**1. Introduction**

Wind energy is one of the most mature forms of renewable energy and is an effective strategy to alleviate energy shortages, reduce environmental pollution and improve climate conditions [1–3]. The utilization of onshore wind energy has encountered bottlenecks due to the restriction of land wind resources, noise and environmental pollution. Hence, in the last two decades, offshore wind farms have been rapidly growing. In 2021, new installations of more than 6 GW were generated all over the world [4]. For the offshore wind turbine, the blade is one of the most important components to convert wind kinetic energy into electrical energy. However, approximately 20% of the failures in wind turbine components occurs in the blades [5,6]. Nowadays, the blade length in offshore wind turbines has dramatically grown over 100 m, resulting in major concerns about the blades' resistance to damage over a life period of 20–25 years [7]. Compared to the onshore wind turbine blades, offshore wind turbine blade damage may happen in different parts due to static, vibration and fatigue loadings [8,9]. Moreover, it is great of importance to lighten the weight of the blades to reduce transportation costs.

Extensive studies for the design of the optimal offshore wind turbine blades have been carried out in recent years [10–13]. Each blade includes skin and web structures, where the skin structure determines the aerodynamic characteristics and the web structure provides the stiffness and strength requirements of the blade. Naung et al. [14] proposed a highly efficient nonlinear frequency-domain solution approach for elaborating the aerodynamic and aeromechanical performances of an oscillating wind turbine blade aerofoil. In comparison to the time-domain method, the frequency-domain method was not only

**Citation:** Song, J.; Chen, J.; Wu, Y.; Li, L. Topology Optimization-Driven Design for Offshore Composite Wind Turbine Blades. *J. Mar. Sci. Eng.* **2022**, *10*, 1487. https://doi.org/10.3390/ jmse10101487

Academic Editors: Eugen Rusu, Kostas Belibassakis and George Lavidas

Received: 28 March 2022 Accepted: 1 August 2022 Published: 13 October 2022

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accurate but also computationally very efficient as the computation time was declined by 90%. Furthermore, Naung et al. [15] also investigated the influence of the wake of neighboring turbines on the aerodynamics of a wind turbine within windfarms based on the aforesaid frequency-domain method. The corresponding conclusions had been also obtained, namely that the frequency-domain solution method provided accurate results while reducing the computational cost by one to two orders of magnitude in comparison with the conventional time-domain method. In addition, Nakhchi and Naung et al. [16] also developed direct numerical simulations (DNS) to reveal the aerodynamic performance, transition to turbulence, and to capture the laminar separation bubble occurring on a wind turbine blade. Mamouri et al. [17,18] designed different shapes of wind turbine airfoil by incorporating entropy generation analysis. Chen et al. [19] performed the lay-up thickness size optimization for a 2 MW composite wind turbine blade with the objective of mass saving based on the particle swarm optimization method. Yet, only the blade stiffness and blade tip displacement were considered, and the extension of weight reduction was limited in accordance with the change of lay-up thickness. Ghiasi et al. [20] carried out the optimization design for the lay-up selection of a composite wind turbine blade with the objective of maximum stiffness. The results found that gradient-based methods were faster than others, but the optimal solution may be a local optimal value. In addition to the composite skin optimization, Zhang et al. [21] compared the maximum deformation, frequency and stress between the single-web and twin-web structures inside an 8 MW wind turbine blade, and the results showed that it was better to choose the twin-web structure form for large-size wind turbine blades. Liao et al. [22] employed an improved particle swarm algorithm (PSA) with the FAST program to optimize the thickness and location of the layers in the spar caps of wind turbine blades. The comparison of the results between the optimal and reference blades indicated that the optimization method was a feasible strategy to obtain the global optimization solution. The aforementioned studies focused on the local structural optimization design of wind turbine blades, whereas investigations on the structural optimization design of blades with the objective of weight reduction are considerably insufficient.

In the structural optimization design, topology optimization design is an effective way to obtain a reasonable internal layout of the blade, which can provide a new configuration and solution for engineering structural design [23]. Nowadays, the main topology optimization methods include the variable thickness method [24], homogenization method [25] and variable density method [26]. Generally, the variable thickness method and homogenization method are basically used for comparatively simple structures. For the variable density method, it has been integrated in finite element simulation software, i.e., ANSYS Workbench. Joncas et al. [27] adopted the topology optimization method to design the end part configuration of a thermoplastic composite wind turbine blade under waving moment and pendulum moment loading. Burton et al. [28] also adopted the topology optimization method to design the inner-surface structures of a wind turbine blade, and the optimization configuration was a non-prismatic structure. Yu et al. [29] designed a novel honeycombfilled main beam cavity of a wind turbine blade based on the variable density topology optimization method [26], and a reasonable layout of honeycomb cells was obtained and the weight of the optimal blade was reduced by 8.41%. Zhang et al. [30] used the variable density topology optimization method to optimize the thickness and location of the main beam and twin-web of a wind turbine blade, and the optimal configuration showed that the webs play a key supporting role for maintaining the aerodynamic shape of the blade and the overall weight of blade obviously decreased though the dimension and location of the inner webs. However, the challenges remain about how many webs should be placed in the blades and the layout of the related webs.

To address this, Aage et al. [31] adopted the variable density topology optimization method to successfully design the internal structure of an aeroplane wing based on the full-scale internal structure. From this viewpoint, in this work, we report the design of the internal layout of a 5 MW offshore wind turbine blade with the objective of maximum stiffness using the variable density topology optimization method. The aerodynamic loads of blades were obtained though computational fluid dynamics (CFD) simulation. Afterwards, the internal structure of the blade was optimized using the variable density topology optimization, and two multi-web internal layouts were obtained through the reverse design inspired by the topology optimization results. Finally, by validating the performance indexes with respect to stress level, maximum displacement and fatigue life, the multi-web structural layout of the second generation optimal wind turbine blade was an optimal feasible structure, which answered the key scientific issues of how many webs should be placed inside the blade and where to array the related webs. We hope the design method and findings could provide novel and efficient routes to high-performance offshore wind turbine blades.

#### **2. Analytical Preliminaries**
