Closed-form solutions for elastic tapered parabolic arches under uniform thermal gradients

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.