Complex Variable Theory and Elastic Stability Problems

by Patricio A. Laura,
Paul Shahady,

Serial Information: Journal of the Engineering Mechanics Division, 1969, Vol. 95, Issue 1, Pg. 59-68

Document Type: Journal Paper


Solution of the eigenvalue problem governing the elastic stability of a thin elastic plate subjected to hydrostatic in-plane compression is easily accomplished when the boundary configuration is natural to one of the common coordinate systems. For more exotic boundaries approximate techniques must be used. If the given domain is mapped onto a simpler one, i.e., the unit circle, the boundary conditions can then be satisfied identically. Since the governing partial differential equation is not invariant under the transformation and becomes considerably more complicated, a variational method is used to solve it. The method is illustrated in the case of clamped and simply supported plates of various configurations.

Subject Headings: Elastic analysis | Plates | Domain boundary | Eigenvalues | Hydrostatics | Compression | Mapping | Boundary conditions

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