Shear Flow Distribution Research Articles

Transport coefficients for an inelastic gas around uniform shear flow: Linear stability analysis

The inelastic Boltzmann equation for a granular gas is applied to spatially inhomogeneous states close to uniform shear flow. A normal solution is obtained via a Chapman-Enskog-like expansion around a local shear flow distribution. The heat and momentum fluxes are determined to first order in the deviations of the hydrodynamic field gradients from their values in the reference state. The corresponding transport coefficients are determined from a set of coupled linear integral equations which are approximately solved by using a kinetic model of the Boltzmann equation. The main new ingredient in this expansion is that the reference state f(0) (zeroth-order approximation) retains all the hydrodynamic orders in the shear rate. In addition, since the collisional cooling cannot be compensated locally for viscous heating, the distribution f(0) depends on time through its dependence on temperature. This means that in general, for a given degree of inelasticity, the complete nonlinear dependence of the transport coefficients on the shear rate requires analysis of the unsteady hydrodynamic behavior. To simplify the analysis, the steady-state conditions have been considered here in order to perform a linear stability analysis of the hydrodynamic equations with respect to the uniform shear flow state. Conditions for instabilities at long wavelengths are identified and discussed.

Closed-form analysis of thin-walled composite I-beams considering non-classical effects

In this work, a closed-form analysis of thin-walled open profile composite beams such as I-beam has been performed. The analysis includes the effects of elastic couplings, shell wall thickness, transverse shear deformation, torsion warping, and constrained warping. A mixed beam approach based on Reissner’s semi-complementary energy functional is used to derive the beam force–displacement relations. A closed-form solution for the static response of both symmetric and anti-symmetric layup beams with transverse shear couplings is derived. The beams considered have the boundary condition of one end fixed and the other end warping restrained and are subjected to unit bending or torque load at the beam tip. The shear flow distribution related with the applied forces and moments along the contour of the beam is also identified. The static results of composite I-beams have been validated against those of detailed two-dimensional finite element analysis. The effects of warping restraint and transverse shear deformation on the static behavior of open-section composite beams are investigated in the analysis.

Numerical Study of the Mechanism of Wavy Interface Generation in Explosive Welding.

Wavy interface generation is an interesting characteristic of explosive welding. There have been many theoretical and experimental discussions of the mechanism of wavy interface generation, but there is no consensus of opinion as yet. We report on a numerical approach to the analysis of the mechanism of wavy interface generation in explosive welding. The wavy interface generation process is calculated using a two-dimensional finite difference scheme for elastic-plastic materials. In this simulation the equations for a symmetric collision between copper plates are solved. The concept behind this study is that the wavy interface and vortex street are caused by the velocity distribution of shear flow and periodic disturbance at the interface. The calculation results show the deformation process of the wavy interface and we obtain qualitative agreements between numerical and experimental results.

Numerical Study of the Mechanism of Wavy Interface Generation in Explosive Welding.

Wavy interface generation is an interesting characteristic of explosive welding. There have been many theoretical and experimental discussions of the mechanism of wavy interface generation, but there is no consensus of opinion as yet. We report a numerical approach to the analysis of the mechanism of interface wave generation in explosive welding. The phenomena of the interface wave generation are calculated using a two-dimensional finite difference scheme for elastic-plastic materials. In this simulation the equations for a symmetric collision between copper plates are solved. The concept behind this study is that the wavy interface and vortex streets are caused by the velocity distribution of shear flow and periodic disturbances at the interface. The calculation results show the deformation process of the wavy interface and we obtain qualitative agreements between numerical and experimental results.

Shear flow distribution in multi-cell girders

A computer program is described for the shear flow analysis of multi-cell girders. The basic assumption of the theory used is that the loading pattern does not cause any distortion of a transverse section of the girder. The computer routine is based on a system of defining girder cross-sectional layouts which can be applied to a wide variety of beams with a minimum of data preparation and coding. The difficulties encountered in devising the routine and the solutions adopted are described in detail. The method is demonstrated on three different beam cross-sections taken from ship structures.

Effect of ship section scantlings and transverse position of longitudinal bulkheads on shear stress distribution and shear carrying capacity of main hull girder

The paper examines the effect of varying the different ship section parameters on the shear flow distribution and maximum shear stresses at the section neutral axis due to longitudinal vertical shear force. The contribution of the side longitudinal b

Differential Shear-Flow Analysis for Nonprismatic Semimonocoque Beams

This paper gives the derivation of a method for obtaining the shear-flow distribution in a nonprismatic semimonocoque beam with nonlinear axial-load variations due to externally applied loads. This method is based on the actual rates of change of segment axial loads at a particular station rather than the average rate of change of segment axial loads between two reasonably separated stations. The particular application presented is for a wing; however, the method is applicable to any semimonocoque structure. I t also has special adaptations for many loading conditions at each station. The shear-flow distribution may be determined for each component of the loading condition such as torsion and beam and chord shear and moment. The location of the shear center may be determined if the shear flow due to pure torsion is desired. This method of analysis is adaptable to International Business Machine operations. The IBM calculations may be performed on machines such as the relatively slow 602 A Multiplier or the faster Card Program Sequence Calculator. The time required by IBM to calculate and check the shear center and unit shear flows and determine, for ten complete loading conditions, the resultant shears for a 20-segment station is approximately 30 min. The results obtained by using the method presented in this paper on two beams, one with straight surfaces and one with curved surfaces, are compared with those obtained by VQ/I and the Unit Method of Beam Analysis.