rather high resistivity at room temperature. However, our preliminary qualitative investigations have shown that the room temperature resistivity of -Fe₂O₃ thin films is highly sensitive to moisture, indicating their potential applicability in moisture sensing systems.     

Strategy for solving semi-analytically three-dimensional transient flow in a coupled <Emphasis Type="Italic">N</Emphasis>-layer aquifer system

Efficient strategies for solving semi-analytically the transient groundwater head in a coupled N-layer aquifer system , i = 1, ... , N, with radial symmetry, with full z-dependency, and partially penetrating wells are presented. Aquitards are treated as aquifers with their own horizontal and vertical permeabilities. Since the vertical direction is fully taken into account, there is no need to pose the Dupuit assumption, i.e., that the flow is mainly horizontal. To solve this problem, integral transforms will be employed: the Laplace transform for the t-variable (with transform parameter p), the Hankel transform for the r-variable (with transform parameter α) and a particular form of a generalized Fourier transform for the vertical direction z with an infinite set of eigenvalues (with the discrete index m). It is possible to solve this problem in the form of a semi-analytical solution in the sense that an analytical expression in terms of the variables r and z, transform parameter p, and eigenvalues of the generalized Fourier transform can be given or in terms of the variables z and t, transform parameter α, and eigenvalues . The calculation of the eigenvalues and the inversion of these transformed solutions can only be done numerically. In this context the application of the generalized Fourier transform is novel. By means of this generalized Fourier transform, transient problems with horizontal symmetries other than radial can be treated as well. The notion of analytical solution versus numerical solution is discussed and a classification of analytical solutions is proposed in seven classes. The expressions found in this paper belong to Class 6, meaning that the transformed solutions are written in terms of eigenvalues which depend on one transform parameter (here p or α). Earlier solutions to the transient problem belong to Class 7, where the eigenvalues depend on two transform parameters. The theory is applied to three examples.     

Rotation and inversion symmetry properties of flux-line lattice in type II superconductors

Magnetic flux lines are arranged regularly in the mixed state of a type II superconductor and form a two-dimensional triangular lattice. This is unaltered on rotation through an angle /3, one of the flux lines being an axis of symmetry of the sixth order. It is also symmetric with respect to the inversion. The center of symmetry is any point on a flux line. The symmetry properties of the magnetic field, the order parameter, and Eilenberger's integrated Green's function are derived. The magnetic field is developed into Fourier series with the help of a two-dimensional reciprocal lattice. The normalized Fourier coefficient is the form factor in neutron diffraction and is shown to have a well-known property of the rotation symmetry. The Fourier transform of the normal Green's function satisfies a similar symmetry relation with an additional phase factor. When we expand the anomalous Green's function in terms of plane wave functions along the direction of one of the nearest-neighbor flux lines, the symmetry properties give useful conditions which the expansion coefficient satisfies as a function of the orthogonal coordinate and wave number vector. In addition to the plane wave expansion, the order parameter can be developed in terms of the harmonic oscillator eigenfunctions of the orthogonal coordinate with 6n quanta. The first term withn = 0 reproduces Abrikosov's solution. The symmetry properties help us effectively simplify the Eilenberger equation. An example of the simplification is given.     

Modeling of coating flows on curved surfaces

The equations describing the temporal evolution of a thin, Newtonian, viscous liquid layer are extended to include the effect of substrate curvature. It is demonstrated that, subject to the standard assumptions required for the validity of lubrication theory, the surface curvature is equivalent to an applied time-independent overpressure distribution. Within the mathematical model, a variety of substrate shapes, possessing both inside and outside corners, are shown to be equivalent. Starting with an initially uniform coating layer, the evolving coating profile is calculated for substrates with piecewise constant curvature. Ultimately, surface tension forces drive the solutions to stable minimum-energy configurations. For small time, the surface profile history, for a substrate with a single curvature discontinuity, is given as the self-similar solution to a linear fourth-order diffusive equation. Using a Fourier transform, the solution to the linear problem is found as a convergent infinite series. This Green's function generates the general solution to the linearized problem for arbitrary substrate shapes. Calculated solutions to the non-linear problem are suggestive of coating defects observed in industrial applications.