Three-Dimensional Elasticity Theory for Flat-Plate Memory Elements Subjected to Space-Variable Normal Traction

摘要

Many of the contemporary memory elements used in high-speed digital computers are flat in the unstressed state. The present work is part of a review and enlargement of applicable elasticity theory in cases of small deformation with space-variable normal traction or pressure. (1) All flat plate results are derived directly with three-dimensional linear elasticity theory - none of the conventional intermediate assumptions being employed. (2) Within the exact theory, certain auxiliary functions are shown to satisfy conventional thin-plate differential equations. In terms of these functions, displacements, stresses, stress resultants and couples are simply expressed by formulas which are either exact, or asymptotically accurate. Boundary conditions are mathematically equivalent to those of Michell plate theory. (3) Solutions obtained from the present theory are 'interior solutions' in the sense of Friedrichs and Dressler (3) and accommodate Kirchoff edge conditions. Their use with more general edge conditions will be the subject of a later report. (Author)