Aerostructural Optimization of Nonplanar Lifting Surfaces

to findoptimalnonplanarliftingsurfacesandtoexplainthevariousfactorsandtradeoffsatplay.Apanelmethodand anequivalentbeam finite-elementmodelareusedtoexplorenonplanarliftingsurfaces,whiletakingintoaccountthe coupling and design tradeoffs between aerodynamics and structures. Both single-discipline aerodynamic optimization and multidisciplinary aerostructural optimization problems are investigated. The design variables are chosen to give the lifting-surface arrangement as much freedom as possible. This is accomplished by allowing a number of wing segments to vary their area, taper, twist, sweep, span, and dihedral, with the constraint that they must not intersect each other. Because of the complexity of the resulting design space and the presence of multiple localminima, anaugmentedLagrangianparticle swarmoptimizer isusedto solvethe optimizationproblems.When only aerodynamics are considered, closed lifting-surface configurations, such as the box wing and joined wing, are found to be optimal. When aerostructural optimization is performed, a winglet configuration is found to be optimal when the overall span is constrained, and a wing with a raked wingtip is optimal when there is no such constraint.

[1]  P. Fourie,et al.  The particle swarm optimization algorithm in size and shape optimization , 2002 .

[2]  Ronald Slingerland,et al.  Drag Characteristics for Optimally Span-Loaded Planar, Wingletted, and C Wings , 2009 .

[3]  Hirokazu Miura,et al.  Analytical Fuselage and Wing Weight Estimation of Transport Aircraft , 1996 .

[4]  Timothy T. Takahashi.  Optimum Transverse Span Loading for Subsonic Transport Category Aircraft , 2012 .

[5]  L. R. Miranda,et al.  A generalized vortex lattice method for subsonic and supersonic flow applications , 1977 .

[6]  Ilan Kroo,et al.  Tip Extensions, Winglets, and C-wings: Conceptual Design and Optimization , 2008 .

[7]  S. G. Flechner,et al.  Experimental results of winglets on first, second, and third generation jet transports , 1978 .

[8]  W Mangler.  The lift distribution of wings with end plates , 1938 .

[9]  Prabhat Hajela,et al.  Preliminary weight estimation of conventional and joined wings usingequivalent beam models , 1988 .

[10]  Paul E Hemke,et al.  Drag of Wings With End Plates , 1928 .

[11]  Richard T. Whitcomb,et al.  A design approach and selected wind tunnel results at high subsonic speeds for wing-tip mounted winglets , 1976 .

[12]  Joaquim R. R. A. Martins,et al.  High-Fidelity Aerostructural Design Optimization of a Supersonic Business Jet , 2002 .

[13]  O. Weck,et al.  A COMPARISON OF PARTICLE SWARM OPTIMIZATION AND THE GENETIC ALGORITHM , 2005 .

[14]  Edward N. Tinoco,et al.  Thirty Years of Development and Application of CFD at Boeing Commercial Airplanes, Seattle , 2003 .

[15]  Ilan Kroo,et al.  A General Approach to Multiple Lifting Surface Design and Analysis , 1984 .

[16]  Saeed Moaveni,et al.  Finite Element Analysis Theory and Application with ANSYS , 2007 .

[17]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[18]  G. R. Hough.  Remarks on vortex-lattice methods. , 1973 .

[19]  Usik Lee,et al.  Equivalent dynamic beam–rod models of aircraft wing structures , 1995, The Aeronautical Journal (1968).

[20]  Michael I. Friswell,et al.  Multi-objective optimization for the multiphase design of active polymorphing wings , 2012 .

[21]  Message P Forum,et al.  MPI: A Message-Passing Interface Standard , 1994 .

[22]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[23]  Ozan Tekinalp,et al.  A new multiobjective simulated annealing algorithm , 2007, J. Glob. Optim..

[24]  Ilan Kroo,et al.  Multidisciplinary Considerations in the Design of Wings and Wing Tip Devices , 2010 .

[25]  J. Alonso,et al.  A Coupled-Adjoint Sensitivity Analysis Method for High-Fidelity Aero-Structural Design , 2005 .

[26]  J. S. Przemieniecki.  Theory of matrix structural analysis , 1985 .

[27]  Philip E. Gill,et al.  Practical optimization , 1981 .

[28]  Joaquim R. R. A. Martins,et al.  The complex-step derivative approximation , 2003, TOMS.

[29]  P. Eberhard,et al.  Using Augmented Lagrangian Particle Swarm Optimization for Constrained Problems in Engineering , 2009 .

[30]  Joaquim R. R. A. Martins,et al.  pyOpt: a Python-based object-oriented framework for nonlinear constrained optimization , 2011, Structural and Multidisciplinary Optimization.

[31]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2002, SIAM J. Optim..

[32]  Kamran Behdinan,et al.  Particle Swarm Optimization in Structural Design , 2007 .

[33]  Ilan Kroo,et al.  Advanced configurations for very large transport airplanes , 1998 .

[34]  Mario A. Storti,et al.  MPI for Python , 2005, J. Parallel Distributed Comput..

[35]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[36]  P. J. Gage,et al.  New approaches to optimization in aerospace conceptual design , 1995 .

[37]  Kamran Behdinan,et al.  Particle swarm approach for structural design optimization , 2007 .

[38]  K. Asai.  Theoretical considerations in the aerodynamic effectiveness of winglets , 1985 .

[39]  Jason E. Hicken.  Efficient Algorithms for Future Aircraft Design: Contributions to Aerodynamic Shape Optimization , 2009 .

[40]  Raymond M. Kolonay,et al.  Structural optimization of a joined wing using equivalent static loads , 2007 .

[41]  W. Phillips,et al.  Application of lifting-line theory to systems of lifting surfaces , 2000 .

[42]  Gary L. Giles.  Further Generalization of an Equivalent Plate Representation for Aircraft Structural Analysis , 1989 .

[43]  Peter W. Jansen,et al.  Aerostructural Optimization of Non – Planar Lifting Surfaces , 2009 .

[44]  Carsten M. Liersch,et al.  A Fast Aerodynamic Tool for Preliminary Aircraft Design , 2008 .

[45]  John E. Dennis,et al.  Problem Formulation for Multidisciplinary Optimization , 1994, SIAM J. Optim..

[46]  R. T. Jones,et al.  Effect of Winglets on the Induced Drag of Ideal Wing Shapes , .

[47]  John E. Terry.  AERODYNAMIC CHARACTERISTICS OF RING WINGS, A BIBLIOGRAPHY , 1964 .

[48]  J. E. Allen,et al.  The use of wing tip sails to reduce vortex drag , 1977, The Aeronautical Journal (1968).

[49]  Russell C. Eberhart,et al.  Solving Constrained Nonlinear Optimization Problems with Particle Swarm Optimization , 2002 .

[50]  Xiaohui Hu,et al.  Engineering optimization with particle swarm , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[51]  C. E. Lan,et al.  A Quasi-Vortex-Lattice Method in Thin Wing Theory , 1974 .

[52]  Jaroslaw Sobieszczanski-Sobieski,et al.  A Parallel Particle Swarm Optimization Algorithm Accelerated by Asynchronous Evaluations , 2005 .

[53]  Harry H. Heyson,et al.  Theoretical parametric study of the relative advantages of winglets and wing-tip extensions , 1977 .

[54]  Ilan Kroo,et al.  Framework for Aircraft Conceptual Design and Environmental Performance Studies , 2005 .

[55]  Jakob Kuttenkeuler,et al.  Aeroelastic Design Optimization with Experimental Verification , 1998 .

[56]  Frans van den Bergh,et al.  An analysis of particle swarm optimizers , 2002 .

[57]  Michael Allen,et al.  Parallel programming: techniques and applications using networked workstations and parallel computers , 1998 .

[58]  J. Wolkovitch,et al.  The joined wing - An overview , 1985 .