任意形状的可压缩液体包含在同位方弹性矩阵中的可压缩液体
Romina Ardeshiri Jouneghani1, Xu Wang2, Peter Schiavone1
1Department of Mechanical Engineering, University of Alberta, Edmonton, AB, Canada.
概括
这项研究使用复杂变量解决了弹性材料中液体包含的平面拉伸问题. 该方法确定了任意纳入形状的内部应力场,并使用低形和矩形示例进行了验证.
科学领域:
- 固体力学 固体力学是什么
- 连续力学 连续力学
- 数学物理 数学物理
背景情况:
- 了解含含的弹性材料的应力分布对于材料科学和工程至关重要.
- 复杂变量方法为解决弹性的边界值问题提供了强大的工具.
研究的目的:
- 开发一种用于分析无限弹性矩阵中可压缩液体包含的平面-应变问题的一般方法.
- 为了确定任意包含形状的内部水静电应力和外部弹性场.
主要方法:
- 使用Mushkhelishvili的复杂变量公式.
- 采用符合性映射来将包含域转换为单位圆.
- 应用修改后的分析连续技术来导出线性代数方程.
主要成果:
- 一个封闭形式的溶液被导出为一个hypotrochoidal液体包含.
- 对n倍对称包含的数值结果表明了映射函数项的影响.
- 对于具有不同面积比的矩形包含物,确定了内部水静压力.
结论:
- 复杂变量方法为解决含有液体的应力问题提供了一个强大的框架.
- 该方法是多功能,适用于各种包含形状和对称度.
- 精确的应力场测定对于预测材料在负载下的行为至关重要.
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