Existence and integral representation of solutions for plane deformations of a micropolar elastic solid with surface elasticity,ZAMM - Journal of Applied Mathematics and Mechanics

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Existence and integral representation of solutions for plane deformations of a micropolar elastic solid with surface elasticity
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-01-14 , DOI: 10.1002/zamm.201900228
Alireza Gharahi ₁ , Peter Schiavone ₁

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We consider a linear theory of elastic boundary reinforcement of a micropolar elastic solid subjected to plane‐strain deformations. The reinforcement consists of a thin micropolar elastic coating bonded to part of the boundary of the solid. The elastic properties of the coating incorporate both classical and micropolar bending, extension and twisting effects. Interior and exterior mixed boundary problems are formulated and analyzed using the boundary integral equation method. The boundary value problems are reduced to systems of singular integro‐differential equations to which Noether‐type theorems are shown to apply. We consider also the corresponding boundary value problems based on an alternative lower‐order shell model of the reinforcement. Finally, existence and uniqueness results are presented for the corresponding interior and exterior boundary value problems in the appropriate classical function spaces.

中文翻译：

具有表面弹性的微极性弹性固体平面变形解的存在性和整体表示

我们考虑了承受平面应变变形的微极性弹性固体的弹性边界增强的线性理论。增强层由粘结在固体边界的一部分上的薄的微极性弹性涂层组成。涂层的弹性特性兼具经典和微极性的弯曲，延伸和扭曲效果。使用边界积分方程法来制定和分析内部和外部混合边界问题。边值问题被简化为奇异的积分微分方程组，证明了Noether型定理适用于该系统。我们还根据钢筋的替代低阶壳模型来考虑相应的边值问题。最后，

更新日期：2020-01-14

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