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The effect of two isolated forces on the elastic stability of a flat rectangular plate

Published online by Cambridge University Press:  24 October 2008

D. M. A. Leggett
D. M. A. Leggett
Affiliation:
Trinity College
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Extract

1. Introduction and summary. The problem of the elastic stability of a simply supported rectangular plate, compressed by two equal and opposite forces acting in the plane of the plate (see Fig. 1), was first attempted by A. Sommerfeld, and later by S. Timoshenko. The former produced a solution which in a later paper he admitted to be liable to very considerable error, while the latter constructed a solution by means of the well-known strain-energy method. In many problems this method gives results in very close agreement with those obtained in a more rigorous manner, but, in the particular case considered here, it appeared likely that the error would be appreciable owing to the underlying assumption that the only stresses in the plate occurred along the common line of action of the two external forces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 33 , Issue 3 , July 1937 , pp. 325 - 339
Copyright
Copyright © Cambridge Philosophical Society 1937

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References

* Sommerfeld, A., Zeit. f. Math. u. Physik, 54 (1906), 113 and 318.Google Scholar

† Timoshenko, S., Zeit. f. Math. u. Physik, 58 (1910), 357;Google ScholarTheory of elastic stability (McGraw-Hill, 1936), § 68.Google Scholar

* For the sake of definiteness we suppose the following remarks to apply to the external force system acting on the side η = 0. In point of fact they are equally applicable to the force system acting over η = b.

* See Timoshenko, S., Theory of elasticity (McGraw-Hill, 1934), § 20.Google Scholar

* Love, A. E. H., Mathematical theory of elasticity, 4th ed. (Cambridge, 1927), § 89.Google Scholar

* See, for example Southwell, R. V., Phil. Trans. Roy. Soc. 213 (1913), 187.CrossRefGoogle Scholar

* Since ω = 0 over the boundary of the plate, the second term in these two equations is automatically zero.

* Theory of elastic stability, loc. cit. p. 1.

* From (37) we deduce that if M is 8, M 1 is 10.

† For a description of the machine and an explanation of the principles on which it works, see Mallock, R. R. M., Proc. Roy. Soc. 140 (1933), 457.CrossRefGoogle Scholar