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Analysis of the Buckling Pressure of an Elastic Plate Floating on Water and Stressed Uniformly along the Periphery of an Internal Hole.
Final rept. 1 Jul 72-31 May 74,
COLD REGIONS RESEARCH AND ENGINEERING LAB HANOVER N H
Pagination or Media Count:
The problem reduces to an eigenvalue problem of a fourth-order ordinary differential equation in a semi-infinite region. Two methods of solution, the Green function method and the contour integral method, are presented. The Green function method yields an integral equation that can be solved only numerically. The contour integral method gives a third-order ordinary differential equation of which the singular points are all regular. Therefore a series solution relative to a singular point can be analytically continued to a linear combination of a set of series solutions relative to another singular point. In this way we find the integrand, required in the contour integral method, that vanishes at x infinity and has a branch point at the lower end of the integration. The contour integral thus formulated is reduced to a linear combination of the fundamental solutions, relative to x 0, of the original fourth-order differential equation. This linear combination can give the solutions to our eigenvalue problem. Author
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