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中文摘要：
工程中存在一类几何边界随时间变化的变边界结构，例如土木工程中处于施工阶段的结构．论文以粘弹性岩体中隧道开挖为背景，尝试用变边界问题对应关系和平面弹性复变方法求取无限平面中椭圆孔口自相似变边界情况下的解析解答．首先建立了复变函数法求解变边界粘弹性问题的基本步骤和公式．然后通过建立逆映射函数将已知ζ平面复位势转至z平面，解耦参与拉普拉斯变换的时间与孔口映射函数所带来的时间，从而导出了粘弹性类材料的应力与位移的统一表达．作为一个例子，论文选择Boltzmann粘弹性模型，代入模型参数后得到积分形式的位移、应力解析解，通过与数值解的比较验证了该解答的可靠性，并通过一个算例分析了变边界过程对位移、应力的影响．分析结果显示，采用不同变边界过程的位移、应力变化形态和数值均有差别．论文解答可用于进行地下椭圆孔型隧道在开挖过程中的力学分析，为实际工程提供初步设计的手段．此外，本文给出的方法可用于推导任意形状孔型变边界问题的解答．
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