Closed-Form Solutions for Elastic Tapered Parabolic Arches Under Uniform Thermal Gradients

Abstract

We investigate tapered elastic arches with parabolic axis under uniform thermal gradients. A perturbation of the finite field equations yields a sequence of first-order differential systems, which is turned into a non-dimensional form. If the arch is shallow and slender and its reference shape is stress-free, a closed-form incremental response is found. We comment on the graphics help presenting the results, as a first step towards the investigation of possible non-linear responses superposed on such first-order thermo-elastic state.