Three configurations of reinforced membranes termed loxodromic, geodesic, and quadratic are considered. Prescriptions for the construction of each design are derived. In all cases the cords are assumed extensible and the case of cylindrical symmetric de formation is considered. The equilibrium shape and stress problem, for each design, is solved. Principal stresses, cord tensions, cord lengths, and membrane strengths are calculated and compared to a standard design. The advantages and disadvantages of each design are discussed.
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References
1.
J.E. Adkins , "Finite Plane Deformation of Thin Elastic Sheets Reinforced with Inextensible Cords," London, Philosophical Transactions Royal Society, Series A, 249, 125-150 (1956).
2.
J.E. Adkins , J. of Rational Mechanics and Analysis189-202 (1956).
3.
W.F. Ames, J. Franklin Inst.272, 185-190 (1961).
4.
W.F. Ames, Textile Res. J.32, 8-13 (1962).
5.
R. Harrinton, Personal Communication.
6.
F.B. Hildebrand, "Introduction to Numerical Analysis," New York, McGraw-Hill Book Co., 1956.
7.
W. Honerberth , Kautschuk Gummi8, WT124-WT130 (1955).
8.
W. Hofferberth , Kautschuk Gummi8, Sonderheft Der Reifen, 3-9 (1955).
9.
W. Hofferberth , Kautschuk Gummi9, WT255-WT231 (1956).
10.
H.G. Lauterbach and W.F. Ames, Textile Res. J.29, 890-900 (1959).
11.
R.S. Rivlin , J. of Rational Mechanics and Analysis4, 951-974 (1955).
12.
R.S. Rivlin , Arch. for Rational Mechanics andAnalysis2, 447-476 (1959).
13.
R.S. Rivlin, "Networks of Inextensible Cords," Chapter in "Nonlinlear Problems of Engineering" (Ed. W. F. Ames), New York, Academic Press, 1964, pp. 51-64.
14.
R.S. Rivlin and J.E. Adkins, "Large Elastic Deformations of Isotropic Material, X-Reinforcement by Inextensible Cords," London, Philosophical Transactions Royal Society, Series A, 248, 201-223, (1955).
15.
D. Widder, "Advanced Calculus," New York, Prentice-Hall, Inc., 1947, Chapter 3.
