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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Shock waves 4 (1995), S. 253-265 
    ISSN: 1432-2153
    Keywords: Expreiment ; theory ; pressure ; heat transfer ; interferogram ; nonequilibrium ; total pressure recovery ; shock/shock interactions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics , Technology
    Notes: Abstract The influence of the nitrogen dissociation on the interactions due to the interference of two planar shock waves in a hypersonic high enthalpy flow is theoretically investigated for infinite reaction rates. The two limiting cases of infinitely slow and infinitely fast reactions are modelled as a perfect gas and an ideal dissociating gas in chemical equilibrium. To investigate the influence of finite reaction rates on the interactions of shock waves, experiments are performed in the “high enthalpy shock tunnel Göttingen” (HEG) with a wind tunnel model consisting of a wedge type shock generator and a transversally mounted cylinder. The pressure and heat transfer loads resulting from the shock wave interferences are measured and the flow field is visualized by means of interferograms. The experimental results are compared with the results of a numerical simulation for a dissociating nitrogen flow and with the experimental results for a perfect gas flow.
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  • 2
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    Plasma chemistry and plasma processing 10 (1990), S. 71-85 
    ISSN: 1572-8986
    Keywords: Thermal plasmas ; spouted bed ; hydrodynamics ; heat transfer
    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 literature reveals very little intformation about plasma spouted bed hydrodynamics. Spouting of corindon particles with diameters ranging from 0.4 to 3.36 mm with argon plasma was conducted in a 90-mm-diameter column in the temperature range 300–1300°C. It was found that the maximum spoutable height (Hm) decreases with increasing particle diameter and decreasing mean bed temperature. A relation between the inlet plasma velocity and Hm is proposed. Concerning heat transport phenomena in the annulus, measurements and calculations indicate a large axial diffusivity but a poor radial mixing. Typical values of Dz and Dr are proposed on the basis of an identification procedure.
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  • 3
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    Plasma chemistry and plasma processing 12 (1992), S. 383-402 
    ISSN: 1572-8986
    Keywords: Rarefied plasma flow ; nonspherical metallic or nonmetallic particle ; particle charging ; heat transfer
    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 interaction of a nonspherical metallic or nonmetallic particle with a rarefied thermal plasma flow is considered. Heat transfer to a particle of arbitrary shape with an extremely thin plasma sheath due to, respectively, gas molecules, electrons, and ions is described. Analytical expressions are derived for charge and heat fluxes in the particular case of a spheroidal metallic or nonmetallic particle in a subsonic plasma flow. It has been shown that the intensity of heat exchange is greatly influenced by gas ionization, charge transfer processes, and particle shape, velocity, and orientation in the plasma flow.
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  • 4
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    Plasma chemistry and plasma processing 3 (1983), S. 97-113 
    ISSN: 1572-8986
    Keywords: Knudsen effect ; heat transfer ; small particles ; thermal plasmas ; analytical studies
    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 Knudsen effect on heat transfer to a particle exposed to a thermal plasma is important for many practical situations experienced in plasma chemistry and plasma processing. This paper provides theoretical results of this effect based on the “heat conduction potential jump” approach. It is shown that a correction factor which depends on the Knudsen number must be introduced into the expressions for heat fluxes obtained previously based on the continuum approach. The Knudsen effect is stronger for smaller particles and it is also more pronounced for an Ar-H2 plasma (compared to Ar and nitrogen plasmas at the same temperature). Since the Knudsen effect depends on the surface temperature of a particle, calculation of particle heating becomes more complicated.
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  • 5
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    Plasma chemistry and plasma processing 2 (1982), S. 361-386 
    ISSN: 1572-8986
    Keywords: Transferred arc ; characteristics ; heat transfer ; experimental
    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 A specially designed plasma chamber was constructed to study the operating characteristics of a dc plasma-transferred arc of argon, struck between a fluid convective cathode and a water-cooled anode. The arc voltage increased markedly with arc length and with an increase in the inlet velocity of the argon flow past the cathode tip, and much less with an increase in current. Radiation from the plasma column to the chamber walls and transfer of energy to the anode were the two principal modes of transfer of the arc energy. The former was dominant in the case of long arcs and at high inlet argon velocities. At the anode, the major contribution was from electron transfer, which occurred on a very small area of the anode (∼5 mm in diameter). Convective heat transfer from the plasma was somewhat less. In all cases, the arc energy contributions to cathode cooling and to the exit gas enthalpy were small. From total heat flux and radiative heat transfer measurements, it was estimated that the plasma temperature just above the anode was in the range 10,000–12,000 K. Preliminary experiments with an anode consisting of molten copper showed that the arc root was no longer fixed but moved around continuously. The arc was othwewise quite stable, and its operating characteristics differed little from those reported for solid anodes, in spite of the greater extent of metal vaporization.
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  • 6
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    Transport in porous media 28 (1997), S. 125-134 
    ISSN: 1573-1634
    Keywords: boundary-layer ; power-law non-Newtonian fluid ; heat transfer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The effect of the presence of an isotropic solid matrix on the forced convection heat transfer rate from a flat plate to power-law non- Newtonian fluid-saturated porous medium, has been investigated. Numerical results are presented for the distribution of velocity and temperature profiles within the boundary layer. The effects of the flow index, first-order and second-order resistance on the velocity, and temperature profiles are discussed. The missing wall values of the velocity and thermal functions are tabulated.
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  • 7
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    Transport in porous media 41 (2000), S. 149-171 
    ISSN: 1573-1634
    Keywords: hydrodynamic isolation ; plume ; remediation ; genetic algorithms ; optimization ; aquifer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Produced water constitutes a large amount of waste fluids during the production operation of an oil field. Underground injection for disposing the wastewater from hydrocarbon production is an engineering problem due to the possibility of leakage of injected pollutant material from receiving medium to a drinking water source. This paper describes a method for optimization of polluted aquifer remediation design using one of the artificial intelligence optimization methods, namely Genetic Algorithms (GAs). As a case study, the contaminated area was created by using a groundwater transport simulator, which is based on Method of Characteristics (MOC). Then, the developed computer program was run to find the optimum solution for remediation, and the solution yielded from the program was verified by using a groundwater simulator. The plume was captured and the concentration level of chloride ion within the aquifer was diminished by using extraction wells. The analytical model approach provided different alternatives for appropriate isolation of plume. GAs were used as an optimization technique for making a decision among the alternatives, by considering operation time, number of wells, pumping rate and drawdown as decision variables and constraints.
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  • 8
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    Transport in porous media 3 (1988), S. 95-106 
    ISSN: 1573-1634
    Keywords: Free convection ; heat transfer ; Porous media ; natural convection
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract An analysis is presented for the calculation of heat transfer due to free convective flow along a vertical plate embedded in a porous medium with an arbitrarily varying surface heat flux. By applying the appropriate coordinate transformations and the Merk series, the governing energy equation is expressed as a set of ordinary differential equations. Numerical solutions are presented for these equations which represent universal functions and several computational examples are provided.
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  • 9
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    Transport in porous media 3 (1988), S. 325-341 
    ISSN: 1573-1634
    Keywords: Natural convection ; heat transfer ; boundaries ; modes ; critical ; Nusselt ; power integral method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The ‘power integral method’ of calculating heat transfer across a convecting porous layer is extended to flux and porous boundaries. Convection starts at lower Rayleigh numbers for constant flux than for isothermal impervious boundaries and the flux is much greater. At higher Rayleigh numbers, as more of the higher modes contribute to the flux, the type of boundary has less influence on the heat transfer across the layer. For constant flux boundaries, simplified equations are developed to determine critical values for the second and higher modes and these values can be related simply to those for isothermal impervious boundaries.
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  • 10
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    Transport in porous media 3 (1988), S. 437-453 
    ISSN: 1573-1634
    Keywords: Natural convection ; heat transfer ; flow ; critical ; Nusselt ; power integral method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Temperature decay in sealed rockbeds has been recorded. The rockbeds lost energy through the top surface and the results indicated that different natural convective flows occurred in beds of fixed depth and rock size but different lateral dimensions. However, the different flows had no effect on the mean power density dissipated through the top of the beds. A simple numerical conduction model based on the ‘power integral method’ was used to calculate the temperature decay. The experimental results suggested that an insulated porous lower boundary was appropriate for the model and this gave the best agreement with the experiments.
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  • 11
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    Transport in porous media 39 (2000), S. 57-71 
    ISSN: 1573-1634
    Keywords: mixed convection ; heat transfer ; nonsimilar solution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Mixed convection along a vertical nonisothermal wedge embedded in a fluid-saturated porous media incorporating the variation of permeability and thermal conductivity is studied. The surface temperature is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A nonsimilar mixed convection parameter ζ and a pseudo-similarity variable η are introduced to cast the governing boundary layer equations into a system of dimensionless equations which are solved numerically using finite difference method. The entire mixed convection regime is covered by the single nonsimilarity parameter ζ=[1+(Ra x /Pe x )1/2]−1 from pure forced convection (ζ=1) to pure free convection (ζ=0). The problem is solved using nonsimilarity solution for the case of variable wall temperature. Velocity and temperature profiles as well as local Nusselt number are presented. The wedge angle geometry parameter is ranged from 0 to 1.
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  • 12
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    Transport in porous media 24 (1996), S. 157-166 
    ISSN: 1573-1634
    Keywords: non-Newtonian fluids ; combined convection ; heat transfer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The problem of combined convection from vertical surfaces in a porous medium saturated with a power-law type non-Newtonian fluid is investigated. The transformed conservation laws are solved numerically for the case of variable surface heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. The viscosity index ranged from 0.5 to 2.0.
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  • 13
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    Transport in porous media 1 (1986), S. 361-370 
    ISSN: 1573-1634
    Keywords: Vertical layers ; mathematical models ; geothermal systems ; heat transfer ; convection
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Some studies already made have investigated the criterion for onset of convection and heat and mass flow distributions in a porous slab composed of horizontal layers of different materials. This paper reports a study of such criteria for the case where the slab is composed of vertically-aligned strata with different permeabilities and thermal conductivities. This has particular relevance to where blocks of different materials abut in a vertical plane, as well as the case of very narrow highly permeable vertical layers which represent vertical faults in a geological structure. Results indicate that permeability and/or thermal conductivity contrasts between layers can significantly affect the flow pattern and the spatial distribution of the surface heat flux. The concentration of flow in highly permeable ‘faults’ produces marked irregularities in the heat flow through the surface above them.
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  • 14
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    Transport in porous media 6 (1991), S. 183-194 
    ISSN: 1573-1634
    Keywords: Free convection ; heat transfer ; porous media ; natural convection
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The effects of anisotropy on the steady laminar boundary-layer free convection over a vertical impermeable surface are analysed by using the method of integral relations. If the permeability in the direction orthogonal to the plate is greater than the permeability along the plate, then there is an increase in the temperature field.
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  • 15
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    Transport in porous media 5 (1990), S. 299-323 
    ISSN: 1573-1634
    Keywords: Supercritical convection ; heat transfer ; numerical simulation ; porous media ; geothermal systems ; water ; critical point
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Fluid and heat flow at temperatures approaching or exceeding that at the critical point (374 °C for pure water, higher for saline fluids) may be encountered in deep zones of geothermal systems and above cooling intrusives. In the vicinity of the critical point the density and internal energy of fluids show very strong variations for small temperature and pressure changes. This suggests that convective heat transfer from thermal buoyancy flow would be strongly enhanced at near-critical conditions. This has been confirmed in laboratory experiments. We have developed special numerical techniques for modeling porous flow at near-critical conditions, which can handle the extreme nonlinearities in water properties near the critical point. Our numerical simulations show strong enhancements of convective heat transfer at near-critical conditions; however, the heat transfer rates obtained in the simulations are considerably smaller than data reported from laboratory experiments by Dunn and Hardee. We discuss possible reasons for this discrepancy and develop suggestions for additional laboratory experiments.
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  • 16
    ISSN: 1573-1634
    Keywords: combined convection ; porous media ; heat transfer ; thermal stratification ; thermal dispersion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The effects of thermal dispersion and thermal stratification on mixed convection about a vertical surface in a porous medium are studied. The conservation equations that govern the problem are reduced to a system of nonlinear ordinary differential equations. The resulting equations are solved on the basis of the local similarity approximation. The results indicate that both dispersion and stratification effects have considerable influence on the heat transfer rate.
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  • 17
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    Transport in porous media 29 (1997), S. 355-364 
    ISSN: 1573-1634
    Keywords: mixed convection ; boundary layers ; similarity solutions ; heat transfer ; Darcy flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The mixed convection boundary-layer flow on a horizontal impermeable surface embedded in a saturated porous medium and driven by a local heat source is considered. Similarity solutions are obtained for specific outer flow variations and these are shown to have a solution only for parameter values greater than some critical value. When this is not the case the solution develops a singularity at a finite distance from the leading edge. The nature of this singularity is also discussed.
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  • 18
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    Transport in porous media 32 (1998), S. 263-283 
    ISSN: 1573-1634
    Keywords: radiation ; natural convection ; porous medium ; heat transfer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A regular two-parameter perturbation analysis based upon the boundary layer approximation is presented here to study the radiative effects of both first- and second-order resistances due to a solid matrix on the natural convection flows in porous media. Four different flows have been studied, those adjacent to an isothermal surface, a uniform heat flux surface, a plane plume and the flow generated from a horizontal line energy source on a vertical adiabatic surface. The first-order perturbation quantities are presented for all these flows. Numerical results for the four conditions with various radiation parameters are tabulated.
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  • 19
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    Transport in porous media 36 (1999), S. 245-254 
    ISSN: 1573-1634
    Keywords: porous media ; heat transfer ; mixed convection.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract In the present work, the effect of mixed convection about vertical surfaces on the phenomenon of melting process in a fluid-saturated porous medium is analyzed on the basis of boundary layer approximations. Similarity solutions are obtained for aiding external flow. The final similarity equations are integrated numerically by use of the fourth-order Runge–Kutta method. Results are reported for the flow and thermal fields in the melt region. The melting phenomenon decreases the local Nusselt number at the solid–liquid interface.
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  • 20
    ISSN: 1573-1634
    Keywords: swelling ; heat transfer ; polymer ; clay ; liquid/vapor transfer ; drying ; unsaturated ; mixture.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A three-spatial scale, single time-scale model for both moisture and heat transport is developed for an unsaturated swelling porous media from first principles within a mixture theoretic framework. On the smallest (micro) scale, the system consists of macromolecules (clay particles, polymers, etc.) and a solvating liquid (vicinal fluid), each of which are viewed as individual phases or nonoverlapping continua occupying distinct regions of space and satisfying the classical field equations. These equations are homogenized forming overlaying continua on the intermediate (meso) scale via hybrid mixture theory (HMT). On the mesoscale the homogenized swelling particles consisting of the homogenized vicinal fluid and colloid are then mixed with two bulk phase fluids: the bulk solvent and its vapor. At this scale, there exists three nonoverlapping continua occupying distinct regions of space. On the largest (macro) scale the saturated homogenized particles, bulk liquid and vapor solvent, are again homogenized forming four overlaying continua: doubly homogenized vicinal fluid, doubly homogenized macromolecules, and singly homogenized bulk liquid and vapor phases. Two constitutive theories are developed, one at the mesoscale and the other at the macroscale. Both are developed via the Coleman and Noll method of exploiting the entropy inequality coupled with linearization about equilibrium. The macroscale constitutive theory does not rely upon the mesoscale theory as is common in other upscaling methods. The energy equation on either the mesoscale or macroscale generalizes de Vries classical theory of heat and moisture transport. The momentum balance allows for flow of fluid via volume fraction gradients, pressure gradients, external force fields, and temperature gradients.
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  • 21
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    Transport in porous media 36 (1999), S. 357-371 
    ISSN: 1573-1634
    Keywords: natural convection ; heat transfer ; Brinkman's model.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A regular perturbation analysis is presented for the following laminar natural convection flows of Newtonian fluids with temperature-dependent effective viscosity: a freely-rising plane plume, the flow above a horizontal line source on an adiabatic surface (a plane wall plume) and the flow adjacent to a vertical uniform flux surface for porous medium. The temperature-dependent effective viscosity introduces nonsimilarity into the governing equations. Numerical results are presented for the flow and heat transfer characteristics.
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  • 22
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    Plasma chemistry and plasma processing 9 (1989), S. 135S 
    ISSN: 1572-8986
    Keywords: Modeling ; thermal plasma processing ; supersonic jets ; heat transfer ; control
    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 Thermal plasma processing of materials is a rapidly growing area of research. The commercialization of these processes, however, has been limited by the lack of fundamental understanding of how the various processes work. Research has historically focused on developing models of fluid flow and heat transfer to particles injected into either DC arc or RF plasma jets. These models in the past have simplified boundary conditions to meet computational limitations. Recent advances in models have now been made, allowing evaluations of more of the plasma process variables. Supersonic flow modeling in a DC jet and modeling of the effects of particle loading (particulate feed rate) have been accomplished and are reviewed here. Materials processing using thermal plasmas has been separated into the categories of synthesis, melting, and deposition, and is discussed in view of the processing effects on the resultant material structures. Process modeling leading to process understanding is reviewed with an emphasis on process control and optimization. Commercialization of plasma processes requires controls and process transducers which result from experimentation and process models. Approaches to develop process controls from the current technical base are presented.
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  • 23
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    Plasma chemistry and plasma processing 13 (1993), S. 633-653 
    ISSN: 1572-8986
    Keywords: Rarefied plasma ; spherical particle ; particle charging ; Debye screening ; heat transfer
    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 methods of the kinetic theory tire applied for the description of charge and heat transfer front a rarefied plasma to a spherical particle for an arbitrary ratio between Dehye length and particle radius. Different models of the velocity distribution functions of the charged plasma species are considered. The results of the numerical analysis show that the intensity of plasma-particle heat exchange is greatly influenced by gas ionization, participation of electrons and ions in the transfer processes, particle charging, and .screening properties of the plasma. Even at a low degree of ionization, the electron and ion contribution to the heat transfer remains significant.
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  • 24
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    Plasma chemistry and plasma processing 3 (1983), S. 351-366 
    ISSN: 1572-8986
    Keywords: Small particles ; heat transfer ; drag ; Knudsen effect ; convection ; thermal plasma ; computation
    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 In this paper computational results are presented which reveal the effects of the Knudsen number on heat transfer and drag of small particles in a flowing thermal argon plasma. The Knudsen number is restricted to moderate values so that “temperature jump” and “velocity slip” conditions may be employed, and for the governing equations the continuum approach remains valid. It is shown that the ratio of the heat fluxes with and without the Knudsen effect is almost identical to the ratio obtained by the authors for the case of pure heat conduction. This fact is very important for modeling of the behavior of particles injected into an actual plasma reactor when the Knudsen effect has to be taken into account.
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    Annals of biomedical engineering 21 (1993), S. 489-499 
    ISSN: 1573-9686
    Keywords: Work of breathing ; Inspiratory pressure-time integral ; Respiratory modeling ; Dogs ; Humans
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract We hypothesized that the viscoelastic properties of the respiratory system should have significant implications for the energetically optimal frequency of breathing, in view of the fact that these properties cause marked dependencies of overall system resistance and elastance on frequency. To test our hypothesis we simulated two models of canine and human respiratory system mechanics during sinusoidal breathing and calculated the inspiratory work ( $$\dot W$$ ) and pressure-time integral (PTI) per minute under both resting and exercise conditions. The two models were a two-compartment viscoelastic model and a single-compartment model. Requiring minute alveolar ventilation to be fixed, we found that both models predicted almost identical optimum breathing frequencies. The calculated PTI was very insensitive to increases in breathing frequency above the optimal frequencies, while $$\dot W$$ was found to increase slowly with frequency above its optimum. In contrast, both $$\dot W$$ and PTI increased sharply as frequency decreased below their respective optima. A sensitivity analysis showed that the model predictions were very insensitive to the elastance and resistance values chosen to characterize tissue viscoelasticity. We conclude that the $$\dot W$$ criterion for choosing the frequency of breathing is compatible with observations in nature, whereas the optimal frequency predictions of the PTI are rather too high. Both criteria allow for a fairly wide margin of choice in frequency above the optimum values without incurring excessive additional energy expenditure. Furthermore, contrary to our expectations, the viscoelastic properties of the respiratory system tissues do not pose a noticeable problem to the respiratory controller in terms of energy expenditure.
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    Optimization and engineering 1 (2000), S. 67-86 
    ISSN: 1573-2924
    Keywords: vibration absorbers ; optimization ; noise reduction ; sound power
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract This paper presents a design methodology for reducing radiated noise from enclosures using multiple optimized tuned absorbers. The methodology starts from the sound power spectrum of the enclosed noise source and ends with optimally sized/located absorbers on a surrounding thin shell enclosure. The design approach combines a finite element method vibration prediction code, a boundary element method sound power prediction code and a combined stochastic/gradient-based optimization algorithm. A design example has been optimized for a thin shell covering a motor/gearbox. The addition of a small amount of weight (130 g or 1.6% of the weight of the shell) produced substantial reductions in radiated sound power (13 dB in the targeted 1/3 octave band centered at 125 Hz). The design has been validated by experiment.
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    Journal of engineering mathematics 31 (1997), S. 59-80 
    ISSN: 1573-2703
    Keywords: soldering ; heat transfer ; Joule heating ; conformal mapping ; thermode
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract The soldering of small, delicate electronic devices by means of a blade thermode (a small, thin, rectangular ⊔ or ⊔⊔ requires the lower side of the thermode to have a uniform temperature distribution. This is not easily obtained: during start-up the corners tend to be too hot, and too cold in the stationary phase. In the present study the various aspects that determine the heat flow and the temperature distribution are analysed, both for the dynamic and the stationary cases. For a temperature-independent (linear) material, approximate solutions are obtained for the dynamic problem. For the stationary problem, an exact solution is utilized that includes temperature-dependent (nonlinear) material. Practical design rules based on these solutions are proposed. The analysis compares very well with a numerical finite-element simulation.
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    Journal of engineering mathematics 36 (1999), S. 241-254 
    ISSN: 1573-2703
    Keywords: flows in porous media ; transformation ; heat transfer ; drying bins ; conformal mapping.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract The design of a drying or cooling store aims to provide an even airflow distribution, when aerated, for preservation purposes. The airflow in some curved bottom bins are studied in this paper. The flow is modelled, using Darcy's law. A generalized Schwarz-Christoffel transformation is employed to reduce the problem of computing streamlines and isobars of airflow to solving a single nonlinear equation for the flow angle along the wall. Corresponding to different bin shapes, a few computed streamlines and isobars of airflow are presented, showing the effect of changing bottom geometries on the air flow. Heat transfer in such bins is also investigated. Based on an analysis of the far field of airflow, finite-height bins are considered. Analytical solutions of the heat conduction equation in terms of streamlines and isobars are obtained.
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    Journal of engineering mathematics 37 (2000), S. 27-43 
    ISSN: 1573-2703
    Keywords: anisotropic elasticity ; Kelvin modes ; optimization ; strain energy.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract Pointwise optimization of the material symmetry of an anisotropic elastic material with respect to fixed and specified stress (or strain) states is accomplished. The conceptual variables in this problem are the type of material symmetry and the orientation of the canonical symmetry axis for the material at a point in the material. The actual variables are the coefficients of the elasticity (or compliance) matrix. The results are presented in the form of the elasticity (or compliance) matrices that minimize the strain energy with respect to specified, but arbitrary, stress (or strain) states.
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    Journal of engineering mathematics 38 (2000), S. 51-76 
    ISSN: 1573-2703
    Keywords: asymptotic expansions ; Ohno casting ; heat transfer ; metal casting ; solidification.
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    Notes: Abstract A model is presented to simulate Ohno Continuous Casting (OCC) of cored rods. Equations describing the axisymmetric transport of heat in the mold and cored rod are discussed. Heat transfer between the system and the surrounding environment is assumed to take place via convection. If the velocity of casting, the external temperature profile, the mold temperature, and the mold-cooler distance are given, asymptotic solutions for the temperature profile in the rod are found and expressions for the solidifying interfacial shapes are developed in the limit of a small melt slenderness ratio (mold radius/mold length). The effect of process parameters on the shape of the cored rod system is investigated.
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    Journal of engineering mathematics 36 (1999), S. 311-326 
    ISSN: 1573-2703
    Keywords: continuous steel casting ; oscillation marks ; lubrication theory ; heat transfer ; flux flows.
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    Notes: Abstract In the industrial process of continuous steel casting, flux added at the top of the casting mould melts and forms a lubricating layer in the gap between the steel and the oscillating mould walls. The flow of flux in the gap plays an essential role in smoothing the casting operation. The aim of the present work is to better understand the mechanics of flux flow, with an emphasis on such problems as how the flux actually moves down the mould, the physical parameters governing the consumption rate of the flux and the geometry of the lubricating layer. The problem considered is a coupled problem of liquid flow and multi-phase heat transfer. In the first part of the paper, the formation of the lubricating layer is analysed and a set of equations to describe the flux flow is derived. Then, based on an analysis of the heat transfer from the molten steel through the lubricating layer to the mould wall, a system of equations correlating the temperature field in the steel and flux with the geometry of the lubricating layer is derived. Subsequently, the equations for the flux flow are coupled with those arising from heat-transfer analysis and then a numerical scheme for the calculation of the consumption rate of flux, the geometry of the lubricating layer and the solidification surface of the steel is presented.
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    Journal of engineering mathematics 31 (1997), S. 411-437 
    ISSN: 1573-2703
    Keywords: Spray-forming ; solidification ; heat transfer ; computation ; moving-boundary problems
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    Notes: Abstract Transient heat transfer and solidification within an axisymmetric spray-formed aluminium billet are investigated. The boundary of the solid billet grows outwards, due to deposition from a stream of atomised semi-solid metal droplets. Within the billet, it is necessary to determine the heat fluxes and, in particular, to determine the position of the solidus isotherm. Mathematically, one must solve a nonlinear two-dimensional parabolic initial-boundary-value problem in an irregular and expanding domain. The problem is formulated within the general framework of billet heat transfer. An effective numerical algorithm is developed and implemented. Results from the numerical algorithm are used to explore thermal transients in the start-up phase of billet spray-forming production runs, the phenomenem of steady-state heat flow in the billet crown and the complex dependence of heat flow on billet-surface movement.
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 4123-4155 
    ISSN: 0029-5981
    Keywords: Petrov-Galerkin methods ; weighting parameters ; optimization ; spectral averaged phase errors ; Engineering ; Engineering General
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    Notes: A Fourier analysis of the linear and quadratic N + 1 and N + 2 Petrov-Galerkin finite element methods applied to the one-dimensional transient convective-diffusion equation is performed. The results show that a priori optimization of the N + 1 method is not possible because dissipative errors are introduced as dispersive errors are reduced (any optimization is subjective). However, a priori optimization of the N + 2 Petrov-Galerkin method is possible because the reduction of dispersion errors can be accomplished without the addition of artificial dissipation.The Spectrally Weighted Average Phase Error Method (SWAPEM) for the optimization of the N + 2 Petrov-Galerkin method is introduced, in which the N + 2 weighting parameter is chosen at each time step to minimize the integral over wave number of the phase error of Fourier modes, weighted by the frequency content of the global solution at the previous time step (obtained via FFT). The method is dynamic, and general in that the dependence of the weighting parameter on the solution waveform is accounted for. Optimal values predicted by the method are in excellent agreement with those suggested by the numerical experimentation of others. Simulations of the pure convective transport of a Gaussian plume and a triangle wave are discussed to illustrate the effectiveness of the method.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 783-792 
    ISSN: 1069-8299
    Keywords: substructure ; frontal technique ; heat transfer ; moisture transfer ; displacement ; Engineering ; Numerical Methods and Modeling
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    Notes: This paper presents a substructuring-frontal combined algorithm for the analysis of fully coupled heat, moisture and displacement problems in unsaturated soil. The method adopted for solving the assembled matrix equations has a significant bearing on the computer storage requirement and execution time. Numerical examples are given to validate the proposed model. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 151-160 
    ISSN: 1069-8299
    Keywords: genetic algorithms ; evolutionary-genetic analogy ; heat transfer ; finite elements ; numerical analysis ; Engineering ; Numerical Methods and Modeling
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    Notes: A new approach was developed for the analysis of problems of physics governed by laws of conservation. The methodology establishes an analogy between various aspects of evolution and genetics of life processes and inanimate physical systems. This analogy is then used to generate solutions to physical problems in a similar way to which organisms in nature solve problems imposed by environmental constraints. Finite difference and finite elements approximations are used in the numerical implementation of the method and a simple two-dimensional problem is solved to illustrate the method. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 13 (1997), S. 977-986 
    ISSN: 1069-8299
    Keywords: sequential function approximation ; interpolation functions ; optimization ; parallel direct search ; Engineering ; Numerical Methods and Modeling
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    Notes: A computational method for the solution of differential equations is proposed. With this method an accurate approximation is built by incremental additions of optimal local basis functions. The parallel direct search software package (PDS), that supports parallel objective function evaluations, is used to solve the associated optimization problem efficiently. The advantage of the method is that, although it resembles adaptive methods in computational mechanics, an a priori grid is not necessary. Moreover, the traditional matrix construction and evaluations are avoided. Computational cost is reduced while efficiency is enhanced by the low-dimensional parallel-executed optimization and parallel function evaluations. In addition, the method should be applicable to a broad class of interpolation functions. Results and global convergence rates obtained for one- and two-dimensional boundary value problems are satisfactorily compared to those obtained by the conventional Galerkin finite element method. © 1997 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 13 (1997), S. 999-1008 
    ISSN: 1069-8299
    Keywords: optimization ; sensitivity analysis ; constraint approximation ; non-linear analysis ; finite element method ; Engineering ; Numerical Methods and Modeling
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    Notes: For the finite element non-linear analysis of engineering problems combined with an optimization method, two techniques - a semi-analytical sensitivity method and bi-point constraint approximation - have been proposed. To validate the proposed methods, a raft foundation on a soil medium has been analysed and the results have been compared. From the numerical results, it has been found that, for non-linear analysis, the semi-analytical sensitivity method is more efficient than the finite difference method and the bi-point approximation gives results which compare favourably with the finite element results. © 1997 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 11 (1995), S. 715-725 
    ISSN: 1069-8299
    Keywords: transient ; heat transfer ; inverse Laplace transforms ; Engineering ; Engineering General
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    Notes: We present a new procedure for the numerical calculation of the transient response of systems characterized by partial differential equations in several space variables and time. The procedure is based on: (i) spatially discretizing the system, (ii) deriving an equivalent circuit for each volume element, (iii) applying a time Laplace transformation and obtaining an admittance matrix, (iv) writing the expressions for the Laplace transforms of the desired variables according to Cramer's determinant rule, (v) interpreting the determinants as generalized eigenvalue problems, (vi) obtaining the proper eigenvalues of the system (poles and zeros), and (vii) finding the time-dependent solutions by ‘trivial’ inverse Laplace transformations. Although the procedure proposed applies to many partial differential equations (fluid flow in porous media, conductive heat transfer with convection, pressure tests in oil wells, electrical conduction, etc.), in the paper we illustrate the procedure in detail for a conduction heat transfer system (nine nodes). The procedure presented is much more efficient numerically than the direct numerical integration (in space and time) of the ruling PDE, or than solutions which require ‘standard’ numerical inverse Laplace transformation after matrix inversion.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 43-50 
    ISSN: 1069-8299
    Keywords: view factor ; radiation ; parallel computation ; heat transfer ; Engineering ; Engineering General
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    Notes: Two implementations for parallel computation of radiation heat transfer view factors are formulated and tested for a model problem. Using a sufficiently large number of processors and a suitable communications paradigm, the solution time for the problem considered here scales linearly with the number of surface elements in the parallel implementation rather than the quadratic scaling obtained using a serial approach. For larger problems, significantly shorter solution times are obtained using the massively parallel Connection Machine 5 than those obtained on a single processor of the Cray C-90, a traditional vector supercomputer. Parallel performance was degraded for implementations using too few processors or data layouts leading to inefficient processor communication.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 777-796 
    ISSN: 0029-5981
    Keywords: finite element method ; force method ; reanalysis ; eigenvalue ; structural variation ; optimization ; Engineering ; Numerical Methods and Modeling
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    Notes: This paper presents a force-based finite element method that involves eigen-space transformation of element stiffness matrices in the first analysis. In each subsequent analysis (‘reanalysis’) associated with structural variations, the solution obtained previously is modified making use of intrinsic properties of eigen solutions and avoiding the time-consuming task of solving a large system of equations. The structural variations may involve changes in material properties, birth or death of elements, or change in boundary conditions. Numerical examples are presented to compare the accuracy and computational efficiency of the proposed method with the displacement-based finite element method. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 41 (1998), S. 1463-1484 
    ISSN: 0029-5981
    Keywords: optimization ; shape design ; heuristics ; evolutionary optimization ; splines ; finite elements ; Engineering ; Numerical Methods and Modeling
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    Notes: The problem of finding the optimal shape of a continuous structure is addressed using, alternatively, heuristic, evolutionary and mixed evolutionary and heuristic optimization strategies. Boundaries are represented by B-splines. Two heuristics for minimizing the weight of a structure subject to limits on von Mises stresses and geometrical constraints are implemented: ‘generalized biological growth’ and ‘penalized biological growth’. Penalized biological growth adds to generalized biological growth a control for shape changes. This control is based on the overall state of constraints satisfaction in the structure. The two heuristics are very efficient at improving the designs, but they do not yield globally optimal shapes. Therefore, they are interfaced with an evolutionary optimizer. Different strategies for mixing evolutionary search and biological growth are compared. Results are obtained for fan disk shape problems. They show that mixing evolutionary search with biological growth improves the efficiency of the optimization. The method offers to the designer new paths for a better component determination. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 293-328 
    ISSN: 0029-5981
    Keywords: structural synthesis ; optimization ; topology optimization ; discrete variable optimization ; Mixed-Integer Non-linear Programming ; MINLP ; the Modified OA/ER algorithm ; MINLP strategy ; Engineering ; Numerical Methods and Modeling
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    Notes: Part II describes the Mixed-Integer Non-linear Programming (MINLP) approach to structural synthesis where standard dimensions are added to simultaneous topology and parameter optimization. For this purpose, the mechanical superstructure has been enhanced and a special MINLP-MS model formulation for mechanical superstructures from Part I adapted to standard dimension alternatives, which give rise to complex MINLP problems that are difficult to solve. A Linked Two-Phase MINLP Strategy has been developed to efficiently accelerate the solutions of highly combinatorial MINLP problems, performed by the Modified OA/ER algorithm. In the first phase, the strategy uses only continuous dimensions making it easier to find an optimal topology. Based on the obtained global linear approximation of the superstructure, the proposed strategy in the second phase continues to perform an overall simultaneous optimization, where standard dimensions are added as additional discrete optimization alternatives. Thus, simultaneous topology, parameter and standard dimension optimization is now performed in the second phase. The synthesis of a multiple cantilever beam, introduced in Part I, was performed in accordance with the steps proposed by the MINLP optimization approach. This approach enables the obtaining of additional savings when compared to the one in Part I. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 655-687 
    ISSN: 0029-5981
    Keywords: crashworthiness ; multibody dynamics ; flexible structures ; simulation ; design ; optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Different formulations based on multibody dynamics are shown to be suitable for the development of a methodology for the impact simulation and crashworthiness design of railway vehicles. The proposed design methodology comprises different computer-aided tools of increasing complexity and accuracy which can be used with greater advantage and efficiency in the different design stages of railway stock. In general, the crashworthiness design methods and associated multibody dynamic tools which are presented in this paper require information to be obtained from numerical or experimental crush tests of specific structural components, subassemblies and critical energy absorption devices normally located in car extremities. This hybrid feature lends to the present design process various efficiency gains as a result of a better understanding of the crash and different collapse mechanisms and ease of use. To access the merits of the present methodologies some new designs are discussed and the application of the proposed numerical tools is illustrated for different structural configurations of car extremities. A formulation for the sensitivity analysis and optimization of planar constrained mechanical systems is also presented. An example of crashworthiness design of an end underframe model of a railway car is solved to demonstrate the use of the methodology. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1109-1126 
    ISSN: 0029-5981
    Keywords: three-dimensional conduction heat transfer ; special boundary integral formulation ; Design Sensitivity Analysis (DSA) ; Direct Differentiation Approach (DDA) ; optimization ; CONMIN algorithm ; Engineering ; Numerical Methods and Modeling
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    Notes: In some steady heat conduction problems in special geometries which consist of a closely spaced surface and circular holes in an infinite domain, thermal system designers may want to optimize the configuration of circular holes in terms of their radii and locations to achieve the goal of uniform temperature distribution over a closely spaced surface. In this paper, an efficient optimization procedure for this kind of problem is proposed utilizing (i) the special boundary element analysis, (ii) the corresponding design sensitivity analysis and (iii) the CONMIN algorithm. Three sample problems were solved to demonstrate the efficiency and the usefulness of the proposed optimization procedure. Some industrial engineering examples of such problems can be found in the injection molding process, the compression molding process, and so on. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 971-1003 
    ISSN: 0029-5981
    Keywords: computer-simulation surrogates ; optimization ; Pareto optimality ; non-parametric statistical validation ; predictability ; quasi-convex analysis ; Engineering ; Numerical Methods and Modeling
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    Notes: In the surrogate approach to simulation-based optimization, the large-scale simulation is evoked only to construct and validate a simplified input-output model; this simplified input-output model then serves as a simulation surrogate in subsequent engineering optimization studies. We present here ‘basic’ and Pareto surrogate formulations through an illustrative application from fluid dynamics.The critical ingredient of both formulations is a non-parametric statistical validation and error estimation procedure which, based on verifiable hypotheses, precisely quantifies the effect of surrogate-for-simulation substitution on system predictability, stability, and optimality. The Pareto formulation improves upon the basic approach by operating only in the vicinity of the efficient frontier of the output achievable set A for problems with many inputs and few outputs, this considerably reduces the dimensionality of the problem, and correspondingly improves the surrogate error estimates. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 1263-1278 
    ISSN: 0029-5981
    Keywords: heat transfer ; collocation ; radial basis functions ; random points ; Engineering ; Numerical Methods and Modeling
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    Notes: Simple, mesh/grid free, numerical schemes for the solution of heat transfer problems are developed and validated. Unlike the mesh or grid-based methods, these schemes use well-distributed quasi-random collocation points and approximate the solution using radial basis functions. The schemes work in a similar fashion as finite differences but with random points instead of a regular grid system. This allows the computation of problems with complex-shaped boundaries in higher dimensions with no extra difficulty. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1-21 
    ISSN: 0029-5981
    Keywords: response surface approximations ; transient thermoelastic analysis ; optimization ; thermal design ; Engineering ; Numerical Methods and Modeling
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    Notes: Response surface methodology is used to construct approximations to temperature and stress in transient thermoelastic analysis of non-linear systems. The analysis forms the core component of a heating/cooling rate maximization problem in which the ordinates of the ambient temperature at equally spaced time intervals are chosen as the design variables. Polynomials or cubic splines are fitted through the ordinates to describe the ambient temperature profile required for the convective heat transfer analysis. An experimental design method based on D-optimality and a genetic algorithm was used to select the design points used to create the approximations. Linear response surfaces were found to be sufficiently accurate, thereby minimizing the number of finite element analyses. Two examples of which one is a thick-walled pressure vessel are used to illustrate the methodology. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 433-450 
    ISSN: 0029-5981
    Keywords: mesh partitioning ; finite elements ; parallel computing ; optimization ; heuristics ; frontal method ; Engineering ; Engineering General
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    Notes: We address the problem of automatic partitioning of unstructured finite element meshes in the context of parallel numerical algorithms based on domain decomposition. A two-step approach is proposed, which combines a direct partitioning scheme with a non-deterministic procedure of combinatorial optimization. In contrast with previously published experiments with non-deterministic heuristics, the optimization step is shown to produce high-quality decompositions at a reasonable compute cost. We also show that the optimization approach can accommodate complex topological constraints and minimization objectives. This is illustrated by considering the particular case of topologically one-dimensional partitions, as well as load balancing of frontal subdomain solvers. Finally, the optimization procedure produces, in most cases, decompositions endowed with geometrically smooth interfaces. This contrasts with available partitioning schemes, and is crucial to some modern numerical techniques based on domain decomposition and a Lagrange multiplier treatment of the interface conditions.
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 1021-1030 
    ISSN: 0029-5981
    Keywords: optimization ; finite element ; magnetostatic ; Engineering ; Engineering General
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    Notes: In this paper, we present an improvement of the optimization technique of the moving asymptotes applied to a class of magnetostatic design problem. Our approach includes, among other aspects, an active set strategy which turns possible to find feasible points during the iterative process. We present some numerical results obtained on real-life case studies where the functions are computed by a complex finite-element routine.
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 1721-1738 
    ISSN: 0029-5981
    Keywords: probabilistic analysis ; optimization ; safety index ; structural reliability ; Engineering ; Engineering General
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    Notes: The objective of this paper is to conduct reliability-based structural optimization in a multidisciplinary environment. An efficient reliability analysis is developed by expanding the limit functions in terms of intermediate design variables. The design constraints are approximated using multivariate splines in searching for the optimum. The reduction in computational cost realized in safety index calculation and optimization are demonstrated through several structural problems. This paper presents safety index computation, analytical sensitivity analysis of reliability constraints and optimization using truss, frame and plate examples.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1659-1680 
    ISSN: 0029-5981
    Keywords: elasticity ; stress singularity ; finite elements ; optimization ; Engineering ; Engineering General
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    Notes: A semianalytical singular element is proposed to model the stress fields in plane and axisymmetric elastic bodies in the vicinity of singular points. The element generation is performed taking into account the structure of analytical solution in the vicinity of such points. This renders the element well suited for any type of singular points. Introduction of specially generated shape functions in the approximating expressions for displacements enables one to ensure the displacement compatibility with the standard elements. A detailed consideration is given to the convergence of the finite-element procedure. The extensive possibilities of the proposed singular element are exemplified by solving particular elastic problems. The applicability of the elaborated singular element is discussed with respect to optimization of geometry and material properties in the vicinity of singular points. Two optimization problems are presented to illustrate a search for the body geometry providing the optimal stress distribution.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1761-1774 
    ISSN: 0029-5981
    Keywords: optimization ; algorithms ; structural ; design ; comparative ; evaluation ; Engineering ; Engineering General
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    Notes: Non-linear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Centre, a project was initiated to assess the performance of eight different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using the eight different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems, however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with Sequential Unconstrained Minimizations Technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 1951-1965 
    ISSN: 0029-5981
    Keywords: optimization ; thermoelasticity ; topology ; Engineering ; Engineering General
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    Notes: This paper presents the development of a computational model for the topology optimization problem, using a material distribution approach, of a 2-D linear-elastic solid subjected to thermal loads, with a compliance objective function and an isoperimetric constraint on volume. Defining formally the augmented Lagrangian associated with the optimization problem, the optimality conditions are derived analytically. The results of analysis are implemented in a computer code to produce numerical solutions for the optimal topology, considering the temperature distribution independent of design. The design optimization problem is solved via a sequence of linearized subproblems. The computational model developed is tested in example problems. The influence of both the temperature and the finite element model on the optimal solution obtained is analysed.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 361-382 
    ISSN: 0029-5981
    Keywords: optimization ; genetic ; algorithms ; trusses ; real-world ; multicriteria ; Engineering ; Engineering General
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    Notes: Genetic algorithms, a search technique which combines Darwinian ‘survival-of-the-fittest’ with randomized well structured information, is applied to the problems of real-world truss optimization. In this work a population of binary strings or ‘chromosomes’, which represent the coded truss design variables, a ‘fitness’ as a ranking measure of the adaptability to the environment, selection criteria and mechanical natural operators such as crossover and mutation are used to improve the population, so that over the generations the genetic algorithm gets better and better and at the end of the convergence, a ‘rebirth’ of the population is used to improve the usual process.An overview of the genetic algorithm will be described, continuing the rebirth effect; then, the chromosome representation of trusses is exposed. Afterwards, the objective scalar function is defined taking into account that it seems reasonable in real world to optimize trusses in minimum weight trying, at the same time, to use the minimum number of cross-section types obtained from the market. It also seems reasonable to have the possibility to change the shape of the conceptual design, moving some joints. To simulate nearly real conditions, several load cases, constraints in the elastic joint displacements, ultimate tensile and elastic and plastic buckling in the bars have been taken into account. A hyperstatic 10 bars truss is subjected to a deep analysis in different situations in order to evaluate with other authors when possible as truss optimization with two criteria and buckling effect has not been found in specialized literature. A 160-bar transmission tower is also optimized.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2055-2071 
    ISSN: 0029-5981
    Keywords: unstructured mesh generation ; optimization ; smoothing ; finite elements ; finite volume methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We propose a new optimization strategy for unstructured meshes that, when coupled with existing automatic generators, produces meshes of high quality for arbitrary domains in 3-D. Our optimizer is based upon a non-differentiable definition of the quality of the mesh which is natural for finite element or finite volume users: the quality of the worst element in the mesh. The dimension of the optimization space is made tractable by restricting, at each iteration, to a suitable neighbourhood of the worst element. Both geometrical (node repositioning) and topological (reconnection) operations are performed. It turns out that the repositioning method is advantageous with respect to both the usual node-by-node techniques and the more recent differentiable optimization methods. Several examples are included that illustrate the efficiency of the optimizer.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1985-2003 
    ISSN: 0029-5981
    Keywords: shape design ; optimization ; boundary integral equation ; design sensitivity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A design optimization procedure is developed using the boundary integral equation (BIE) method for linear elastostatic two-dimensional domains. Optimal shape design problems are treated where design variables are geometric parameters such as the positions and sizing dimensions of entire features on a component or structure. A fully analytical approach is adopted for the design sensitivity analysis where the BIE is implicitly differentiated. The ability to evaluate response sensitivity derivatives with respect to design variables such as feature positions is achieved through the definition of appropriate design velocity fields for these variables. How the advantages of the BIE method are amplified when extended to sensitivity analysis for this category of shape design problems is also highlighted. A mathematical programming approach with the penalty function method is used for solving the overall optimization problem. The procedure is applied to three example problems to demonstrate the optimum positioning of holes and optimization of radial dimensions of circular arcs on structures.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3305-3325 
    ISSN: 0029-5981
    Keywords: global ; optimization ; algorithms ; nonlinear ; engineering ; design ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: After a brief overview of the methods from the literature, two new algorithms (zooming and domain elimination) for global optimization of general NLP problems are introduced. Operations analysis and stopping criteria for the methods are discussed. Numerical evaluation of the methods is carried out using a set of mathematical programming test problems. Performance of the methods is compared with the Controlled Random Search (CRS) and the Simulated Annealing (SA) methods. The methods are superior to SA for the test problems, as they are more robust, efficient and accurate. The CRS is more efficient than the new methods; however, it is applicable to unconstrained problems only. Therefore, it is concluded that the new methods are useful for engineering optimization applications.
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 399-419 
    ISSN: 0029-5981
    Keywords: flaw identification ; boundary element method ; inverse analysis ; crack problems ; optimization ; sensitivity analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a new boundary element formulation is presented for the identification of the location and size of internal flaws in two-dimensional structures. An introduction to inverse analysis is given, with special reference to methods of flaw identification, along with a brief review of the optimization methods employed. Both the standard boundary element and the dual boundary element method are presented, with the dual boundary element method proposed as the basis for the new formulation. The flaw identification method is presented, along with the computation of the boundary displacement and traction derivatives and the specialized analytical integration used for cracked boundaries. Examples are given to demonstrate the accuracy of the sensitivity values and the performance of flaw location.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1933-1953 
    ISSN: 0029-5981
    Keywords: structures ; optimization ; large scale ; structural design ; sequential quadratic programming ; self-scaling ; numerical algorithms ; algorithm evaluation ; test problems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The basic idea of an implicit sequential quadratic programming (ISQP) method for constrained problems is to use the approximate Hessian of the Lagrangian without explicitly calculating and storing it. This overcomes one of the major drawbacks of the traditional SQP method where a large matrix needs to be calculated and stored. This concept of an implicit method is explained and an algorithm based on it is presented. The proposed method extends a similar algorithm for unconstrained problems where a two-loop recursion formula is used for the inverse Hessian matrix. The present paper develops a similar algorithm for not only the constrained problem but also the direct Hessian updates. Several scaling procedures for the Hessian are also presented and evaluated. The basic method and some of its variations are evaluated using a set of mathematical programming test problems, and a set of structural design test problems - small to larger scale. The ISQP method performs much better than a method that does not use any approximate Hessian matrix. Its performance is better than the full SQP method for larger scale problems. The test results also show that an appropriate scaling of the Hessian can improve both efficiency and reliability substantially.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 1213-1230 
    ISSN: 0029-5981
    Keywords: metal forming ; preform design ; forging ; sensitivity analysis ; optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An optimization algorithm for preform die shape design in metal-forming processes is developed in this paper. The preform die shapes are represented by cubic B-spline curves. The control points of the B-spline are used as the design variables. The optimization objective is to reduce the difference between the realized and desired final forging shapes. The sensitivities of the objective function with respect to the design variables are developed in detail. The numerical examples show that the optimization method and the sensitivity analysis developed in this paper are very useful and the design results are satisfactory. Importantly, the preform die shapes designed by this method are easily manufacturable and can be implemented in practical metal-forming operations. This optimization method and the sensitivity analysis can also be applied in the preform design of complex industrial metal-forming problems. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 1505-1524 
    ISSN: 0029-5981
    Keywords: linkages ; synthesis ; position problems ; optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper describes a procedure for the optimal dimensional synthesis of mechanisms which is based on the solution of non-linear position problems. Planar mechanisms are modelled very easily by means of finite elements of bi-hinged rod type. The judicious choice of constraint conditions makes possible the solution of classical position problems: initial, finite-displacement, deformed and static-equilibrium problems, as well as the main types of dimensional synthesis: path generation, functions, rigid body guidance, mixed, and multiple. A single synthesis error function applies to all these types, and moreover is general since it is valid for mechanisms of any configuration. This function is based on the idea that the best mechanism for the given synthesis conditions is the one that least needs to be deformed when it is obliged to satisfy them exactly, to which end the elastic deformation of the elements is permitted. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 165-188 
    ISSN: 0029-5981
    Keywords: engineering design ; optimization ; discrete variables ; numerical methods ; test problems ; evaluation of methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Continuous-discrete variable non-linear optimization problems are defined and categorized into six different types. These include a full range of problems from continuous to purely discrete and non-differentiable. Methods for solution of these problems are studied and their characteristics are catalogued. The branch and bound, simulated annealing and genetic algorithms are found to be the most general methods for solving discrete problems. After some enhancements, these and two other methods are implemented into a program for certain applications. Several example problems are solved to study performance of the methods. It is concluded that solution of the mixed variable non-linear optimization problems usually requires considerable more computational effort compared to the continuous variable optimization problems. In addition, there is no guarantee that the best solution has been obtained; however, good practical solutions are usually obtained. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 1525-1550 
    ISSN: 0029-5981
    Keywords: adjoint problem ; discrete curvature ; finite element method ; free surface flow ; optimization ; quasi-Newton method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Optimal shape design approach is applied to numerical computation of a model potential free boundary value problem. The problem is discretized using the finite element method. To test the approach the problem is formulated in both velocity potential and stream function formulation and four different finite element discretizations are used. Associated minimization problem is solved using the quasi-Newton method. Gradient of the cost function is computed by solving the algebraic adjoint equation. Gravity and surface tension forces are included in the model. Viability of the method is showed by solving problems with important effects of gravity and surface tension forces. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 787-803 
    ISSN: 0029-5981
    Keywords: multi-point approximations ; multivariate Hermite ; optimization ; design ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An approximation based on multiple function and gradient information is developed using Hermite interpolation concepts. The goal is to build a high-quality approximation for complex and multidisciplinary design optimization problems employing analysis such as aeroservoelasticity, structural control, probability, etc. The proposed multidimensional approximation utilizes exact analyses data generated during the course of iterative optimization. The approximation possesses the property of reproducing the function and gradient information of known data points. The accuracy of the new approach is compared with linear, reciprocal and other standard approximations. Because the proposed algorithm uses more data points, its efficiency has to be compared in the context of iterative optimization.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 263-292 
    ISSN: 0029-5981
    Keywords: structural synthesis ; optimization ; topology optimization ; mixed-integer nonlinear programming ; MINLP ; Modified OA/ER algorithm ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the Mixed-Integer Non-linear Programming (MINLP) optimization approach to structural synthesis. Non-linear continuous/discrete non-convex problems of structural synthesis are proposed to be solved by means of simultaneous topology, parameter and standard dimension optimization.Part I of this three-part series of papers contains a general view of the MINLP approach to simultaneous topology and continuous parameter optimization. The MINLP optimization approach is performed through three steps. The first one includes the generation of a mechanical superstructure of different topology alternatives, the second one involves the development of an MINLP model formulation and the last one consists of a solution for the formulated MINLP problem. Some MINLP methods are also presented. A Modified OA/ER algorithm is applied to solve the MINLP problem and a simple example of a multiple cantilever beam is given to demonstrate the steps of the proposed MINLP optimization approach.As simultaneous optimization, extended to include also standard dimensions, requires additional effort, the development of suitable strategies to carry out the optimization is further discussed in Part II. The modelling of MINLP superstructures and the topology and parameter optimization of roller and sliding hydraulic steel gate structures are shown in Part III of the paper. An example of the synthesis of an already erected roller gate, i.e. the Intake Gate of Aswan II in Egypt, is presented as a comparative design research work. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 329-364 
    ISSN: 0029-5981
    Keywords: structural synthesis ; optimization ; topology optimization ; discrete variable optimization ; Mixed-Integer Non-linear Programming ; MINLP ; the Modified OA/ER algorithm ; MINLP strategy ; hydraulic gate ; sliding gate ; roller gate ; Aswan ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Part III of this three-part series of papers describes the synthesis of roller and sliding hydraulic steel gate structures performed by the Mixed-Integer Non-linear Programming (MINLP) approach. The MINLP approach enables the determination of the optimal number of gate structural elements (girders, plates), optimal gate geometry, optimal intermediate distances between structural elements and all continuous and standard crossectional sizes. For this purpose, special logical constraints for topology alterations and interconnection relations between the alternative and fixed structural elements are formulated. They have been embedded into a mathematical optimization model for roller and sliding steel gate structures GATOP. GATOP has been developed according to a special MINLP model formulation for mechanical superstructures (MINLP-MS), introduced in Parts I and II. The model contains an economic objective function of self-manufacturing and transportation costs of the gate. As the GATOP model is non-convex and highly non-linear, it is solved by means of the Modified OA/ER algorithm accompanied by the Linked Two-Phase MINLP Strategy, both implemented in the TOP computer code. An example of the synthesis is presented as a comparative design research work of the already erected roller gate, the so-called Intake Gate in Aswan II in Egypt. The optimal result yields 29·4 per cent of net savings when compared to the actual costs of the erected gate. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 517-534 
    ISSN: 0029-5981
    Keywords: structural optimization ; optimization ; function approximation ; response surface methodology ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Response surface methodology can be used to construct global and midrange approximations to functions in structural optimization. Since structural optimization requires expensive function evaluations, it is important to construct accurate function approximations so that rapid convergence may be achieved. In this paper techniques to find the region of interest containing the optimal design, and techniques for finding more accurate approximations are reviewed and investigated. Aspects considered are experimental design techniques, the selection of the ‘best’ regression equation, intermediate response functions and the location and size of the region of interest. Standard examples in structural optimization are used to show that the accuracy is largely dependent on the choice of the approximating function with its associated subregion size, while the selection of a larger number of points is not necessarily cost-effective. In a further attempt to improve efficiency, different regression models were investigated. The results indicate that the use of the two methods investigated does not significantly improve the results. Finding an accurate global approximation is challenging, and sufficient accuracy could only be achieved in the example problems by considering a smaller region of the design space. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 3087-3120 
    ISSN: 0029-5981
    Keywords: structures ; structural design ; optimization ; Lagrangian ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The merits and limitations of the Optimality Criteria (OC) method for the minimum weight design of structures subjected to multiple load conditions under stress, displacement and frequency constraints were investigated by examining several numerical examples. The examples were solved utilizing the OC design code that was developed for this purpose at the NASA Lewis Research Center. This OC code incorporates OC methods available in the literature with generalizations for stress constraints, fully utilized design concepts, and hybrid methods that combine both techniques. It includes multiple choices for Lagrange multiplier and design variable update methods, design strategies for several constraint types, variable linking, displacement and integrated force method analysers, and analytical and numerical sensitivities. On the basis of the examples solved, the optimality criteria for general application were found to be satisfactory for problems with few active constraints or with small numbers of design variables. However, the OC method without stress constraints converged to optimum even for large structural systems. For problems with large numbers of behaviour constraints and design variables, the method appears to follow a subset of active constraints that can result in a heavier design. The computational efficiency of OC methods appears to be similar to some mathematical programming techniques.
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