Abstract
In this paper, the general solution for the mixed boundary value problem with two external force boundaries and two displacement boundaries is described. Rational mapping and complex stress functions are used for the analysis. The problem with two displacement boundaries is mathematically more difficult to solve than that with one displacement boundary because integral constants (C 1, C 2, C 3in (15.2)) appear and must be determined. Also, the Plemelj function used is more complicated than that of the latter. A mixed boundary value problem for thin plate bending of arbitrary shapes, for example, a half plane with one clamped boundary under out-of-plane loading, has been analyzed [1]. Developing it into the problem with two clamped boundaries is very useful for wide applicability to more complicated structural analysis. As an application of the solution, a semi-infinite plate with two clamped edges within a semi-elliptic notch under uniform bending (see Fig. 15.2) is analyzed. Analysis of a problem for one clamped boundary on a semi-elliptic notch on a semi-infinite plate was reported in [2].
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