Matched Interface and Boundary Method for Elasticity Interface Problems.
Matched Interface and Boundary Method for Elasticity Interface Problems.
复制标题
弹性界面问题的匹配界面和边界法。
DOI：
10.1016/j.cam.2015.02.005
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发表时间：
2015-09-01
影响因子：
2.4
通讯作者：
Wei GW
中科院分区：
文献类型：
--
作者：
Wang B;Xia K;Wei GW
弹性理论是连续介质力学的重要组成部分，在科学和工程中有着广泛的应用。材料界面在自然界和人造器件中普遍存在，并且经常引起弹性力学方程中的不连续系数。在这项工作中，匹配界面和边界（MIB）的方法来解决弹性界面问题。采用各向同性均匀和非均匀介质的线弹性理论。在我们的方法中，Lamé的参数可以有跨越界面的跳跃，并允许在建模各向同性非均匀材料的位置依赖。两个强不连续性，即，间断解和弱间断解，即解的间断导数。在所提出的方法中，利用虚拟值，使标准的中心有限差分格式可以采用无论接口。接口跳转条件在接口上强制执行，这反过来又准确地确定了虚拟值。我们设计新的MIB计划，以考虑复杂的接口几何形状。特别是，交叉导数的弹性方程是难以处理复杂的界面几何形状。我们提出了二次虚拟值和构造几何插值方案，以克服这一困难。大量的分析实例被用来验证本MIB方法的精度，收敛性和鲁棒性的弹性界面问题的小和大的曲率，强和弱的不连续性，常数和变系数。数值试验表明，在L∞和L2范数下都具有二阶精度。
Elasticity theory is an important component of continuum mechanics and has had widely spread applications in science and engineering. Material interfaces are ubiquity in nature and man-made devices, and often give rise to discontinuous coefficients in the governing elasticity equations. In this work, the matched interface and boundary (MIB) method is developed to address elasticity interface problems. Linear elasticity theory for both isotropic homogeneous and inhomogeneous media is employed. In our approach, Lamé’s parameters can have jumps across the interface and are allowed to be position dependent in modeling isotropic inhomogeneous material. Both strong discontinuity, i.e., discontinuous solution, and weak discontinuity, namely, discontinuous derivatives of the solution, are considered in the present study. In the proposed method, fictitious values are utilized so that the standard central finite different schemes can be employed regardless of the interface. Interface jump conditions are enforced on the interface, which in turn, accurately determines fictitious values. We design new MIB schemes to account for complex interface geometries. In particular, the cross derivatives in the elasticity equations are difficult to handle for complex interface geometries. We propose secondary fictitious values and construct geometry based interpolation schemes to overcome this difficulty. Numerous analytical examples are used to validate the accuracy, convergence and robustness of the present MIB method for elasticity interface problems with both small and large curvatures, strong and weak discontinuities, and constant and variable coefficients. Numerical tests indicate second order accuracy in both L∞ and L2 norms.
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影响因子：
2.4
作者：
Wei GW
通讯作者：
Wei GW
影响因子：
2.9
作者：
LEVEQUE, RJ;LI, ZL
通讯作者：
LI, ZL
影响因子：
10.2
作者：
Fornberg, B
通讯作者：
Fornberg, B
DOI：
10.1002/nme.201
发表时间：
2001-07-20
影响因子：
2.9
作者：
Stolarska, M;Chopp, DL;Belytschko, T
通讯作者：
Belytschko, T
弹性界面问题的自适应浸入界面有限元法
影响因子：
0.9
作者：
Chang, Yanzhen
通讯作者：
Chang, Yanzhen