Anti-Plane Shear Deformations in Linear and Nonlinear Solid Mechanics
Anti-Plane Shear Deformations in Linear and Nonlinear Solid Mechanics
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DOI：
10.1137/1037003
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发表时间：
1995-03
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影响因子：
--
通讯作者：
C. Horgan
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文献类型：
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作者：
C. Horgan
本文的目的是提请应用数学界的注意，一个有趣的二维数学模型所产生的固体力学涉及一个单一的二阶线性或准线性偏微分方程。该模型具有数学上相对简单的优点，而不会损失基本的物理相关性。反平面剪切变形是固体可以经历的最简单的变形类型之一。在圆柱体的反平面剪切（或纵向剪切，广义剪切）中，位移平行于圆柱的母线，与轴向坐标无关。因此，反平面剪切，只有一个标量轴向位移场，可以被视为补充更复杂的（但可能更熟悉）的平面应变变形，其两个面内位移。近年来，反平面剪切变形的分析在不同的工程背景下得到了相当的重视。
The intent of this expository paper is to draw the attention of the applied mathematics community to an interesting two-dimensional mathematical model arising in solid mechanics involving a single second-order linear or quasi-linear partial differential equation. This model has the virtue of relative mathematical simplicity without loss of essential physical relevance. Anti-plane shear deformations are one of the simplest classes of deformations that solids can undergo. In anti-plane shear (or longitudinal shear, generalized shear) of a cylindrical body, the displacement is parallel to the generators of the cylinder and is independent of the axial coordinate. Thus anti-plane shear, with just a single scalar axial displacement field, may be viewed as complementary to the more complicated (yet perhaps more familiar) plane strain deformation, with its two in-plane displacements. In recent years, considerable attention has been paid to the analysis of anti-plane shear deformations within the context of variou...