Optimum design of truss structures undergoing large deflections subject to a system stability constraint
A structural optimization algorithm is developed for shallow trusses undergoing large deflections subject to a system stability constraint. The method combines the non‐linear buckling analysis, through displacement control technique, with the optimality criteria approach. Four examples illustrate th...
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| Published in | International journal for numerical methods in engineering Vol. 48; no. 3; pp. 421 - 434 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
30.05.2000
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0029-5981 1097-0207 |
| DOI | 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X |
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| Abstract | A structural optimization algorithm is developed for shallow trusses undergoing large deflections subject to a system stability constraint. The method combines the non‐linear buckling analysis, through displacement control technique, with the optimality criteria approach. Four examples illustrate the procedure and allow the results obtained to be compared with those in the literature. It is shown that a design based on the generalized eigenvalue problem (linear buckling) highly underestimates the optimum mass for these types of structures so a design based on the linear buckling analysis can result in catastrophic failure. In one of the design examples the stresses in the elements, in the optimum design, exceed the allowable stresses, pointing out the need for a design that accounts for both non‐linear buckling and stress constraints. Copyright © 2000 John Wiley & Sons, Ltd. |
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| AbstractList | A structural optimization algorithm is developed for shallow trusses undergoing large deflections subject to a system stability constraint. The method combines the non‐linear buckling analysis, through displacement control technique, with the optimality criteria approach. Four examples illustrate the procedure and allow the results obtained to be compared with those in the literature. It is shown that a design based on the generalized eigenvalue problem (linear buckling) highly underestimates the optimum mass for these types of structures so a design based on the linear buckling analysis can result in catastrophic failure. In one of the design examples the stresses in the elements, in the optimum design, exceed the allowable stresses, pointing out the need for a design that accounts for both non‐linear buckling and stress constraints. Copyright © 2000 John Wiley & Sons, Ltd. A structural optimization algorithm is developed for shallow trusses undergoing large deflections subject to a system stability constraint. The method combines the nonlinear buckling analysis, through displacement control technique, with the optimality criteria approach. Four examples illustrate the procedure and allow the results obtained to be compared with those in the literature. It is shown that a design based on the generalized eigenvalue problem (linear buckling) highly underestimates the optimum mass for these types of structures so a design based on the linear buckling analysis can result in catastrophic failure. In one of the design examples the stresses in the elements, in the optimum design, exceed the allowable stresses, pointing out the need for a design that accounts for both nonlinear buckling and stress constraints. (Author) |
| Author | Sedaghati, R. Tabarrok, B. |
| Author_xml | – sequence: 1 givenname: R. surname: Sedaghati fullname: Sedaghati, R. email: rsedagha@me.uvic.ca organization: Department of Mechanical Engineering, University of Victoria, P.O. Box 3055, Victoria, BC, Canada V8W 3P6 – sequence: 2 givenname: B. surname: Tabarrok fullname: Tabarrok, B. email: tabarrok@me.uvic.ca organization: Department of Mechanical Engineering, University of Victoria, P.O. Box 3055, Victoria, BC, Canada V8W 3P6 |
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| Cites_doi | 10.2514/3.8882 10.1016/0020-7683(73)90008-5 10.1016/0045-7949(88)90286-6 10.2514/3.8224 10.1002/nme.1620110103 10.1002/nme.1620100510 10.1080/03052158508902488 10.2514/3.48461 10.1002/nme.1620140811 10.1016/0045-7949(94)90161-9 10.2514/3.11739 10.1016/0045-7949(89)90411-2 10.1002/nme.1620030412 10.1016/0045-7949(94)90160-0 |
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| References | Kamat MP, Raungasilasingha P. Optimization of space truss against instability using design sensitivity derivatives. Engineering Optimization 1985; 8:177-188. Khot NS. Nonlinear analysis of optimized structure with constraints on system stability. AIAA Journal 1983; 21(8):1181-1186. Levy R. Optimization for buckling with exact geometries. Computers and Structures 1994; 53(5):1139-1144. Canfield RA. Design of frames against buckling using a Rayleigh quotient approximation. AIAA Journal 1993; 31(6):1144-1149. Kamat MP, Khot NS, Venkayya VB. Opimization of shallow trusses against limit point instability. AIAA Journal 1984; 22(3):403-408. Szyskowski W, Watson LG, Fietkiewicz B. Bimodal optimization of frames for maximum stability. Computers and Structures 1989; 32(5):1093-1104. Haisler WE, Stricklin JA, Key JE. Incrementation in nonlinear structural analysis by self-correcting method. International Journal for Numerical Methods in Engineering 1977; 11:3-10. Crisfield MA. Non-Linear Finite Element Analysis of Solids and Structures, Vol. 1, Wiley: New York, 1991. Levy R. Optimal design of trusses for overall stability. Computers and Structures 1994; 53(5):1133-1138. Kiusalaas J. Optimal design of structures with buckling constraints. International Journal of Solids and Structures 1973; 9:863-878. Khot NS, Kamat MP. Minimum weight design of truss structures with geometric nonlinear behavior. AIAA Journal 1985; 23(1):139-144. Zienkiewicz OC. Incremental displacements in nonlinear problems. International Journal for Numerical Methods in Engineering 1971; 3:587-592. Levy R, Perng HS. Optimization for nonlinear stability. Computers and Structures 1988; 30(3):529-535. Batoz JL, Dhatt G. Incremental displacement algorithms for nonlinear problems. International Journal for Numerical Methods in Engineering 1979; 14:1262-1267. Khot NS,Venkayya VB, Berke L. Optimum structural design with stability constraints. International Journal for Numerical Methods in Engineering 1976; 10:1097-1114. Bathe KJ. Finite Element Procedures. Prentice-Hall: Englewood Cliffs, NJ, 1996. 1976; 10 1991; 1 1973; 9 1989; 32 1979; 14 1990 1985; 8 1984; 22 1993; 31 1983; 21 1996 1977; 11 1981 1988; 30 1985; 23 1994; 53 1971; 3 Khot (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB4) 1983; 21 Kiusalaas (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB1) 1973; 9 Crisfield (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB18) 1991; 1 Kamat (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB10) 1985; 8 Haisler (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB15) 1977; 11 Khot (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB2) 1976; 10 Levy (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB8) 1994; 53 Kamat (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB12) 1984; 22 Khot (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB3) 1981 Khot (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB9) 1985; 23 Batoz (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB16) 1979; 14 Levy (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB5) 1988; 30 Canfield (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB7) 1993; 31 Szyskowski (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB6) 1989; 32 Choi (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB11) 1990 Levy (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB13) 1994; 53 Zienkiewicz (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB14) 1971; 3 Bathe (10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB17) 1996 |
| References_xml | – reference: Zienkiewicz OC. Incremental displacements in nonlinear problems. International Journal for Numerical Methods in Engineering 1971; 3:587-592. – reference: Haisler WE, Stricklin JA, Key JE. Incrementation in nonlinear structural analysis by self-correcting method. International Journal for Numerical Methods in Engineering 1977; 11:3-10. – reference: Levy R. Optimization for buckling with exact geometries. Computers and Structures 1994; 53(5):1139-1144. – reference: Crisfield MA. Non-Linear Finite Element Analysis of Solids and Structures, Vol. 1, Wiley: New York, 1991. – reference: Khot NS. Nonlinear analysis of optimized structure with constraints on system stability. AIAA Journal 1983; 21(8):1181-1186. – reference: Kamat MP, Raungasilasingha P. Optimization of space truss against instability using design sensitivity derivatives. Engineering Optimization 1985; 8:177-188. – reference: Kamat MP, Khot NS, Venkayya VB. Opimization of shallow trusses against limit point instability. AIAA Journal 1984; 22(3):403-408. – reference: Canfield RA. Design of frames against buckling using a Rayleigh quotient approximation. AIAA Journal 1993; 31(6):1144-1149. – reference: Bathe KJ. Finite Element Procedures. Prentice-Hall: Englewood Cliffs, NJ, 1996. – reference: Khot NS,Venkayya VB, Berke L. Optimum structural design with stability constraints. International Journal for Numerical Methods in Engineering 1976; 10:1097-1114. – reference: Khot NS, Kamat MP. Minimum weight design of truss structures with geometric nonlinear behavior. AIAA Journal 1985; 23(1):139-144. – reference: Szyskowski W, Watson LG, Fietkiewicz B. Bimodal optimization of frames for maximum stability. Computers and Structures 1989; 32(5):1093-1104. – reference: Batoz JL, Dhatt G. Incremental displacement algorithms for nonlinear problems. International Journal for Numerical Methods in Engineering 1979; 14:1262-1267. – reference: Levy R, Perng HS. Optimization for nonlinear stability. Computers and Structures 1988; 30(3):529-535. – reference: Levy R. Optimal design of trusses for overall stability. Computers and Structures 1994; 53(5):1133-1138. – reference: Kiusalaas J. Optimal design of structures with buckling constraints. International Journal of Solids and Structures 1973; 9:863-878. – volume: 31 start-page: 1144 issue: 6 year: 1993 end-page: 1149 article-title: Design of frames against buckling using a Rayleigh quotient approximation publication-title: AIAA Journal – year: 1981 – volume: 30 start-page: 529 issue: 3 year: 1988 end-page: 535 article-title: Optimization for nonlinear stability publication-title: Computers and Structures – start-page: 131 year: 1990 end-page: 143 – volume: 32 start-page: 1093 issue: 5 year: 1989 end-page: 1104 article-title: Bimodal optimization of frames for maximum stability publication-title: Computers and Structures – volume: 53 start-page: 1133 issue: 5 year: 1994 end-page: 1138 article-title: Optimal design of trusses for overall stability publication-title: Computers and Structures – volume: 3 start-page: 587 year: 1971 end-page: 592 article-title: Incremental displacements in nonlinear problems publication-title: International Journal for Numerical Methods in Engineering – volume: 22 start-page: 403 issue: 3 year: 1984 end-page: 408 article-title: Opimization of shallow trusses against limit point instability publication-title: AIAA Journal – volume: 23 start-page: 139 issue: 1 year: 1985 end-page: 144 article-title: Minimum weight design of truss structures with geometric nonlinear behavior publication-title: AIAA Journal – volume: 21 start-page: 1181 issue: 8 year: 1983 end-page: 1186 article-title: Nonlinear analysis of optimized structure with constraints on system stability publication-title: AIAA Journal – year: 1996 – volume: 1 year: 1991 – volume: 9 start-page: 863 year: 1973 end-page: 878 article-title: Optimal design of structures with buckling constraints publication-title: International Journal of Solids and Structures – volume: 10 start-page: 1097 year: 1976 end-page: 1114 article-title: Optimum structural design with stability constraints publication-title: International Journal for Numerical Methods in Engineering – volume: 53 start-page: 1139 issue: 5 year: 1994 end-page: 1144 article-title: Optimization for buckling with exact geometries publication-title: Computers and Structures – volume: 11 start-page: 3 year: 1977 end-page: 10 article-title: Incrementation in nonlinear structural analysis by self‐correcting method publication-title: International Journal for Numerical Methods in Engineering – volume: 14 start-page: 1262 year: 1979 end-page: 1267 article-title: Incremental displacement algorithms for nonlinear problems publication-title: International Journal for Numerical Methods in Engineering – volume: 8 start-page: 177 year: 1985 end-page: 188 article-title: Optimization of space truss against instability using design sensitivity derivatives publication-title: Engineering Optimization – volume: 23 start-page: 139 year: 1985 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB9 publication-title: AIAA Journal doi: 10.2514/3.8882 – volume: 1 volume-title: Non-Linear Finite Element Analysis of Solids and Structures year: 1991 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB18 – volume: 9 start-page: 863 year: 1973 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB1 publication-title: International Journal of Solids and Structures doi: 10.1016/0020-7683(73)90008-5 – volume: 30 start-page: 529 year: 1988 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB5 publication-title: Computers and Structures doi: 10.1016/0045-7949(88)90286-6 – volume: 21 start-page: 1181 year: 1983 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB4 publication-title: AIAA Journal doi: 10.2514/3.8224 – volume: 11 start-page: 3 year: 1977 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB15 publication-title: International Journal for Numerical Methods in Engineering doi: 10.1002/nme.1620110103 – volume-title: Finite Element Procedures year: 1996 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB17 – volume: 10 start-page: 1097 year: 1976 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB2 publication-title: International Journal for Numerical Methods in Engineering doi: 10.1002/nme.1620100510 – volume: 8 start-page: 177 year: 1985 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB10 publication-title: Engineering Optimization doi: 10.1080/03052158508902488 – year: 1990 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB11 – volume: 22 start-page: 403 year: 1984 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB12 publication-title: AIAA Journal doi: 10.2514/3.48461 – volume: 14 start-page: 1262 year: 1979 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB16 publication-title: International Journal for Numerical Methods in Engineering doi: 10.1002/nme.1620140811 – year: 1981 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB3 – volume: 53 start-page: 1139 year: 1994 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB13 publication-title: Computers and Structures doi: 10.1016/0045-7949(94)90161-9 – volume: 31 start-page: 1144 year: 1993 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB7 publication-title: AIAA Journal doi: 10.2514/3.11739 – volume: 32 start-page: 1093 year: 1989 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB6 publication-title: Computers and Structures doi: 10.1016/0045-7949(89)90411-2 – volume: 3 start-page: 587 year: 1971 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB14 publication-title: International Journal for Numerical Methods in Engineering doi: 10.1002/nme.1620030412 – volume: 53 start-page: 1133 year: 1994 ident: 10.1002/(SICI)1097-0207(20000530)48:3<421::AID-NME885>3.0.CO;2-X-BIB8 publication-title: Computers and Structures doi: 10.1016/0045-7949(94)90160-0 |
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| SubjectTerms | geometrical non-linearity large deflections optimum design stability constraint truss structures |
| Title | Optimum design of truss structures undergoing large deflections subject to a system stability constraint |
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