不可伸长纤维增强线弹性固体中的普适位移
Universal Displacements in Inextensible Fiber-Reinforced Linear Elastic Solids
AI总结：
本文研究了由不可伸长纤维增强的可压缩各向异性线弹性固体中的普适位移，表征了各对称类下的普适位移，发现内部约束在三斜和立方类外的五个类中扩大了普适位移集合。
摘要：
对于给定的一类材料，普适位移是指仅通过施加边界牵引力即可对该类中任何成员维持的位移。本文研究由一族不可伸长纤维增强的可压缩各向异性线弹性固体中的普适位移。对于每种对称类以及遵循相应对称性的直纤维均匀分布，我们表征了相应的普适位移。本文旨在研究内部约束如何影响普适位移集合。我们观察到，除了三斜和立方固体外，在其他五个类（具有直纤维的纤维增强固体不可能是各向同性的）中，不可伸长纤维的存在扩大了普适位移的集合。
英文摘要：
For a given class of materials, universal displacements are those displacements that can be maintained for any member of the class by applying only boundary tractions. In this paper we study universal displacements in compressible anisotropic linear elastic solids reinforced by a family of inextensible fibers. For each symmetry class and for a uniform distribution of straight fibers respecting the corresponding symmetry we characterize the respective universal displacements. A goal of this paper is to investigate how an internal constraint affects the set of universal displacements. We have observed that other than the triclinic and cubic solids in the other five classes (a fiber-reinforced solid with straight fibers cannot be isotropic) the presence of inextensible fibers enlarges the set of universal displacements.
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