Shape-optimization of 2D hydrofoils using an Isogeometric BEM solver

Abstract

In this paper, an optimization procedure, based on an Isogeometric BEM solver for the potential flow, is developed and used for the shape optimization of hydrofoils. The formulation of the exterior potential-flow problem reduces to a Boundary-Integral Equation (BIE) for the associated velocity potential exploiting the null-pressure jump Kutta condition at the trailing edge. The numerical solution of the BIE is performed by an Isogeometric Boundary-Element Method (BEM) combining a generic B-splines parametric modeler for generating hydrofoil shapes, using a set of eight parameters, the very same basis of the geometric representation for representing the velocity potential and collocation at the Greville abscissas of the knot vector of the hydrofoil's B-splines representation. Furthermore, the optimization environment is developed based on the geometric parametric modeler for the hydrofoil, the Isogeometric BEM solver and an optimizer employing a controlled elitist genetic algorithm. Multi-objective hydrofoil shape optimization examples are demonstrated with respect to the criteria i) maximum lift coefficient and ii) minimum deviation of the hydrofoil area from a reference area.

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

“…Representative works of such studies can be found in Benzaken et al [Benzaken, Herrema, Hsu et al (2017)] and Herrema et al [Herrema, Wiese, Darling et al (2017)], where a surrogate model technique and a generalized pattern search algorithm, respectively, are adopted to optimize the wind turbine blades (see Fig. 6(c)) with complex geometries, Kostas et al [Kostas, Ginnis, Politis et al (2015)] where evolutionary algorithms are utilized to optimize ship-hull shape, Herath et al [Herath, Natarajan, Prusty et al (2015); Kostas, Ginnis, Politis et al (2017); Kostas, Fyrillas, Politis et al (2018)] with genetic algorithms, Lieu et al [Lieu, Lee, Lee et al (2018); Lieu and Lee (2019)] with an adaptive hybrid evolutionary firefly algorithm, Wang et al [Wang, Yu, Shao et al(2018)] with a chaotic particle swarm optimization method, and Zhang et al [Zhang, Li, Shen et al (2019)] with multi-island genetic algorithm and adaptive simulated annealing methods.…”

A dual boundary element based implicit differentiation method for determining stress intensity factor sensitivities for plate bending problems

“…When dealing with weakly singular integrals with singularities of the order ln(1/r) or 1/r such as those seen in equations ( 2)-( 4), ( 8), ( 9), ( 12)-( 13), (16), the transformation of variable technique proposed by Telles [28] is used. For equations (2) and (12), rigid body motion is also applied.…”

“…One recent variation of the BEM is the isogeometric BEM [14,15,16]. The isogeometric BEM involves the use of Non-Uniform Rational B-Splines (NURBS) to represent the boundaries of the structure.…”

“…The isogeometric BEM involves the use of Non-Uniform Rational B-Splines (NURBS) to represent the boundaries of the structure. Since NURBS are also commonly used in Computer Aided Design (CAD), data can be transferred between isogeometric BEM and CAD tools relatively easily [16]. Some relevant past examples of its use include applications to fracture mechanics, [14,15] and shape optimisation [16].…”

Reliability-based fracture analysis for plate bending problems with the dual boundary element method

“…Due to the effectiveness of the DBEM in fracture analysis, it has been extensively used in the research community mainly for problems involving 2D problems. Examples include topology optimisation [1], reliability analysis of structures subjected to fatigue [2], shape optimisation of hydrofoils [3], and the modelling of creep in concrete [4].…”