Shape Sensitivity Analysis of a 2D Fluid–Structure Interaction Problem
研究了二维稳态斯托克斯-弹性系统中小载荷下一般泛函对弹性结构参考域的形状可微性，利用速度法计算形状导数并通过伴随方法简化表达式，适用于流固耦合问题的形状优化。
Abstract We study the shape differentiability of a general functional depending on the solution of a bidimensional stationary Stokes–elasticity system with small loads, with respect to the reference domain of the elastic structure immersed in a viscous fluid. The differentiability with respect to reference elastic domain variations is considered under shape perturbations with diffeomorphisms. The shape derivative is then calculated with the use of the velocity method. This derivative involves the material derivatives of the solution of this fluid–structure interaction problem. The adjoint method is then used to obtain a simplified expression for the shape derivative.