Bending of thin elastic plates containing line discontinuities

[摘要] The purpose of this work is to examine the stress distribution caused by the bending of a thin elastic plate containing a line discontinuity. Specifically, the plate under consideration is of constant thickness and occupies a whole plane exterior to the line discontinuity. The line discontinuity is either a crack or a rigid inclusion.The loading is applied to the plate at infinity by certain combinations of tractions which leave the plate in equilibirum.The analysis of the problems considered here is based onan approximate theory which is more refined than the classical theory ordinarily applied to problems of bending of plates. This is because results based on the classical theory may be incorrect, even in first approximation for thin plates, near a boundary, and it is precisely the region near a boundary (in this case, the linediscontinuity) which is of primary interest in these problems. In fact one of the principal objectives in this work is to compare the stress distributions near the line discontinuity as predicted by the two theories.The principal techniques used in this work are based on integral equations and the calculus of variations.Results based on the two theories are found to agree forthin plates away from the line discontinuity, but differ significantly in the vicinity of the discontinuity, even for very thin plates.

[发布机构] University:California Institute of Technology;Department:Engineering and Applied Science

[关键词] Engineering