Aerodynamic-driven topology optimization of compliant airfoils

Abstract

A strategy for density-based topology optimization of fluid-structure interaction problems is proposed that deals with some shortcomings associated to non stiffness-based design. The goal is to improve the passive aerodynamic shape adaptation of highly compliant airfoils at multiple operating points. A two-step solution process is proposed that decouples global aeroelastic performance goals from the search of a solid-void topology on the structure. In the first step, a reference fully coupled fluid-structure problem is solved without explicitly penalizing non-discreteness in the resulting topology. A regularization step is then performed that solves an inverse design problem, akin to those in compliant mechanism design, which produces a discrete-topology structure with the same response to the fluid loads. Simulations are carried out with the multi-physics suite SU2, which includes Reynolds-averaged Navier-Stokes modeling of the fluid and hyper-elastic material behavior of the geometrically nonlinear structure. Gradient-based optimization is used with the exterior penalty method and a large-scale quasi-Newton unconstrained optimizer. Coupled aerostructural sensitivities are obtained via an algorithmic differentiation based coupled discrete adjoint solver. Numerical examples on a compliant aerofoil with performance objectives at two Mach numbers are presented.

Structure-material Integrated Design for a Spacecraft Rib

“…These four structures are all less than 122.73%, demonstrating the structure-material integrated design framework's effectiveness when designing the spacecraft rib. However, considering the aircraft's actual service situation, when designing the spacecraft rib, it is necessary to consider further the constraints of fatigue, aerodynamic load, and uncertainty [32][33][34] in the future study.…”

Calibration of elastoplastic constitutive model parameters from full‐field data with automatic differentiation‐based sensitivities

“…[72][73][74][75] Its use in solid mechanics is limited to 1D wave propagation 76 and more recently fluid-structure interaction. 77 Lastly, the work of References 78-80 is notable in that it describes fully automated approach that utilizes source transformation AD for forward sensitivity analyses in computational plasticity, but it does not consider its use in constitutive model calibration problems. In these approaches AD is used to compute both the residual vector and its associated tangent matrix from a single scalar function that is derived from a strain-energy density function and the equations that govern plastic deformation, while in our formulation AD implementations of coupled residuals are the fundamental objects from which tangent matrices are obtained.…”

A Sequential Approach for Aerodynamic Shape Optimization with Topology Optimization of Airfoils

“…Despite these optimization algorithms having been employed in several wing and airfoil applications, their combined application is much less common in the literature. ASO is normally done before the TO as in [26], although there are some papers where two optimizations process are carried out simultaneous for performance [27] or aeroelastic applications [28]. Maute and Reich [26] developed a sequential framework to design morphing structures based firstly on ASO and secondly on TO.…”

“…They noticed that their coupled approach was able to achieve a wing model with 18% less drag than with the sequential approach. Gomes and Palacios [28] applied a fully-coupled aerodynamic and stiffness-based TO methodology for designing a compliant airfoil using FSI. Their methodology consists in two sequential steps: (i) firstly, the airfoil shape is optimized for a given aerodynamic-related objective and a set of constraints considering both ASO and TO; (ii) followed by an inverse design where the internal structure is optimized for a mass minimization objective.…”

“…These works [26][27][28] use the Solid Isotropic Material with Penalization (SIMP) model [29] to parameterize the structural domain, while in the present work the Bidirectional Evolutionary Structural Optimization (BESO) model [30] is used. BESO has the main advantage of being able to both remove and add material, and it has been applied to solve both academic and industrial problems [31].…”