弹性薄壳的材料均匀性和应变协调性
Material homogeneity and strain compatibility in thin elastic shells
摘要：
我们讨论了几个问题，关于材料均匀的薄弹性壳的材料均匀性和应变相容性从一个3维理论的观点，与小厚度，以及一个2维Cosserat理论。根据这两种描述的不均匀性和不相容性措施之间的关系。更具体地说，我们得到明确的形式的内禀位错密度张量表征的不均匀性的位错Cosserat壳。我们还制定了一个系统的残余应力场出现的应变不相容性，这反过来又与不均匀性的控制方程。在Kirchhoff-Love假设下，对几种情况进行了简化。
英文摘要：
We discuss several issues regarding material homogeneity and strain compatibility for materially uniform thin elastic shells from the viewpoint of a 3-dimensional theory, with small thickness, as well as a 2-dimensional Cosserat theory. A relationship between inhomogeneity and incompatibility measures under the two descriptions is developed. More specifically, we obtain explicit forms of intrinsic dislocation density tensors characterising inhomogeneity of a dislocated Cosserat shell. We also formulate a system of governing equations for the residual stress field emerging out of strain incompatibilities which in turn are related to inhomogeneities. The equations are simplified for several cases under the Kirchhoff-Love assumption.
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