In this paper we consider a family of three-dimensional problems in thermoelasticity for elliptic membrane shells and study the asymptotic behaviour of the solution when the thickness tends to zero. We fully characterize with strong convergence results the limit as the unique solution of a two-dimensional problem, where the reference domain is the common middle surface of the family of three-dimensional shells. The problems are dynamic and the constitutive thermoelastic law is given by the Duhamel-Neumann relation.

中文翻译：

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椭圆膜壳热弹性动力学的渐近分析

在本文中，我们考虑了椭圆膜壳的热弹性三维问题，并研究了当厚度趋于零时溶液的渐近行为。我们以强大的收敛性结果为特征来充分描述极限是二维问题的唯一解，其中参考域是三维壳族的公共中间表面。这些问题是动态的，本构热弹性定律由杜哈默尔-纽曼关系给出。