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Erschienen in: Structural and Multidisciplinary Optimization 1/2018

01.02.2018 | RESEARCH PAPER

A lagrange parametrization for the design of variable stiffness laminates

verfasst von: Hugo Borges de Quadros, José Antonio Hernandes

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 1/2018

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Abstract

A Lagrange parameterization of lamination parameters which are used for optimization of variable stiffness laminates is presented. The advantages of the approach are: a) the design variables become independent of the finite element mesh and, b) the smoothness of the solution is inherently guaranteed. Due to independency of design variables of the finite element mesh, the reduction in the number of design variables is drastic, once variable stiffness laminates usually demand a fine mesh. The lamination parameters formulation allows a more precise and concise approach to laminate design, removing difficulties related to fiber direction and stacking sequence, increasing the chances to find a global optimal solution. In this paper, the Lagrange parameterization is used for the maximization of the buckling load of a variable stiffness composite plate.

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Literatur
Zurück zum Zitat Alhajahmad A, Abdalla MM, Gürdal Z (2008) Design tailoring for pressure pillowing using tow-placed steered fibers. J Aircr 45(2):630–640CrossRef Alhajahmad A, Abdalla MM, Gürdal Z (2008) Design tailoring for pressure pillowing using tow-placed steered fibers. J Aircr 45(2):630–640CrossRef
Zurück zum Zitat Autio M (2001) Optimization of coupled thermal-structural problems of laminated plates with lamination parameters. Struct Multidiscip Optim 21(1):40–51CrossRef Autio M (2001) Optimization of coupled thermal-structural problems of laminated plates with lamination parameters. Struct Multidiscip Optim 21(1):40–51CrossRef
Zurück zum Zitat Blom AW, Setoodeh S, Hol JM, Gürdal Z (2008) Design of variable-stiffness conical shells for maximum fundamental eigenfrequency. Comput Struct 86(9):870–878CrossRef Blom AW, Setoodeh S, Hol JM, Gürdal Z (2008) Design of variable-stiffness conical shells for maximum fundamental eigenfrequency. Comput Struct 86(9):870–878CrossRef
Zurück zum Zitat Bloomfield M, Diaconu C, Weaver P (2009) On feasible regions of lamination parameters for lay-up optimization of laminated composites. Proc R Soc London, Ser A 465:1123–1143MathSciNetCrossRefMATH Bloomfield M, Diaconu C, Weaver P (2009) On feasible regions of lamination parameters for lay-up optimization of laminated composites. Proc R Soc London, Ser A 465:1123–1143MathSciNetCrossRefMATH
Zurück zum Zitat Dassault Systèmes (2010) Abaqus/CAE Users Manual. Providence, Rhode Island USA. Abaqus 6.10 Dassault Systèmes (2010) Abaqus/CAE Users Manual. Providence, Rhode Island USA. Abaqus 6.10
Zurück zum Zitat Grenestedt J, Gudmundson P (1993) Layup optimization of composite material structures. In: Optimal design with advanced materials, pp 311–336 Grenestedt J, Gudmundson P (1993) Layup optimization of composite material structures. In: Optimal design with advanced materials, pp 311–336
Zurück zum Zitat Grenestedt JL (1994) Lamination parameters for reissner-mindlin plates. AIAA J 32(11):2328–2331CrossRefMATH Grenestedt JL (1994) Lamination parameters for reissner-mindlin plates. AIAA J 32(11):2328–2331CrossRefMATH
Zurück zum Zitat Gürdal Z, Olmedo R (1993) In-plane response of laminates with spatially varying fiber orientations: variable stiffness concept. AIAA J 31(4):751–758CrossRefMATH Gürdal Z, Olmedo R (1993) In-plane response of laminates with spatially varying fiber orientations: variable stiffness concept. AIAA J 31(4):751–758CrossRefMATH
Zurück zum Zitat Gürdal Z, Tatting BF, Wu C (2008) Variable stiffness composite panels: effects of stiffness variation on the in-plane and buckling response. Compos A: Appl Sci Manuf 39(5):911–922CrossRef Gürdal Z, Tatting BF, Wu C (2008) Variable stiffness composite panels: effects of stiffness variation on the in-plane and buckling response. Compos A: Appl Sci Manuf 39(5):911–922CrossRef
Zurück zum Zitat Hahn HT, Tsai SW (1980) Introduction to composite materials. CRC Press, Boca Raton Hahn HT, Tsai SW (1980) Introduction to composite materials. CRC Press, Boca Raton
Zurück zum Zitat Hammer VB, Bendsøe M, Lipton R, Pedersen P (1997) Parametrization in laminate design for optimal compliance. Int J Solids Struct 34(4):415–434CrossRefMATH Hammer VB, Bendsøe M, Lipton R, Pedersen P (1997) Parametrization in laminate design for optimal compliance. Int J Solids Struct 34(4):415–434CrossRefMATH
Zurück zum Zitat Honda S, Narita Y, Sasaki K (2009) Maximizing the fundamental frequency of laminated composite plates with optimally shaped curvilinear fibers. Journal of System Design and Dynamics 3(6):867–876CrossRef Honda S, Narita Y, Sasaki K (2009) Maximizing the fundamental frequency of laminated composite plates with optimally shaped curvilinear fibers. Journal of System Design and Dynamics 3(6):867–876CrossRef
Zurück zum Zitat Honda S, Oonishi Y, Narita Y, Sasaki K (2008) Vibration analysis of composite rectangular plates reinforced along curved lines. Journal of System Design and Dynamics 2(1):76–86CrossRef Honda S, Oonishi Y, Narita Y, Sasaki K (2008) Vibration analysis of composite rectangular plates reinforced along curved lines. Journal of System Design and Dynamics 2(1):76–86CrossRef
Zurück zum Zitat Hyer MW, Lee H (1991) The use of curvilinear fiber format to improve buckling resistance of composite plates with central circular holes. Compos Struct 18(3):239–261CrossRef Hyer MW, Lee H (1991) The use of curvilinear fiber format to improve buckling resistance of composite plates with central circular holes. Compos Struct 18(3):239–261CrossRef
Zurück zum Zitat Ijsselmuiden ST, Abdalla MM, Gürdal Z (2008) Implementation of strength-based failure criteria in the lamination parameter design space. AIAA J 46(7):1826–1834CrossRef Ijsselmuiden ST, Abdalla MM, Gürdal Z (2008) Implementation of strength-based failure criteria in the lamination parameter design space. AIAA J 46(7):1826–1834CrossRef
Zurück zum Zitat Ijsselmuiden ST, Abdalla MM, Gürdal Z (2010) Optimization of variable-stiffness panels for maximum buckling load using lamination parameters. AIAA J 48(1):134–143CrossRef Ijsselmuiden ST, Abdalla MM, Gürdal Z (2010) Optimization of variable-stiffness panels for maximum buckling load using lamination parameters. AIAA J 48(1):134–143CrossRef
Zurück zum Zitat Jones RM (1998) Mechanics of composite materials. CRC Press, Boca Raton Jones RM (1998) Mechanics of composite materials. CRC Press, Boca Raton
Zurück zum Zitat Khani A, IJsselmuiden ST, Abdalla MM, Gürdal Z. (2011) Design of variable stiffness panels for maximum strength using lamination parameters. Compos Part B 42(3):546–552CrossRef Khani A, IJsselmuiden ST, Abdalla MM, Gürdal Z. (2011) Design of variable stiffness panels for maximum strength using lamination parameters. Compos Part B 42(3):546–552CrossRef
Zurück zum Zitat Lipton R (1994) On optimal reinforcement of plates and choice of design parameters. Control Cybernetics 23 (3):481–493MathSciNetMATH Lipton R (1994) On optimal reinforcement of plates and choice of design parameters. Control Cybernetics 23 (3):481–493MathSciNetMATH
Zurück zum Zitat Nagendra S, Kodiyalam S, Davis J, Parthasarathy V (1995) Optimization of tow fiber paths for composite design. In: 36Th structures, structural dynamics and materials conference, New Orleans, p 1275 Nagendra S, Kodiyalam S, Davis J, Parthasarathy V (1995) Optimization of tow fiber paths for composite design. In: 36Th structures, structural dynamics and materials conference, New Orleans, p 1275
Zurück zum Zitat Narita Y (2003) Layerwise optimization for the maximum fundamental frequency of laminated composite plates. J Sound Vib 263(5):1005–1016CrossRef Narita Y (2003) Layerwise optimization for the maximum fundamental frequency of laminated composite plates. J Sound Vib 263(5):1005–1016CrossRef
Zurück zum Zitat Narita Y, Hodgkinson J (2005) Layerwise optimisation for maximising the fundamental frequencies of point-supported rectangular laminated composite plates. Compos Struct 69(2):127–135CrossRef Narita Y, Hodgkinson J (2005) Layerwise optimisation for maximising the fundamental frequencies of point-supported rectangular laminated composite plates. Compos Struct 69(2):127–135CrossRef
Zurück zum Zitat Olmedo R, Gurdal Z (1993) Buckling response of laminates with spatially varying fiber orientations. In: 34Th structures, structural dynamics and materials conference, La Jolla, vol 96, pp 2261–2269 Olmedo R, Gurdal Z (1993) Buckling response of laminates with spatially varying fiber orientations. In: 34Th structures, structural dynamics and materials conference, La Jolla, vol 96, pp 2261–2269
Zurück zum Zitat Parnas L, Oral S, Ceyhan Ü (2003) Optimum design of composite structures with curved fiber courses. Combust Sci Technol 63(7):1071–1082CrossRef Parnas L, Oral S, Ceyhan Ü (2003) Optimum design of composite structures with curved fiber courses. Combust Sci Technol 63(7):1071–1082CrossRef
Zurück zum Zitat Peeters DM, Hesse S, Abdalla MM (2015) Stacking sequence optimisation of variable stiffness laminates with manufacturing constraints. Compos Struct 125:596–604CrossRef Peeters DM, Hesse S, Abdalla MM (2015) Stacking sequence optimisation of variable stiffness laminates with manufacturing constraints. Compos Struct 125:596–604CrossRef
Zurück zum Zitat Reddy JN (2006) An introduction to the finite element method, 3rd edn. McGraw-Hill Education, Singapore Reddy JN (2006) An introduction to the finite element method, 3rd edn. McGraw-Hill Education, Singapore
Zurück zum Zitat Setoodeh S, Abdalla M, Gürdal Z (2006) Approximate feasible regions for lamination parameters aiaa-2006-6973. In: 11Th AIAA/ISSMO multidisciplinary analysis and optimisation conference, Portsmouth Setoodeh S, Abdalla M, Gürdal Z (2006) Approximate feasible regions for lamination parameters aiaa-2006-6973. In: 11Th AIAA/ISSMO multidisciplinary analysis and optimisation conference, Portsmouth
Zurück zum Zitat Setoodeh S, Abdalla MM, Gürdal Z (2005) Combined topology and fiber path design of composite layers using cellular automata. Struct Multidiscip Optim 30(6):413–421CrossRef Setoodeh S, Abdalla MM, Gürdal Z (2005) Combined topology and fiber path design of composite layers using cellular automata. Struct Multidiscip Optim 30(6):413–421CrossRef
Zurück zum Zitat Setoodeh S, Abdalla MM, Gürdal Z (2006) Design of variable–stiffness laminates using lamination parameters. Compos Part B Eng 37(4):301–309CrossRef Setoodeh S, Abdalla MM, Gürdal Z (2006) Design of variable–stiffness laminates using lamination parameters. Compos Part B Eng 37(4):301–309CrossRef
Zurück zum Zitat Setoodeh S, Abdalla MM, IJsselmuiden ST, Gürdal Z (2009) Design of variable-stiffness composite panels for maximum buckling load. Compos Struct 87(1):109–117CrossRef Setoodeh S, Abdalla MM, IJsselmuiden ST, Gürdal Z (2009) Design of variable-stiffness composite panels for maximum buckling load. Compos Struct 87(1):109–117CrossRef
Zurück zum Zitat Setoodeh S, Blom A, Abdalla M, Gürdal Z (2006) Generating curvilinear fiber paths from lamination parameters distribution. In: 47Th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference 14th AIAA/ASME/AHS adaptive structures conference 7th, New Port, p 1875 Setoodeh S, Blom A, Abdalla M, Gürdal Z (2006) Generating curvilinear fiber paths from lamination parameters distribution. In: 47Th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference 14th AIAA/ASME/AHS adaptive structures conference 7th, New Port, p 1875
Zurück zum Zitat Tatting BF, Gürdal Z (2002) Design and manufacture of elastically tailored tow placed plates. NASA technical report. Document ID 20020073162 (Acquired Sep 27, 2002). Report No. NASA/CR-2002-211919, Subject Category: Structural Mechanics, 34p, English Tatting BF, Gürdal Z (2002) Design and manufacture of elastically tailored tow placed plates. NASA technical report. Document ID 20020073162 (Acquired Sep 27, 2002). Report No. NASA/CR-2002-211919, Subject Category: Structural Mechanics, 34p, English
Zurück zum Zitat Waldhart C (1996) Analysis of tow-placed, variable-stiffness laminates. Ph.D. thesis, Virginia Polytechnic Institute and State University, Blacksburg Waldhart C (1996) Analysis of tow-placed, variable-stiffness laminates. Ph.D. thesis, Virginia Polytechnic Institute and State University, Blacksburg
Zurück zum Zitat Wu KC, Gürdal Z (2006) Variable stiffness panel structural analyses with material nonlinearity and correlation with tests. In: 47Th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Hampton, p 2165 Wu KC, Gürdal Z (2006) Variable stiffness panel structural analyses with material nonlinearity and correlation with tests. In: 47Th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Hampton, p 2165
Zurück zum Zitat Wu Z, Weaver PM, Raju G, Kim BC (2012) Buckling analysis and optimisation of variable angle tow composite plates. Thin-Walled Struct 60:163–172CrossRef Wu Z, Weaver PM, Raju G, Kim BC (2012) Buckling analysis and optimisation of variable angle tow composite plates. Thin-Walled Struct 60:163–172CrossRef
Metadaten
Titel
A lagrange parametrization for the design of variable stiffness laminates
verfasst von
Hugo Borges de Quadros
José Antonio Hernandes
Publikationsdatum
01.02.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 1/2018
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-017-1882-2

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