Two forms of continuum shape sensitivity method for fluid–structure interaction problems

• Published in: Journal of fluids and structures Vol. 62; pp. 46 - 64
• Main Authors: Liu, Shaobin, Canfield, Robert A.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2016
• Subjects: Airfoils; Computational fluid dynamics; Continuum sensitivity equation method; Derivatives; Design analysis; Design optimization; Fluid flow; Fluids; Fluid–structure interaction; Mathematical analysis; Mathematical models; Shape sensitivity analysis; Fluid–structure interaction; Continuum sensitivity equation method; Shape sensitivity analysis; Design optimization
• ISSN: 0889-9746; 1095-8622
• DOI: 10.1016/j.jfluidstructs.2015.12.013

Continuum Sensitivity Equation (CSE) methods for deriving and computing derivatives with respect to shape design variables are developed in two forms and compared in their application to fluid–structure interaction (FSI) problems. The local derivative form poses the CSEs in terms of the partial derivatives of the state variables with respect to shape parameters, while the CSEs in total derivative form are posed in terms of the total derivative, also known as the material or substantial derivative. In the literature CSEs are often posed in local form for fluids and total form for solids. The two forms are compared here for the purpose of applying a single form to both fluid and structure domains. The local form, also known as the boundary velocity method, requires design velocity only at the boundaries and interfaces of the domains to pose the CSEs. In contrast, the total form, also known as the domain velocity method, requires the design velocity in the whole domain. The local form requires higher-order spatial derivatives of the analysis solution than the total form, which affects the accuracy of its results. Higher order p-elements are shown to be a remedy to the inaccuracy of local form CSE seen in the literature for finite element solutions. The practicality, accuracy, and efficiency of these two CSE forms are compared based on the implementation and computed derivatives for three examples: a linear Timoshenko beam subject to a tip force, fluid flow around an airfoil, and an airfoil attached to a nonlinear joined beam subject to a gust load. •Two forms of the continuum sensitivity method are developed for fluid and structure shape design problems.•The accuracy, efficiency and practicality of these two forms are compared based on the implementation and the sensitivity results.•Higher order p-elements are shown to be a remedy for local form sensitivity method.•Total form CSE is implemented for dynamic aeroelastic shape design sensitivity problems.