997 resultados para Critic theory
Resumo:
Texto em português e inglês.
Resumo:
An optimal theory on how database analysis to capture the flow structures has been developed in this paper, which include the POD method as its special case. By means of the remainder minimization method in the Sobolev space, for more general optimal conditions the new theory has the potential to overcome an inherent limitation of the POD method, i.e., it cannot be used to the situations in which the optimal condition is other than the inner product global one. As an example, using the new theory, the database of a two-dimensional flow over a backward-facing step is analyzed in detail, with velocity and vorticity bases.
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A new high-order refined shear deformation theory based on Reissner's mixed variational principle in conjunction with the state- space concept is used to determine the deflections and stresses for rectangular cross-ply composite plates. A zig-zag shaped function and Legendre polynomials are introduced to approximate the in-plane displacement distributions across the plate thickness. Numerical results are presented with different edge conditions, aspect ratios, lamination schemes and loadings. A comparison with the exact solutions obtained by Pagano and the results by Khdeir indicates that the present theory accurately estimates the in-plane responses.
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A previously published discrete-layer shear deformation theory is used to analyze free vibration of laminated plates. The theory includes the assumption that the transverse shear strains across any two layers are linearly dependent on each other. The theory has the same dependent variables as first order shear deformation theory, but the set of governing differential equations is of twelfth order. No shear correction factors are required. Free vibration of simply supported symmetric and antisymmetric cross-ply plates is calculated. The numerical results are in good agreement with those from three-dimensional elasticity theory.
Resumo:
On the basis of a brief review of the continuum theory for macroscopic descriptions and the kinetic theory for microscopic descriptions in solid/liquid two-phase flows, some suggestions are presented, i.e. the solid phase may be described by the Boltzmann equation and the liquid phase still be described by conservation laws in the continuum theory. Among them the action force on the particles by the liquid fluid is a coupling factor which connects the phases. For dilute steady solid/liquid two-phase flows, the particle velocity distribution function can be derived by analogy with the procedures in the kinetic theory of gas molecules for the equilibrium state instead of being assumed, as previous investigators did. This done, more detailed information, such as the velocity probability density distribution, mean velocity distribution and fluctuating intensity etc. can be obtained directly from the particle velocity distribution function or from its integration. Experiments have been performed for dilute solid/liquid two-phase flow in a 4 x 6 cm2 sized circulating square pipe system by means of laser Doppler anemometry so that the theories can be examined. The comparisons show that the theories agree very well with all the measured data.
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In this paper, a theory is developed to calculate the average strain field in the materials with randomly distributed inclusions. Many previous researches investigating the average field behaviors were based upon Mori and Tanaka's idea. Since they were restricted to studying those materials with uniform distributions of inclusions they did not need detailed statistical information of random microstructures, and could use the volume average to replace the ensemble average. To study more general materials with randomly distributed inclusions, the number density function is introduced in formulating the average field equation in this research. Both uniform and nonuniform distributions of inclusions are taken into account in detail.
Resumo:
The results of experiments in open channels and closed pipelines show two kinds of patterns for the vertical distribution of particle concentration (i.e., pattern I and pattern II). The former shows a pattern of maximum concentration at some location above the bottom and the downward decay of the concentration below the location. The latter always shows an increase of the particle concentration downward over the whole vertical, with the maximum value at the bottom. Many investigations were made on the pattern II, but few were made on pattern I. In this paper, a particle velocity distribution function is first obtained in the equilibrium state or in dilute steady state for the particle in two-phase flows, then a theoretical model for the particle concentration distribution is derived from the kinetic theory. More attention is paid to the predictions of the concentration distribution of pattern I and comparisons of the present model are made with the data measured by means of laser doppler anemometry (LDA). Very good agreements are obtained between the measured and calculated results.
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To gain some insight into the behaviour of low-gravity flows in the material processing in space, an approximate theory has been developed for the convective motion of fluids with a small Grashof number Gr. The expansion of the variables into a series of Gr reduces the Boussinesq equation to a system of weakly coupled linearly inhomogeneous equations. Moreover, the analogy concept is proposed and utilized in the study of the plate bending problems in solid mechanics. Two examples are investigated in detail, i. e. the 2-dimensional steady flows in either circular or square infinite closed cylinder, which is horizontally imposed at a specified temperature of linear distribution on the boundaries. The results for stream function ψ, velocity u and temperature T are provided. The analysis of the influences of some parameters such as the Grashof number Gr and the Prandtl number Pr, on motions will lead to several interesting conclusions. The theory seems to be useful for seeking for an analytical solutions. At least, it will greatly simplify the complicated problems originally governed by the Navier-Stokes equation including buoyancy. It is our hope that the theory might be applicable to unsteady or 3-dimensional cases in future.
Resumo:
that the Stokes-interaction relation is reasonable qualitatively but not correct