The application of limit analysis to the determination of the strength of butt joints
Author:
R. T. Shield
Journal:
Quart. Appl. Math. 15 (1957), 139-147
MSC:
Primary 73.2X
DOI:
https://doi.org/10.1090/qam/92463
MathSciNet review:
92463
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Abstract: The technique of limit analysis is applied to determine upper and lower bounds for the tensile strength of a butt joint consisting of a thin layer of adhesive joining the parallel flats of two rigid adherends. The adhesive is assumed to be an elastic-perfectly plastic material which yields when the maximum shear stress reaches a critical value. The methods used apply to any joint with a convex area of cross-section. Particular application is made to joints whose cross-sections are circular, rectangular, or a polygon circumscribed about a circle.
J. W. McBain and W. B. Lee, Adhesion and adhesives: gums, resins and waxes between polished metal surfaces, J. Phys. Chem. 31, 1674-1680 (1927)
N. A. de Bruyne and R. Houwink (Eds.), Adhesion and adhesives, Chap. 3, Rheology of adhesives by J. Hoekstra and C. P. Fritzius, Elsevier, Amsterdam, 1951
N. A. de Bruyne and R. Houwink (Eds.), Adhesion and adhesives, Chap. 4, Static problems by C. Mylonas and N. A. de Bruyne, Elsevier, Amsterdam, 1951
H. J. Greenberg and W. Prager, Limit design of beams and frames, Trans. Amer. Soc. Civ. Engrs. 117, 447-484 (1952)
- D. C. Drucker, H. J. Greenberg, and W. Prager, The safety factor of an elastic-plastic body in plane strain, J. Appl. Mech. 18 (1951), 371–378. MR 0051119
- D. C. Drucker, W. Prager, and H. J. Greenberg, Extended limit design theorems for continuous media, Quart. Appl. Math. 9 (1952), 381–389. MR 45573, DOI https://doi.org/10.1090/S0033-569X-1952-45573-2
L. M. Kachanov, On a problem of deformation in plastic layers, Doklady Akad. Nauk S.S.S.R. (N.S.) 96, 249-252 (1954)
W. Schroeder and D. A. Webster, Press-forging thin sections: effect of friction, area, and thickness on pressure required, J. Appl. Mech. 16, 289-294 (1949)
G. G. Meyerhof and T. K. Chaplin, The compression and bearing capacity of cohesive layers, Brit. J. Appl. Phys. 4, 20-26 (1953)
R. T. Shield and D. C. Drucker, The application of limit analysis to punch-indentation problems, J. Appl. Mech. 20, 453-460 (1953)
- R. T. Shield, The plastic indentation of a layer by a flat punch, Quart. Appl. Math. 13 (1955), 27–46. MR 67719, DOI https://doi.org/10.1090/S0033-569X-1955-67719-0
J. W. McBain and W. B. Lee, Adhesion and adhesives: gums, resins and waxes between polished metal surfaces, J. Phys. Chem. 31, 1674-1680 (1927)
N. A. de Bruyne and R. Houwink (Eds.), Adhesion and adhesives, Chap. 3, Rheology of adhesives by J. Hoekstra and C. P. Fritzius, Elsevier, Amsterdam, 1951
N. A. de Bruyne and R. Houwink (Eds.), Adhesion and adhesives, Chap. 4, Static problems by C. Mylonas and N. A. de Bruyne, Elsevier, Amsterdam, 1951
H. J. Greenberg and W. Prager, Limit design of beams and frames, Trans. Amer. Soc. Civ. Engrs. 117, 447-484 (1952)
D. C. Drucker, H. J. Greenberg and W. Prager, The safety factor of an elastic-plastic body in plane strain, J. Appl. Mech. 73, 371-378 (1951)
D. C. Drucker, W. Prager and H. J. Greenberg, Extended limit design theorems for continuous media, Quart. Appl. Math. 9, 381-389 (1952)
L. M. Kachanov, On a problem of deformation in plastic layers, Doklady Akad. Nauk S.S.S.R. (N.S.) 96, 249-252 (1954)
W. Schroeder and D. A. Webster, Press-forging thin sections: effect of friction, area, and thickness on pressure required, J. Appl. Mech. 16, 289-294 (1949)
G. G. Meyerhof and T. K. Chaplin, The compression and bearing capacity of cohesive layers, Brit. J. Appl. Phys. 4, 20-26 (1953)
R. T. Shield and D. C. Drucker, The application of limit analysis to punch-indentation problems, J. Appl. Mech. 20, 453-460 (1953)
R. T. Shield, The plastic indentation of a layer by a flat punch, Quart. Appl. Math. 13, 27-46 (1955)
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Article copyright:
© Copyright 1957
American Mathematical Society
