论文标题
图像电荷的方法，用于描述带有圆形孔和夹杂物的有界2D实体结构的线性变形
Method of image charges for describing linear deformation of bounded 2D solid structures with circular holes and inclusions
论文作者
论文摘要
我们提出了一种方法，可以通过使用具有图像电荷的类似物和静电诱导来预测有限和半侵入2D固体结构的线性响应变形。静电中的电荷诱导导电边界附近的图像电荷，外部电场可诱导导电和介电物体的极化（偶极，四极和其他多物）。同样，弹性中的电荷会诱导边界附近的图像电荷，外部应力诱导孔和夹杂物内部的极化（四倍和其他多物）。这些诱导的弹性多物产生的应力以及其图像在边界附近产生的应力，然后导致孔与夹杂物及其图像之间的相互作用，从而诱导额外的极化，从而增加了孔和夹杂物的额外变形。我们提出了一种在一系列弹性多物中扩展诱导极化的方法，该方法系统地考虑了夹杂物和孔与外部场，它们之间以及它们的图像的相互作用。我们在直线和弯曲边界附近的圆形孔和夹杂物线性变形的方法的结果与线性有限元模拟和实验均显示出良好的一致性。
We present a method for predicting the linear response deformation of finite and semi-infinite 2D solid structures with circular holes and inclusions by employing the analogies with image charges and induction in electrostatics. Charges in electrostatics induce image charges near conductive boundaries and an external electric field induces polarization (dipoles, quadrupoles, and other multipoles) of conductive and dielectric objects. Similarly, charges in elasticity induce image charges near boundaries and external stress induces polarization (quadrupoles and other multipoles) inside holes and inclusions. Stresses generated by these induced elastic multipoles as well as stresses generated by their images near boundaries then lead to interactions between holes and inclusions and with their images, which induce additional polarization and thus additional deformation of holes and inclusions. We present a method that expands induced polarization in a series of elastic multipoles, which systematically takes into account the interactions of inclusions and holes with the external field, between them, and with their images. The results of our method for linear deformation of circular holes and inclusions near straight and curved boundaries show good agreement with both linear finite element simulations and experiments.
