A Domain Optimization Technique For EllipticBoundary Value Problems
A Domain Optimization Technique For EllipticBoundary Value Problems
复制标题
椭圆边值问题的域优化技术
DOI：
10.2495/op950071
复制
发表时间：
1970
影响因子：
3.4
通讯作者：
Z. Wu
中科院分区：
文献类型：
--
作者：
H. Azegami;M. Shimoda;E. Katamine;Z. Wu
提出了一种数值分析技术，用于解决定义了椭圆边值问题的几何域优化问题。正如 Zolesio 所提倡的，域变化是通过一对一映射及其与速度场的无穷小变化来制定的。 * 域变化的灵敏度函数，我们称之为形状梯度函数，是使用拉格朗日乘子法或伴随法导出的。 3 通过在具有形状梯度函数的函数空间*中应用梯度方法，我们建议将最佳速度场分析为伪弹性问题的位移，该问题在设计域上定义，并加载与形状梯度函数成比例的伪分布外力或牵引力。由于所使用的程序，该技术被称为牵引法。给出了几个线性弹性问题和流场问题的数值结果。
A numerical analysis technique is presented for solving optimization problems of geometrical domains in which elliptic boundary value problems are defined. Domain variation is formulated with a one-to-one mapping and its infinitesimal variation with a speed field as advocated by Zolesio. * The sensitivity functions, which we call the shape gradient functions, of domain variation are derived using the Lagrange multiplier method or the adjoint method. 3 By applying the gradient method in functional space* with the shape gradient functions, we propose to analyze an optimal speed field as a displacement of a pseudo-elastic problem that is defined on the design domain and loaded with pseudo-distributed external force, or traction, in proportion to the shape gradient function. This technique is called the traction method because of the procedure used. Numerical results for several linear elastic problems and flow field problems are given.