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  • Articles  (27)
  • Engineering  (26)
  • Engineering General  (26)
  • Silicon  (1)
  • Life and Medical Sciences
  • 1980-1984  (27)
  • 1940-1944
  • 1982  (14)
  • 1981  (13)
  • Technology  (27)
  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1505-1520 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper deals with the theoretical and numerical treatment of dynamic unilateral problems. The governing equations are formulated as an equivalent variational inequality expressing D' Alembert's principle in its inequality form. The discretization with respect to time and space leads to a static nonlinear programming problem which is solved by an appropriate algorithm. Some properties of dynamic unilateral problems are outlined and the influence of several parameters on the solution is investigated by means of numerical examples.
    Additional Material: 9 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 573-599 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic stress field and its concentrations around holes of arbitrary shape in infinitely extended bodies under plane stress or plane strain conditions are numerically determined. The material may be linear elastic or viscoelastic, while the dynamic load consists of plane compressional waves of harmonic or general transient nature. The method consists of applying the Laplace transform with respect to time to the governing equations of motion and formulating and solving the problem numerically in the transfomed domain by the boundary integral equation method. The stress field can then be obtaind by a numerical inversion of the trasformed solution. The correspondence principle is invoked for the case of viscoelastic material behavious. The method is simplified for the case of harmonic waves where no numerical inversion is involved.
    Additional Material: 21 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Plasma chemistry and plasma processing 1 (1981), S. 397-418 
    ISSN: 1572-8986
    Keywords: Silicon ; metallic impurities ; plasma zone melting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract The main methods of silicon purification involve physicochemical techniques of separation. They yield an ultrapure metal, but its price is not compatible with photovoltaic central power generation. The plasma zone melting process consists in the horizontal displacement of a melted zone under an argon-hydrogen-oxygen plasma. The melt zone is characterized by a vertical gradient of concentration and temperature which drains impurities toward the upper surface of the bar. Moreover, the displacement of the zone from the head to the tail of the bar ensures a horizontal drainage of impurities toward the tail. This technique has been used with success for purification of metallurgical grade silicon; for example, iron was reduced from 3500 ppm to 0.5 ppm at a displacement rate between 20 and 40 cm/h. The final impurity level was less than 1 ppm. The mass transfer was independent of the displacement rate at 40 cm/h, but dependent on the heat transfer rate. The segregation of the metals is caused by drainage toward the tail of the bar, while the plasma vaporizes impurities since the metallic and metalloidic impurities have high vapor pressures (e.g., S, P, C, O, Mn). Acid (HF-HNO3) is used to dissolve the impurities between each passage of the zone. Boron elimination depends directly on the plasma oxygen concentration. Classical mathematic models of zone melting are not valid for plasma melting zone processes.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 133-139 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Some new formulae are presented for numerical integration over triangular regions. These formulae, which are triangularly symmetric, involve four, six, and seven integration points, respectively. They were derived by determining co-ordinates and weight factors for which polynomial functions of up to a certain degree are integrated exactly. The effectiveness of the formulae is demonstrated by applying them to the integration of five non-polynomial functions, two of which are singular within the region of integration. Results obtained with the new formulae are compared with results obtained with other, comparable formulae. It is seen that the new formulae are more accurate than some existing ones with the same numbers of points.
    Additional Material: 7 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 99-109 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two highly accurate implicit Padé approximations to the transient heat conduction equation are investigated using the conjugate gradient method to solve, for the temperatures. The accuracy and stability of the approximations are discussed and numerical examples are presented showing the relative performance. Comparisons with the Crank-Nicolson method are also presented.
    Additional Material: 4 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 967-979 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple, efficient and economical numerical technique for the analysis of shallow shells-of arbitrary shape is presented. The technique is based upon the method of constant-deflection contours combined with the well-known finite element method. In the proposed method the elemental stiffness matrix is derived from a system of two consistent partial differential equations for two scalar functions using Galerkin's method. Several representative examples are included to indicate the effectiveness of the method.
    Additional Material: 6 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1829-1854 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general and systematic discussion on the use of the operational method of Laplace transform for numerically solving complex time-dependent linear problems is presented. Application of Laplace transform with respect to time on the governing differential equations as well as the boundary and initial conditions of the problem reduces it to one independent of time, which is solved in the transform domain by any convenient numerical technique, such as the finite element method, the finite difference method or the boundary integral equation method. Finally, the time domain solution is obtained by a numerical inversion of the transformed solution. Eight existing methods of numerical inversion of the Laplace transform are systematically discussed with respect to their use, range of applicability, accuracy and computational efficiency on the basis of some framework vibration problems. Other applications of the Laplace transform method in conjunction with the finite element method or the boundary integral equation method in the areas of earthquake dynamic response of frameworks, thermaliy induced beam vibrations, forced vibrations of cylindrical shells, dynamic stress concentrations around holes in plates and viscoelastic stress analysis are also briefly described to demonstrate the generality and advantages of the method against other known methods.
    Additional Material: 12 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 310-311 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 1069-1079 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a series summation computation method for calculating temperatures arising from some geometries which commonly occur in microelectronics. The method, which is suitable for use with pocket calculators, involves an exchange of terms with those of a known series. At each stage of the summation a state of convergence (SOC) is calculated in terms of the maximum possible error, thus enabling the calculation to be terminated as soon as the required accuracy has been obtained.
    Additional Material: 3 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 1273-1278 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present two self-contained programs which have given excellent results for uniform approximation of functions (or discrete data) by generalized rational functions. The first program is an extension of a program published in 1975 which uses a linear programming approach known as the differential correction algorithm. The present version is more robust, and allows for the use of a multiplicative weight function and restrictions on the values of the approximating function. These features make the program more suitable for applications such as digital filter approximation. The second program uses a combination of the Remes and differential correction algorithms which combines some of the good features of both algorithms. Given here is a discussion of the algorithms together with several examples. A FORTRAN listing can be obtained from the first author.
    Type of Medium: Electronic Resource
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