Steady Creep of a Nonhomogeneous Plate

The stress distribution in a moderately thick, linear, steadily creeping plate loaded only by edge tractions (symmetrical about the plate midplane), and having a viscosity coefficient varying in the plane of the plate is investigated. By utilizing the three Maxwell stress functions and using a double power series expansion in the nondimensional thickness coordinate and thickness of the plate, the three-dimensional problem is reduced to an infinite number of uncoupled, successive, two-dimensional problems. The first two-dimensional problem of this type corresponds to the usual generalized plane stress problem for the nonhomogeneous plate, and its solution provides the leading terms of the series solution obtained herein. The method developed is such that the average value (over the plate thickness) of the edge traction may vary arbitrarily around the plate perimeter, but the solution itself defines the edge traction variation through the plate thickness. By invoking St. Venant' s principle, these results may be applied to technical problems in which the applied edge traction has a different variation through the plate thickness than that required by the series solution. The application of the method of solution is illustrated in two examples. These examples show that if the variation of properties in the plane of the plate is large, then the solution obtained herein can differ significantly from the less descriptive generalized plane stress solution, even for relatively thin plates.