论文标题
线性弹性中的Lamé操作员的Steklov特征值
Steklov eigenvalues for the Lamé operator in linear elasticity
论文作者
论文摘要
在本文中，我们研究了在线性弹性理论中出现的Lamé操作员的Steklov特征值。在此本本本特征中，光谱参数出现在罗宾边界条件下，连接了牵引力和位移。为了确定这个问题的可数谱，我们提出了Korn不平等的扩展。我们还表明，提出的符合galerkin方案为真实特征值提供了收敛的近似值。标准有限元方法用于对2D和3D域进行数值实验，以支持我们的理论发现。
In this paper we study Steklov eigenvalues for the Lamé operator which arise in the theory of linear elasticity. In this eigenproblem the spectral parameter appears in a Robin boundary condition, linking the traction and the displacement. To establish the existence of a countable spectrum for this problem, we present an extension of Korn's inequality. We also show that a proposed conforming Galerkin scheme provides convergent approximations to the true eigenvalues. A standard finite element method is used to conduct numerical experiments on 2D and 3D domains to support our theoretical findings.
