Global laminate optimization on geometrically partitioned shell structures

A method aimed at the optimization of locally varying laminates is investigated. The structure is partitioned into geometrical sections. These sections are covered by global plies. A variable-length representation scheme for an evolutionary algorithm is developed. This scheme encodes the number of global plies, their thickness, material, and orientation. A set of genetic variation operators tailored to this particular representation is introduced. Sensitivity information assists the genetic search in the placement of reinforcements and optimization of ply angles. The method is investigated on two benchmark applications. There it is able to find significant improvements. A case study of an airplane’s side rudder illustrates the applicability of the method to typical engineering problems.

[1]  Srinivasan Gopalakrishnan,et al.  Design optimization of composites using genetic algorithms and failure mechanism based failure criterion , 2008 .

[2]  P. B. Sujit,et al.  Particle swarm optimization approach for multi-objective composite box-beam design , 2007 .

[3]  C. M. Mota Soares,et al.  Sensitivity analysis and optimal design of thin laminated composite structures , 1991 .

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

[5]  Naveen Rastogi.  Stress analysis and lay-up optimization of an all-composite pick-up truck chassis structure , 2004 .

[6]  Paul M. Weaver,et al.  Optimization of Long Anisotropic Laminated Fiber Composite Panels with T-Shaped Stiffeners , 2007 .

[7]  W. Beluch.  Evolutionary Identification and Optimization of Composite Structures , 2007 .

[8]  Paolo Ermanni,et al.  A graph-based parameterization concept for global laminate optimization , 2008 .

[9]  M. Autio,et al.  Determining the real lay-up of a laminate corresponding to optimal lamination parameters by genetic search , 2000 .

[10]  Christof Ledermann.  Parametric associative CAE methods in preliminary aircraft design , 2006 .

[11]  Peter J. Bentley,et al.  Evolutionary Design by Computers with CDrom , 1999 .

[12]  Nozomu Kogiso,et al.  Genetic algorithms with local improvement for composite laminate design , 1993 .

[13]  Jiho Yoo,et al.  Optimization of La2CuO4 Sensing Electrodes for a NOx Potentiometric Sensor , 2006 .

[14]  Autar Kaw,et al.  Optimization of laminate stacking sequence for failure load maximization using Tabu search , 2003 .

[15]  Robert E. Rowlands,et al.  Reducing Tensile Stress Concentration in Perforated Hybrid Laminate by Genetic Algorithm , 2007 .

[16]  Dimitri P. Bertsekas,et al.  Constrained Optimization and Lagrange Multiplier Methods , 1982 .

[17]  Mitsuo Gen,et al.  Genetic Algorithms , 1999, Wiley Encyclopedia of Computer Science and Engineering.

[18]  M. Giger,et al.  Development of CFRP racing motorcycle rims using a heuristic evolutionary algorithm approach , 2005 .

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

[20]  S. Vel,et al.  MULTI-OBJECTIVE OPTIMIZATION OF FIBER REINFORCED COMPOSITE LAMINATES FOR STRENGTH, STIFFNESS AND MINIMAL MASS , 2006 .

[21]  C. M. Mota Soares,et al.  Sensitivity analysis and optimization of thin laminated structures with a nonsmooth eigenvalue based criterion , 1997 .

[22]  R. Haftka,et al.  Optimization of fiber orientations near a hole for increased load-carrying capacity of composite laminates , 2005 .

[23]  D. Sauter,et al.  A Graph-based Optimization Method for the Design of Compliant Mechanisms and Structures , 2008 .

[24]  Paolo Ermanni,et al.  A methodology for the global optimization of laminated composite structures , 2006 .

[25]  Tomasz Arciszewski,et al.  Evolutionary computation and structural design: A survey of the state-of-the-art , 2005 .

[26]  Martin P. Bendsøe,et al.  Parametrization in Laminate Design for Optimal Compliance , 1997 .

[27]  Jung-Seok Kim,et al.  Development of a user-friendly expert system for composite laminate design , 2007 .

[28]  Z. Gürdal,et al.  Design of variable stiffness composite panels for maximum fundamental frequency using lamination parameters , 2007 .

[29]  C. M. Mota Soares,et al.  Sensitivity analysis and optimal design of geometrically non-linear laminated plates and shells , 2000 .

[30]  Paolo Vannucci,et al.  Exact optimal flexural design of laminates , 2009 .

[31]  R. Haftka,et al.  Improved genetic algorithm for minimum thickness composite laminate design , 1995 .

[32]  Cheng Wang,et al.  Optimum design of composite laminates , 1992 .

[33]  Erik Lund,et al.  Eigenfrequency and Buckling Optimization of Laminated Composite Shell Structures Using Discrete Material Optimization , 2006 .

[34]  B. Farshi,et al.  Optimum design of composite laminates for frequency constraints , 2007 .

[35]  Mathias Giger.  Representation concepts in evolutionary algorithm-based structural optimization , 2007 .

[36]  Christian Gram Hvejsel,et al.  Efficient finite element formulation for analysis and optimization of laminated composite shell structures , 2007 .

[37]  Woo Suck Han,et al.  Improved genetic algorithm for multidisciplinary optimization of composite laminates , 2008 .

[38]  Fazil O. Sonmez,et al.  Optimum design of composite laminates for minimum thickness , 2008 .

[39]  Raphael T. Haftka,et al.  Stacking sequence matching by two-stage genetic algorithm with consanguineous initial population , 1997 .

[40]  Erik Lund,et al.  On structural optimization of composite shell structures using a discrete constitutive parametrization , 2004 .

[41]  Akira Todoroki,et al.  Design of experiments for stacking sequence optimizations with genetic algorithm using response surface approximation , 2004 .

[42]  Martin P. Bendsøe,et al.  Free material optimization via mathematical programming , 1997, Math. Program..

[43]  Assimina A. Pelegri,et al.  Design of composites using a generic unit cell model coupled with a hybrid genetic algorithm , 2008 .

[44]  Sarp Adali,et al.  Optimization of laminated composites subject to uncertain buckling loads , 2003 .

[45]  A. Rama Mohan Rao,et al.  A scatter search algorithm for stacking sequence optimisation of laminate composites , 2005 .

[46]  Michaël Bruyneel,et al.  Composite structures optimization using sequential convex programming , 2000 .

[47]  Michal Kočvara,et al.  Free Material Optimization , 2003 .

[48]  S. N. Omkar,et al.  Vector evaluated particle swarm optimization (VEPSO) for multi-objective design optimization of composite structures , 2008 .

[49]  J. Grenestedt,et al.  Layup optimization against buckling of shear panels , 1991 .

[50]  S. D. Chatterji.  Proceedings of the International Congress of Mathematicians , 1995 .

[51]  Christine M. Anderson-Cook,et al.  Genetic algorithm optimization and blending of composite laminates by locally reducing laminate thickness , 2004 .

[52]  W. Prager.  Optimization of structural design , 1970 .

[53]  David Christian Keller,et al.  Evolutionary design of laminated composite structures , 2010 .

[54]  Akira Todoroki,et al.  Stacking Sequence Optimization using Fractal Branch and Bound Method , 1999 .

[55]  R. Haftka,et al.  Review of options for structural design sensitivity analysis. Part 1: Linear systems , 2005 .

[56]  Oliver König,et al.  Evolutionary design optimization: Tools and applications , 2004 .

[57]  Akira Todoroki,et al.  New iteration fractal branch and bound method for stacking sequence optimizations of multiple laminates , 2007 .

[58]  G. Duvaut,et al.  Optimization of fiber reinforced composites , 2000 .

[59]  P. Pedersen.  On optimal orientation of orthotropic materials , 1989 .

[60]  L. Tsau,et al.  A comparison between two optimization methods on the stacking sequence of fiber-reinforced composite laminate , 1995 .

[61]  Raphael T. Haftka,et al.  Design and optimization of laminated composite materials , 1999 .

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

[63]  Peter J. Bentley,et al.  Evolutionary Design By Computers , 1999 .

[64]  Umut Topal,et al.  Strength Optimization of Laminated Composite Plates , 2008 .

[65]  Marc Wintermantel.  Design-encoding for evolutionary algorithms in the field of structural optimization , 2004 .

[66]  Francesco Aymerich,et al.  Optimization of laminate stacking sequence for maximum buckling load using the ant colony optimization (ACO)metaheuristic , 2008 .

[67]  Raphael T. Haftka,et al.  A Segregated Genetic Algorithm for Constrained Structural Optimization , 1995, ICGA.

[68]  Erik Lund,et al.  Failure optimization of geometrically linear/nonlinear laminated composite structures using a two-step hierarchical model adaptivity , 2009 .

[69]  N. Olhoff,et al.  A general approach forcing convexity of ply angle optimization in composite laminates , 1998 .

[70]  Arkadi Nemirovski,et al.  Free Material Design via Semidefinite Programming: The Multiload Case with Contact Conditions , 1999, SIAM J. Optim..

[71]  G. N. Vanderplaats,et al.  Strength optimization of laminated composites with respect to layer thickness and/or layer orientation angle , 1991 .

[72]  Ramin Sedaghati,et al.  Design of laminated composite structures for optimum fiber direction and layer thickness, using optimality criteria , 2008 .

[73]  Nino Zehnder.  Global optimization of laminated structures , 2007 .

[74]  J. Grenestedt,et al.  Composite plate optimization only requires one parameter , 1990 .

[75]  G. Soremekun.  Genetic Algorithms for Composite Laminate Design and Optimization , 1997 .

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

[77]  Mitsuo Gen,et al.  Genetic algorithms and engineering optimization , 1999 .

[78]  Akira Todoroki,et al.  Permutation genetic algorithm for stacking sequence design of composite laminates , 2000 .

[79]  Pauli Pedersen,et al.  On thickness and orientational design with orthotropic materials , 1991 .

[80]  M. Walker,et al.  A technique for the multiobjective optimisation of laminated composite structures using genetic algorithms and finite element analysis , 2003 .