Comment on ?a simple approximate solution for horizontal infiltration in a Brooks-Corey medium? by R. W. Zimmerman and G. S. Bodvarsson

1992 ◽  
Vol 9 (3) ◽  
pp. 297-301 ◽  
Author(s):  
J. -Y. Parlange ◽  
D. A. Barry ◽  
R. Haverkamp
Keyword(s):  
Approximate Solution ◽  
Horizontal Infiltration ◽  
Simple Approximate Solution

scholarly journals Approximate Biaxial Stress Solution for Orthotropic Open-Hole Composite Laminates

1996 ◽  
Vol 5 (4) ◽  
pp. 096369359600500
Author(s):  
C. Filiou ◽  
C. Soutis
Keyword(s):  
Approximate Solution ◽  
Stress Distribution ◽  
Circular Hole ◽  
Composite Laminates ◽  
Composite Laminate ◽  
Biaxial Loading ◽  
Biaxial Stress ◽  
Orthotropic Composite ◽  
Open Hole ◽  
Simple Approximate Solution

A simple approximate solution has been derived for the stress distribution near a circular hole applicable to any orthotropic composite laminate subjected to biaxial loading. The degree of accuracy of this solution was found to be overall acceptable, but strongly dependent upon the laminate lay-up and biaxiality ratio.

scholarly journals Spring-mass running: simple approximate solution and application to gait stability

2005 ◽  
Vol 232 (3) ◽  
pp. 315-328 ◽  
Author(s):  
Hartmut Geyer ◽  
Andre Seyfarth ◽  
Reinhard Blickhan
Keyword(s):  
Approximate Solution ◽  
Gait Stability ◽  
Simple Approximate Solution

Approximate Solutions for Symmetrically Loaded Thick-Walled Cylinders

1947 ◽  
Vol 14 (4) ◽  
pp. A301-A311
Author(s):  
C. W. MacGregor ◽  
L. F. Coffin
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Approximate Solutions ◽  
Fourier Integral ◽  
Integral Methods ◽  
Pressure Distributions ◽  
Internal Strains ◽  
Walled Cylinder ◽  
Simple Approximate Solution ◽  
Good Agreement

Abstract Based upon an extension of the theory of a bar on an elastic foundation, a simple approximate solution is given in closed form for the analysis of the stresses and strains in a thick-walled cylinder loaded either internally or externally by an axially symmetrical system of forces. The analysis avoids the tedious computation of stresses inherent in exact solutions of this problem by the Fourier series or Fourier integral methods and is in a form which can easily be used by designers. The approximate solution for both semi-infinite pressure distributions and shorter bands of internal pressure are compared with the mathematically exact solutions and with experiment. Good agreement is found in all cases for external strains, while for internal strains the agreement is good except very close to the discontinuity in pressure. Since it is doubtful in practice that an abrupt discontinuity in pressure is often realized in such cases, the approximate solution may also be useful near this discontinuity. More important, however, is the fact that the effective stresses (based upon the distortion-energy theory of yielding), as determined both by the exact and approximate solutions, are in close agreement.

On the structure of a class of aerothermodynamic shocks

1969 ◽  
Vol 37 (2) ◽  
pp. 349-370 ◽  
Author(s):  
P. A. Blythe ◽  
D. G. Petty ◽  
D. A. Schofield ◽  
J. L. Wilson
Keyword(s):  
Approximate Solution ◽  
Asymptotic Solution ◽  
Recent Work ◽  
Numerical Solutions ◽  
Rate Process ◽  
Adiabatic Shock ◽  
Nozzle Flows ◽  
Shock Solution ◽  
Arbitrary Rate ◽  
Simple Approximate Solution

Some recent work on the existence of vibrational de-excitation shocks (δ-shocks) in expanding non-equilibrium nozzle flows is extended to include situations in which an adiabatic shock (δ-shocks) may be embedded within the de-excitation shock. A discussion of some further properties of the shock solution is given and some examples are worked out. Numerical solutions of the full equations are also presented. These solutions confirm the existence of the δ-shocks but bring to light certain anomalies in the simple approximate solution. The modifications necessary to remove these discrepancies are outlined, and the implications of the numerical results are briefly discussed. Finally, some comments on the nature of the asymptotic solution for an arbitrary rate process are made.

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