Structural boundary design via level set and immersed interface methods
Structural boundary design via level set and immersed interface methods
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DOI：
10.1006/jcph.2000.6581
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发表时间：
2000-09-20
影响因子：
4.1
通讯作者：
Wiegmann, A
中科院分区：
文献类型：
--
作者：
Sethian, JA;Wiegmann, A
我们开发并测试了弹性结构边界设计的算法方法。我们的方法的目标是双重的：首先，开发一种方法，它允许一个快速解决二维拉梅方程在任意域和计算，例如，应力，第二，开发一个系统的方式修改设计，以优化选择的属性。我们的方法的核心依赖于两个不同的步骤。给定一个设计，我们首先应用显式跳跃浸入界面方法来计算给定设计形状的应力。然后，我们使用窄带水平集的方法来扰动这种形状和进步的改进设计。通过区域嵌入和快速弹性静力求解器的使用，快速求解任意区域上的位移列式中的二维线性弹性静力方程。这有效地将问题的维度减少了一个。一旦应力被发现，水平集方法，它表示的设计结构，通过一个嵌入的隐式功能，在第二步中使用改变的形状，速度取决于当前设计中的应力，提供标准，以推进形状在一个适当的方向和毛皮纠正演变的形状时，给定的约束被违反。(C)北京大学出版社.
We develop and test an algorithmic approach to the boundary design of elastic structures. The goal of our approach is two-fold: first, to develop a method which allows one to rapidly solve the two-dimensional Lame equations in arbitrary domains and compute, for example, the stresses, and second, to develop a systematic way of modifying the design to optimize chosen properties. At the core, our approach relies on two distinct steps. Given a design, we first apply an explicit jump immersed interface method to compute the stresses for a given design shape. We then use a narrow band level set method to perturb this shape and progress towards an improved design. The equations of 2D linear elastostatics in the displacement formulation on arbitrary domains are solved quickly by domain embedding and the use of fast elastostatic solvers. This effectively reduces the dimensionality of the problem by one. Once the stresses are found, the level set method, which represents the design structure through an embedded implicit function, is used in the second step to alter the shape, with velocities depending on the stresses in the current design, Criteria are provided for advancing the shape in an appropriate direction and fur correcting the evolving shape when given constraints are violated. (C) 2000 Academic Press.