A systematic approach to shape sensitivity analysis
A systematic approach to shape sensitivity analysis
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DOI：
10.1016/0020-7683(93)90012-v
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发表时间：
1993
影响因子：
3.6
通讯作者：
D. Tortorelli;Zi-Xian Wang
中科院分区：
文献类型：
--
作者：
D. Tortorelli;Zi-Xian Wang
一个全面详细的发展领域参数化方法的形状敏感性分析。结果表明，材料导数法得到了等效结果。实际上，材料导数方法可以看作是区域参数化方法的一种特殊情况，它发生在参考构形与物体构形重合的情况下。该方法示出的拉普拉斯问题，其中明确的形状灵敏度推导出的伴随和直接微分法。有限元和边界元的应用进行了讨论。这种方法和等参有限元/边界元方法之间的相似之处是透明的。在有限元方法中，它表明，灵敏度积分可以转换到边界（通常是在材料导数方法）的伴随方法，然而，这似乎是不可能的直接微分法。最后，在边界元法中，灵敏度不需要基本解的微分。
A fully detailed development of the domain parameterization method is presented for shape sensitivity analysis. It is shown that equivalent results are obtained from the material derivative method. In fact, the material derivative method may be viewed as a special case of the domain parameterization method which occurs when the reference configuration coincides with the body configuration. The method is illustrated for the Laplace problem in which explicit shape sensitivities are derived by the adjoint and direct differentiation methods. Both finite element and boundary element applications are discussed. The similarities between this approach and the isoparametric finite/boundary element method are transparent. In the finite element approach, it is shown that the sensitivity integrals may be transformed to the boundary (as is commonly done in the material derivative method) for the adjoint method, however, this does not seem possible for the direct differentiation method. Finally, in the boundary element approach, the sensitivities do not require the differentiation of the fundamental solutions.