Modeling of anisotropic boundary layer effects in plate theory

PAMM ◽  
2018 ◽  
Vol 18 (1) ◽  
Author(s):  
Patrick Schneider ◽  
Reinhold Kienzler
Keyword(s):  
Boundary Layer ◽  
Plate Theory

Comparison of Inviscid Computations With Theory and Experiment in Vibrating Transonic Compressor Cascades

1990 ◽  
Author(s):  
G. A. Gerolymos ◽  
E. Blin ◽  
H. Quiniou
Keyword(s):  
Boundary Layer ◽  
Plate Theory ◽  
Strong Shock ◽  
Acoustic Resonance ◽  
Boundary Layer Separation ◽  
Computational Method ◽  
Viscous Effects ◽  
Transonic Compressor ◽  
Boundary Layer Interaction ◽  
Interaction Regions

The prediction of unsteady flow in vibrating transonic cascades is essential in assessing the aeroelastic stability of fans and compressors. In the present work an existing computational code, based on the numerical integration of the unsteady Euler equations, in blade-to-blade surface formulation, is validated by comparison with available theoretical and experimental results. Comparison with the flat plate theory of Verdon is, globally, satisfactory. Nevertheless, the computational results do not exhibit any particular behaviour at acoustic resonance. The use of a 1-D nonreflecting boundary condition does not significantly alter the results. Comparison of the computational method with experimental data from started and unstarted supersonic flows, with strong shock waves, reveals that, notwithstanding the globally satisfactory performance of the method, viscous effects are prominent at the shock wave/boundary layer interaction regions, where boundary layer separation introduces a pressure harmonic phase shift, which is not presicted by inviscid methods.

A Simple Theory for the Two-Dimensional Compressible Turbulent Boundary Layer

1972 ◽  
Vol 94 (3) ◽  
pp. 636-642 ◽  
Author(s):  
F. M. White ◽  
G. H. Christoph
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Skin Friction ◽  
Plate Theory ◽  
Momentum Equation ◽  
Shape Factors ◽  
Law Of The Wall ◽  
Compressible Turbulent Flow ◽  
New Equation

A new approach is proposed for analyzing the compressible turbulent boundary layer with arbitrary pressure gradient. Utilizing a compressible law-of-the-wall and a Crocco energy approximation, the new theory integrates the momentum equation across the boundary layer in terms of inner variables only. The result is a single first-order ordinary differential equation for skin friction, devoid of integral thicknesses and shape factors. When analyzed for flat plate flow, this new equation has an exact solution apparently superior in accuracy to any other flat plate theory (Table 1). The new equation also agrees well with supersonic skin friction data in both favorable and adverse pressure gradients. The new theory contains an explicit separation criterion and is the simplest and possibly most accurate existing analysis for compressible turbulent flow.

On a boundary layer phenomenon in Mindlin-Reissner plate theory for laminated circular sector plates

2001 ◽  
Vol 151 (3-4) ◽  
pp. 149-161 ◽  
Author(s):  
A. Nosier ◽  
A. Yavari ◽  
S. Sarkani
Keyword(s):  
Boundary Layer ◽  
Plate Theory ◽  
Circular Sector ◽  
Reissner Plate

Interlaminar Stresses in Composite Laminates Subjected to Anticlastic Bending Deformation

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
Johnathan Goodsell ◽  
Nicholas J. Pagano ◽  
Oleksandr Kravchenko ◽  
R. Byron Pipes
Keyword(s):  
Boundary Layer ◽  
Temperature Change ◽  
Plate Theory ◽  
Finite Width ◽  
Uniform Temperature ◽  
Interlaminar Stresses ◽  
Poisson Effect ◽  
Bending Deformation ◽  
Axial Extension ◽  
Deformation State

Approximate elasticity solutions for prediction of the displacement, stress, and strain fields within the m-layer, symmetric and balanced angle-ply composite laminate of finite-width and subjected to uniform axial extension and uniform temperature change were developed earlier by the authors. In the present paper, the authors have extended these solutions to treat bending deformation. Bending and torsion moments are combined to yield a deformation state without twisting curvature and with transverse curvature due only to the laminate Poisson effect. This state of deformation is termed anticlastic bending. The approximate elasticity solution for this bending deformation is shown to recover laminated plate theory predictions at interior regions of the laminate and thereby illustrates the boundary layer character of this interlaminar phenomenon. The results exhibit the anticipated response in congruence with the solutions for uniform axial extension and uniform temperature change, where divergence of the interlaminar shearing stress is seen to occur at the intersection of the free edge and planes between lamina of +θ and –θ orientation. The analytical results show excellent agreement with the finite-element predictions for the same boundary-value problem and thereby provide an efficient and compact solution available for parametric studies of the influence of geometry and material properties. Finally, the solution was exercised to determine the dimensions of the boundary layer in bending for very large numbers of layers.

On the Stress Singularities and Boundary Layer in Moderately Thick Functionally Graded Sectorial Plates

2010 ◽  
Author(s):  
A. R. Saidi ◽  
F. Hejripour ◽  
E. Jomehzadeh
Keyword(s):  
Boundary Layer ◽  
Plate Theory ◽  
Functionally Graded ◽  
Stress Singularities ◽  
Equilibrium Equations ◽  
Arbitrary Boundary ◽  
Edge Zone ◽  
Layer Function ◽  
Sector Plate ◽  
Boundary Layer Function

In this paper, the stress analysis of moderately thick functionally graded (FG) sector plate is developed for studying the singularities in vicinity of the vertex. Based on the first-order shear deformation plate theory, the governing partial differential equations are obtained. Using an analytical method and defining some new functions, the stretching and bending equilibrium equations are decoupled. Also, introducing a function, called boundary layer function, the three bending equations are converted into two decoupled equations called edge-zone and interior equations. These equations are solved analytically for the sector plate with the simply supported radial edges and arbitrary boundary condition along the circular edge. The singularities of shear force and moment resultants are discussed for both salient and re-entrant sectorial plates. Also, the effects of power of the FGM, thickness to length ratio on the stress singularities of the FG sector plates are investigated.

Bending of a Thin Reissner Plate With a Through Crack

1991 ◽  
Vol 58 (3) ◽  
pp. 842-846 ◽  
Author(s):  
P. F. Joseph ◽  
F. Erdogan
Keyword(s):  
Boundary Layer ◽  
Plate Theory ◽  
Plate Thickness ◽  
Asymptotic Result ◽  
Leading Order ◽  
Classical Plate Theory ◽  
Outer Solution ◽  
Reissner Plate ◽  
Perturbation Problem ◽  
Title Problem

The title problem was first considered by Knowles and Wang (1960) and was shown to be related to the solution given by the classical plate theory. This solution is actually the outer solution of a singular perturbation problem, and therefore is valid only away from the crack-tip region. Within a boundary layer of order h/a, where h is the plate thickness and a is the half-crack length, the two theories differ considerably. In this study the leading order solution is obtained for h/a - 0 and it is shown that the limiting stress intensity factor given by the Reissner plate theory is more than 50 percent higher than the asymptotic result (1 + v)/(3 + v) which is obtained from the displacement field as given by the classical plate theory.

Boundary Layer Phenomena in Large Deflection, Small Strain Plate Theory

1993 ◽  
Vol 60 (1) ◽  
pp. 229-232
Author(s):  
L. J. Berg
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Boundary Layers ◽  
Large Deflection ◽  
Large Deformations ◽  
Plate Theory ◽  
Small Strain ◽  
Thin Plates ◽  
Large Deflections ◽  
Layer Solution

Boundary layers exist at the edges of thin plates undergoing large deformations because the interior of the plate must assume a developable shape. The developable shape is sometimes incompatible with the force and moment resultants prescribed at the plate’s boundary, in particular when the edge of the plate is stress free. A boundary layer solution is presented which describes the shape of a boundary layer in a plate undergoing large deflections. The boundary layer is a slight perturbation of the interior shape which allows the appropriate boundary conditions to be satisfied. Since developable shells are applicable to a plane, the boundary layer is also appropriate for arbitrary developable shells.

Effects of continental boundary layer evolution, convection, turbulence and entrainment, on aerosol formation

Tellus B ◽  
2001 ◽  
Vol 53 (4) ◽  
pp. 441-461 ◽  
Author(s):  
E. D. NILSSON ◽  
Ü. RANNIK ◽  
M. KULMALA ◽  
G. BUZORIUS ◽  
C. D. O'DOWD
Keyword(s):  
Boundary Layer ◽  
Aerosol Formation
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