Abstract This study presents a novel, linear superposition method (LSM) to compute the stress tensor field and displacement vector field in a homogeneous elastic medium with an unlimited (but finite) number of circular cylindrical holes. The displacement field and the associated stress concentrations are due to a far-field stress. The method allows for the hole-centers to occur in arbitrary locations, and the hole-radii may vary over a wide range (but holes may not overlap). The holes may also induce additional elastic displacement due to internal pressure loading that will affect the local stress field, which is fully accounted for in the method. Each hole may be loaded by either equal or individual pressure loads. The underlying algorithms and solution methodology are explained and examples are given for a variety of cases. Selected case study examples show excellent matches with results obtained via independent methods (photo-elastics, complex analysis, and discrete volume solution methods). The LSM provides several advantages over alternative methods: (1) Being closed-form solutions, infinite resolution is preserved throughout, (2) Being grid-less, no time is lost on gridding, and (3) fast computation times. The specific examples of LSM applications to the multi-hole problem developed here, allow for an unlimited number of holes, with either equal or varying radii, in arbitrary constellations. The solutions further account for variable combinations of far-field stress and pressure loads on individual holes. The method can be applied for either plane strain or plane stress boundary conditions. A constitutive equation for linear elasticity controls the stress field solutions, which can be scaled for the full range of Poisson's ratios and Young moduli possible in linear elastic materials.

中文翻译：

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用于求解应力张量场和位移矢量场的线性叠加法 (LSM)：应用于具有远场应力的弹性板中的多个压力加载圆孔

摘要 本研究提出了一种新颖的线性叠加方法 (LSM)，用于计算具有无限（但有限）数量的圆柱孔的均匀弹性介质中的应力张量场和位移矢量场。位移场和相关的应力集中是由远场应力引起的。该方法允许孔中心出现在任意位置，孔半径可以在很宽的范围内变化（但孔可能不会重叠）。由于内部压力载荷，这些孔还可能引起额外的弹性位移，这会影响局部应力场，这在方法中得到了充分考虑。每个孔可承受相等或单独的压力载荷。解释了底层算法和解决方案方法，并针对各种情况给出了示例。选定的案例研究示例与通过独立方法（光弹性、复杂分析和离散体积求解方法）获得的结果非常匹配。与替代方法相比，LSM 提供了几个优点：(1) 作为封闭形式的解决方案，始终保持无限分辨率，(2) 无网格，网格化不会浪费时间，以及 (3) 计算速度快。此处开发的针对多孔问题的 LSM 应用的具体示例允许在任意星座中具有无限数量的孔，具有相同或不同的半径。这些解决方案进一步考虑了单个孔上远场应力和压力载荷的可变组合。该方法可应用于平面应变或平面应力边界条件。