The Plate Problem for a Cantilever Sector of Uniform Thickness

Citation

Williams, Max Lea (1950) The Plate Problem for a Cantilever Sector of Uniform Thickness. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/WFM9-RR55. https://resolver.caltech.edu/CaltechETD:etd-07202004-095445

Abstract

As one approach to the problem of analyzing missile wings of approximately delta configuration for stress and deflection characteristics, a uniformly thin plate of sector planform clamped along one radial edge has been considered. It is shown that an infinite set of deflection functions, resulting from a product solution to the double Laplacian, may be generated, but practical utility is impeded because the functions are non-orthogonal. It is believed that should the importance of the solution warrant, the deflection of a sector under normal loading may be found by using a combination of the deflection functions, the Trefftz variational method, and high speed computing machinery. Another section of the report is devoted to a study of the stress along the clamped edge in the vicinity of the corner, and it is shown that the stress varies from zero to a mathematical infinity as the opening angle of the sector increases from zero through ninety degrees with the stress singularity becoming progressivev stronger as the opening angle is increased. Experimental data are included that show engineering agreement with the theoretical results, for the case of a delta plate of thirty degree opening angle and varying trailing edge angle. In conclusion, some remarks are made upon the application of the sector results to swept rectangular plates by mans of a hydrodynamic analogy wherein the possibility of obtaining approximate overall stress distributions is indicated.

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