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The Quarterly Journal of Mechanics and Applied Mathematics 1959 12(1):72-81; doi:10.1093/qjmam/12.1.72
© 1959 by Oxford University Press
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SOME MIXED BOUNDARY-VALUE PROBLEMS OF AEOLOTROPIC THIN PLATE THEORY

G. M. L. GLADWELL

( (Department of Math., University College London) )

This paper applies the theory of sectionally holomorphic functions, developed by N. I. Muskhelishvili and others, to some mixed boundary-value problems of aeolotropic thin plate theory. The mixed boundary conditions are derived from plates having boundaries which are partly clamped, and partly free or subjected to specified bending moment and shear. Each problem is reduced to the solution of a series of equations relating the boundary values of sectionally holomorphic functions on opposite sides of one or more arcs; these are problems solved in (2). Details of the solution are given for the problem of a plate in the form of the upper half-plane, subjected to constant bending moment and shear on a segment of the real axis, and clamped along the remainder.


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