Thermoelastic deformation of geometries of double curvature due to anisotropic shrinkage

Abstract

The earlier work of Radford [1] for prediction of the angular deformation of a body of single curvature due to thermal expansion, wherein the radial and circumferential coefficients of thermal expansion of the body are unequal, is extended to geometries of double curvature with two orthogonal radii of curvature. Predictions for a specific geometry of positive, double curvature are compared to experimental results and found to be favorable. Positive and negative curvature geometries are examined with predictions by finite-element analyses. Thermoelastic deformations in bodies of revolution are discussed to clarify the final geometry consequences of dividing the body of revolution into individual segments, often required for re-assembly. Finally, the conservation of Gaussian curvature, Ҡ, for an isometric deformation state will be developed and shown to bring a unifying foundation for thermoelastic deformation of simply-connected geometries of double curvature.