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.

中文翻译：

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均匀热梯度下弹性锥形抛物线拱的封闭形式解

我们研究了在均匀热梯度下具有抛物线轴的锥形弹性拱。有限域方程的微扰产生一阶微分系统序列，该序列变为无量纲形式。如果拱形浅而细长且其参考形状无应力，则会发现闭合形式的增量响应。我们评论图形有助于呈现结果，这是研究叠加在这种一阶热弹性状态上的可能非线性响应的第一步。