Calculus of Variations and Geometric Measure Theory

V. Calisti - I. Lucardesi - J. F. Scheid

Shape Sensitivity Analysis of a 2D Fluid-Structure Interaction Problem

created by lucardesi on 28 Nov 2022
modified on 21 Apr 2023


Published Paper

Inserted: 28 nov 2022
Last Updated: 21 apr 2023

Journal: Journal of Optimization Theory and Applications
Year: 2023
Doi: 10.1007/s10957-023-02213-4

ArXiv: 2210.05850 Search... PDF


We study the shape differentiability of a general functional depending on the solution of a bidimensional stationary Stokes-Elasticity system, with respect to the reference domain of the elastic structure immersed in a viscous fluid. The differentiability with respect to reference elastic domain variations are 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 used to obtain a simplified expression for the shape derivative.