An optimization method based on the evolutionary and topology approaches to reduce the mass of composite wind turbine blades

The design of large and lightweight wind turbines is a current challenge in the wind energy industry. In this context, this work aims to present a novel methodology to reduce the mass of composite wind turbine blades by combining evolutionary and topology optimization schemes in a staggered mode. First, the optimal laminate layout in the outer shell skin of the blade is determined by using genetic algorithms and by assuming that the shear webs are fully dense. Considering this optimized shell skin, the material is removed from the shear webs by using topology optimization. In both cases, the blade is assumed to be subjected to an extreme load scenario, with constraints on the tip displacement, the stresses, the natural vibration frequencies, and buckling phenomena. As an extra feature, the methodology integrates the inverse finite element method to recover the aerodynamically efficient shape of the blade when it is working in normal load scenario as well as to increase the tower clearance safety margin under the extreme load scenario. To illustrate the performance of the methodology, the design of a 28.5-m composite blade is presented. Results show mass savings of up to 23% and a significant increase of the tower clearance safety margin. Furthermore, it is observed that after the classical genetic optimization of the shell skin, there is still margin to achieve additional mass savings via topology optimization of the shear webs without compromising the structural response of the blade.

[1]  O. Sigmund.  Morphology-based black and white filters for topology optimization , 2007 .

[2]  E. Allgower,et al.  Introduction to Numerical Continuation Methods , 1987 .

[3]  J. Sørensen.  General Momentum Theory for Horizontal Axis Wind Turbines , 2015 .

[4]  Ernesto Benini,et al.  Proposal for a coupled aerodynamic–structural wind turbine blade optimization , 2017 .

[5]  Akira Todoroki,et al.  Stacking sequence optimization by a genetic algorithm with a new recessive gene like repair strategy , 1998 .

[6]  Pu Liu,et al.  Wind turbine blade waste in 2050. , 2017, Waste management.

[7]  Paul M. Weaver,et al.  On the structural topology of wind turbine blades , 2013 .

[8]  David E. Goldberg,et al.  Genetic algorithms and Machine Learning , 1988, Machine Learning.

[9]  Mehrdad Javadi,et al.  Optimization of thickness and delamination growth in composite laminates under multi-axial fatigue loading using NSGA-II , 2019, Composites Part B: Engineering.

[10]  E. Sacco,et al.  Topology optimization-guided stiffening of composites realized through Automated Fiber Placement , 2019, Composites Part B: Engineering.

[11]  Alejandro Eduardo Albanesi.  Inverse design methods for compliant mechanisms , 2011 .

[12]  Damiano Pasini,et al.  Optimum stacking sequence design of composite materials Part I: Constant stiffness design , 2009 .

[13]  A. Kashani,et al.  Additive manufacturing (3D printing): A review of materials, methods, applications and challenges , 2018, Composites Part B: Engineering.

[14]  Ervin Bossanyi,et al.  Wind Energy Handbook , 2001 .

[15]  Anders Eriksson,et al.  Constrained stability of conservative static equilibrium , 2019, Computational Mechanics.

[16]  Ernesto Benini,et al.  Multi-objective structural optimization of a HAWT composite blade , 2013 .

[17]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part III: computational aspects of the nonlinear theory , 1990 .

[18]  James F. Doyle,et al.  Nonlinear analysis of thin-walled structures : statics, dynamics, and stability , 2001 .

[19]  Xiaowei Deng,et al.  Integrated design framework of next-generation 85-m wind turbine blade: Modelling, aeroelasticity and optimization , 2019, Composites Part B: Engineering.

[20]  Martin P. Bendsøe.  Topology Optimization , 2009, Encyclopedia of Optimization.

[21]  Simon Joncas,et al.  Development of a structural optimization strategy for the design of next generation large thermoplastic wind turbine blades , 2011, Structural and Multidisciplinary Optimization.

[22]  D. Peeters,et al.  A new thickness parameterization for Discrete Material and Thickness Optimization , 2018, Structural and Multidisciplinary Optimization.

[23]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[24]  D. Lin,et al.  A review on additive manufacturing of polymer-fiber composites , 2017 .

[25]  Jinsong Leng,et al.  Multi-stiffness topology optimization of zero Poisson's ratio cellular structures , 2018 .

[26]  Grégoire Allaire,et al.  Introducing a level-set based shape and topology optimization method for the wear of composite materials with geometric constraints , 2017 .

[27]  Erik Lund,et al.  Topology and thickness optimization of laminated composites including manufacturing constraints , 2013 .

[28]  Cristian Guillermo Gebhardt,et al.  Simultaneous ply-order, ply-number and ply-drop optimization of laminate wind turbine blades using the inverse finite element method , 2018 .

[29]  Ignacio Peralta,et al.  Optimization-based design of an elastostatic cloaking device , 2018, Scientific Reports.

[30]  Sean B. Leen,et al.  Physical experimental static testing and structural design optimisation for a composite wind turbine blade , 2017 .

[31]  Damiano Pasini,et al.  Optimum stacking sequence design of composite materials Part II: Variable stiffness design , 2010 .

[32]  A. Safonov.  3D topology optimization of continuous fiber-reinforced structures via natural evolution method , 2019, Composite Structures.

[33]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[34]  Mathias Stolpe,et al.  Global blending optimization of laminated composites with discrete material candidate selection and thickness variation , 2015 .

[35]  Lin Wang,et al.  Structural optimisation of vertical-axis wind turbine composite blades based on finite element analysis and genetic algorithm , 2016 .

[36]  Venkadesh Raman,et al.  Numerical simulation analysis as a tool to identify areas of weakness in a turbine wind-blade and solutions for their reinforcement , 2016 .

[37]  Layne T. Watson,et al.  Optimal design of composite wing structures with blended laminates , 2004 .

[38]  Cristian Guillermo Gebhardt,et al.  Application of the inverse finite element method to design wind turbine blades , 2017 .

[39]  Ole Sigmund,et al.  A 99 line topology optimization code written in Matlab , 2001 .

[40]  N. Jenkins,et al.  Wind Energy Handbook: Burton/Wind Energy Handbook , 2011 .

[41]  V. Fachinotti,et al.  Inverse finite element modeling of shells using the degenerate solid approach , 2015 .

[42]  Shutian Liu,et al.  A Realization Method for Transforming a Topology Optimization Design into Additive Manufacturing Structures , 2018 .

[43]  Marc Parizeau,et al.  DEAP: evolutionary algorithms made easy , 2012, J. Mach. Learn. Res..

[44]  Kusum Deep,et al.  A real coded genetic algorithm for solving integer and mixed integer optimization problems , 2009, Appl. Math. Comput..

[45]  E. Barbero.  Introduction to Composite Materials Design , 1998 .

[46]  Ignacio Peralta,et al.  Optimization-based design of easy-to-make devices for heat flux manipulation , 2018, International Journal of Thermal Sciences.

[47]  O. Sigmund,et al.  Topology optimization approaches , 2013, Structural and Multidisciplinary Optimization.

[48]  Enedir Ghisi,et al.  Residential building design optimisation using sensitivity analysis and genetic algorithm , 2016 .

[49]  Gene H. Golub,et al.  Matrix computations , 1983 .

[50]  K. Bathe,et al.  A continuum mechanics based four‐node shell element for general non‐linear analysis , 1984 .

[51]  E. Lund,et al.  Structural gradient based sizing optimization of wind turbine blades with fixed outer geometry , 2018, Composite Structures.

[52]  Simon Joncas,et al.  Preliminary design of large wind turbine blades using layout optimization techniques , 2004 .

[53]  Evgeny V. Morozov,et al.  Structural optimisation of composite wind turbine blade structures with variations of internal geometry configuration , 2016 .

[54]  J. E. Akin,et al.  Finite element analysis concepts: via solidworks , 2010 .

[55]  K. Saitou,et al.  Topology optimization of composite structures with data-driven resin filling time manufacturing constraint , 2017 .

[56]  Erik Lund,et al.  Discrete material optimization of general composite shell structures , 2005 .

[57]  Christophe Geuzaine,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[58]  J. L. Tangler,et al.  NREL airfoil families for HAWTs , 1995 .

[59]  Thomas D. Ashwill.  Parametric Study for Large Wind Turbine Blades: WindPACT Blade System Design Studies , 2002 .

[60]  Martín A. Pucheta,et al.  A new method to design compliant mechanisms based on the inverse beam finite element model , 2013 .

[61]  M. A. Luersen,et al.  Optimization of laminated composites considering different failure criteria , 2009 .

[62]  K. P. Padmanaban,et al.  Stacking sequence optimization of horizontal axis wind turbine blade using FEA, ANN and GA , 2015 .

[63]  Thomas D. Ashwill,et al.  Blade System Design Studies Volume I: Composite Technologies for Large Wind Turbine Blades , 2002 .

[64]  Alejandro E. Albanesi,et al.  A metamodel-based optimization approach to reduce the weight of composite laminated wind turbine blades , 2018, Composite Structures.

[65]  Dayton A. Griffin,et al.  Blade System Design Studies Volume II: Preliminary Blade Designs and Recommended Test Matrix , 2004 .