Optimal design of cantilevered elastica for minimum tip deflection under self-weight
Abstract The optimal distribution of material to minimize the vertical deflection of the free end of a horizontal cantilever is determined. The beam is only subjected to its own weight. Large deflections are considered, and the structure is modeled as an inextensible elastica. A minimum-area constra...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Plaut, Raymond H. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2010 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 2010 |
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| Übergeordnetes Werk: |
Enthalten in: Structural and multidisciplinary optimization - Berlin : Springer, 1989, 43(2010), 5 vom: 24. Dez., Seite 657-664 |
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| Übergeordnetes Werk: |
volume:43 ; year:2010 ; number:5 ; day:24 ; month:12 ; pages:657-664 |
| Links: |
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| DOI / URN: |
10.1007/s00158-010-0611-x |
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SPR001314289 |
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| 100 | 1 | |a Plaut, Raymond H. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Optimal design of cantilevered elastica for minimum tip deflection under self-weight |
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| 520 | |a Abstract The optimal distribution of material to minimize the vertical deflection of the free end of a horizontal cantilever is determined. The beam is only subjected to its own weight. Large deflections are considered, and the structure is modeled as an inextensible elastica. A minimum-area constraint is included, and is active in a region near the tip. After the problem is formulated, numerical results are obtained with the use of a shooting method. The moment of inertia is assumed to be proportional to the area or its square or cube. The results depend on this relationship, the minimum-area constraint, and a nondimensional parameter depending on the beam’s density, length, and modulus of elasticity. In the numerical results presented, if the minimum area is 1/20 of the area of the uniform beam, the tip deflection for the optimal design is 78–89% smaller than that for the uniform beam. An experiment is conducted and the data are in close agreement with the numerical results. | ||
| 650 | 4 | |a Optimal beam |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Cantilever |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Self-weight |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Minimum deflection |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Large deflections |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Elastica |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Virgin, Lawrence N. |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Structural and multidisciplinary optimization |d Berlin : Springer, 1989 |g 43(2010), 5 vom: 24. Dez., Seite 657-664 |w (DE-627)271602503 |w (DE-600)1481279-4 |x 1615-1488 |7 nnns |
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10.1007/s00158-010-0611-x doi (DE-627)SPR001314289 (SPR)s00158-010-0611-x-e DE-627 ger DE-627 rakwb eng Plaut, Raymond H. verfasserin aut Optimal design of cantilevered elastica for minimum tip deflection under self-weight 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2010 Abstract The optimal distribution of material to minimize the vertical deflection of the free end of a horizontal cantilever is determined. The beam is only subjected to its own weight. Large deflections are considered, and the structure is modeled as an inextensible elastica. A minimum-area constraint is included, and is active in a region near the tip. After the problem is formulated, numerical results are obtained with the use of a shooting method. The moment of inertia is assumed to be proportional to the area or its square or cube. The results depend on this relationship, the minimum-area constraint, and a nondimensional parameter depending on the beam’s density, length, and modulus of elasticity. In the numerical results presented, if the minimum area is 1/20 of the area of the uniform beam, the tip deflection for the optimal design is 78–89% smaller than that for the uniform beam. An experiment is conducted and the data are in close agreement with the numerical results. Optimal beam (dpeaa)DE-He213 Cantilever (dpeaa)DE-He213 Self-weight (dpeaa)DE-He213 Minimum deflection (dpeaa)DE-He213 Large deflections (dpeaa)DE-He213 Elastica (dpeaa)DE-He213 Virgin, Lawrence N. aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 43(2010), 5 vom: 24. Dez., Seite 657-664 (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:43 year:2010 number:5 day:24 month:12 pages:657-664 https://dx.doi.org/10.1007/s00158-010-0611-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 43 2010 5 24 12 657-664 |
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10.1007/s00158-010-0611-x doi (DE-627)SPR001314289 (SPR)s00158-010-0611-x-e DE-627 ger DE-627 rakwb eng Plaut, Raymond H. verfasserin aut Optimal design of cantilevered elastica for minimum tip deflection under self-weight 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2010 Abstract The optimal distribution of material to minimize the vertical deflection of the free end of a horizontal cantilever is determined. The beam is only subjected to its own weight. Large deflections are considered, and the structure is modeled as an inextensible elastica. A minimum-area constraint is included, and is active in a region near the tip. After the problem is formulated, numerical results are obtained with the use of a shooting method. The moment of inertia is assumed to be proportional to the area or its square or cube. The results depend on this relationship, the minimum-area constraint, and a nondimensional parameter depending on the beam’s density, length, and modulus of elasticity. In the numerical results presented, if the minimum area is 1/20 of the area of the uniform beam, the tip deflection for the optimal design is 78–89% smaller than that for the uniform beam. An experiment is conducted and the data are in close agreement with the numerical results. Optimal beam (dpeaa)DE-He213 Cantilever (dpeaa)DE-He213 Self-weight (dpeaa)DE-He213 Minimum deflection (dpeaa)DE-He213 Large deflections (dpeaa)DE-He213 Elastica (dpeaa)DE-He213 Virgin, Lawrence N. aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 43(2010), 5 vom: 24. Dez., Seite 657-664 (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:43 year:2010 number:5 day:24 month:12 pages:657-664 https://dx.doi.org/10.1007/s00158-010-0611-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 43 2010 5 24 12 657-664 |
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10.1007/s00158-010-0611-x doi (DE-627)SPR001314289 (SPR)s00158-010-0611-x-e DE-627 ger DE-627 rakwb eng Plaut, Raymond H. verfasserin aut Optimal design of cantilevered elastica for minimum tip deflection under self-weight 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2010 Abstract The optimal distribution of material to minimize the vertical deflection of the free end of a horizontal cantilever is determined. The beam is only subjected to its own weight. Large deflections are considered, and the structure is modeled as an inextensible elastica. A minimum-area constraint is included, and is active in a region near the tip. After the problem is formulated, numerical results are obtained with the use of a shooting method. The moment of inertia is assumed to be proportional to the area or its square or cube. The results depend on this relationship, the minimum-area constraint, and a nondimensional parameter depending on the beam’s density, length, and modulus of elasticity. In the numerical results presented, if the minimum area is 1/20 of the area of the uniform beam, the tip deflection for the optimal design is 78–89% smaller than that for the uniform beam. An experiment is conducted and the data are in close agreement with the numerical results. Optimal beam (dpeaa)DE-He213 Cantilever (dpeaa)DE-He213 Self-weight (dpeaa)DE-He213 Minimum deflection (dpeaa)DE-He213 Large deflections (dpeaa)DE-He213 Elastica (dpeaa)DE-He213 Virgin, Lawrence N. aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 43(2010), 5 vom: 24. Dez., Seite 657-664 (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:43 year:2010 number:5 day:24 month:12 pages:657-664 https://dx.doi.org/10.1007/s00158-010-0611-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 43 2010 5 24 12 657-664 |
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10.1007/s00158-010-0611-x doi (DE-627)SPR001314289 (SPR)s00158-010-0611-x-e DE-627 ger DE-627 rakwb eng Plaut, Raymond H. verfasserin aut Optimal design of cantilevered elastica for minimum tip deflection under self-weight 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2010 Abstract The optimal distribution of material to minimize the vertical deflection of the free end of a horizontal cantilever is determined. The beam is only subjected to its own weight. Large deflections are considered, and the structure is modeled as an inextensible elastica. A minimum-area constraint is included, and is active in a region near the tip. After the problem is formulated, numerical results are obtained with the use of a shooting method. The moment of inertia is assumed to be proportional to the area or its square or cube. The results depend on this relationship, the minimum-area constraint, and a nondimensional parameter depending on the beam’s density, length, and modulus of elasticity. In the numerical results presented, if the minimum area is 1/20 of the area of the uniform beam, the tip deflection for the optimal design is 78–89% smaller than that for the uniform beam. An experiment is conducted and the data are in close agreement with the numerical results. Optimal beam (dpeaa)DE-He213 Cantilever (dpeaa)DE-He213 Self-weight (dpeaa)DE-He213 Minimum deflection (dpeaa)DE-He213 Large deflections (dpeaa)DE-He213 Elastica (dpeaa)DE-He213 Virgin, Lawrence N. aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 43(2010), 5 vom: 24. Dez., Seite 657-664 (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:43 year:2010 number:5 day:24 month:12 pages:657-664 https://dx.doi.org/10.1007/s00158-010-0611-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 43 2010 5 24 12 657-664 |
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10.1007/s00158-010-0611-x doi (DE-627)SPR001314289 (SPR)s00158-010-0611-x-e DE-627 ger DE-627 rakwb eng Plaut, Raymond H. verfasserin aut Optimal design of cantilevered elastica for minimum tip deflection under self-weight 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2010 Abstract The optimal distribution of material to minimize the vertical deflection of the free end of a horizontal cantilever is determined. The beam is only subjected to its own weight. Large deflections are considered, and the structure is modeled as an inextensible elastica. A minimum-area constraint is included, and is active in a region near the tip. After the problem is formulated, numerical results are obtained with the use of a shooting method. The moment of inertia is assumed to be proportional to the area or its square or cube. The results depend on this relationship, the minimum-area constraint, and a nondimensional parameter depending on the beam’s density, length, and modulus of elasticity. In the numerical results presented, if the minimum area is 1/20 of the area of the uniform beam, the tip deflection for the optimal design is 78–89% smaller than that for the uniform beam. An experiment is conducted and the data are in close agreement with the numerical results. Optimal beam (dpeaa)DE-He213 Cantilever (dpeaa)DE-He213 Self-weight (dpeaa)DE-He213 Minimum deflection (dpeaa)DE-He213 Large deflections (dpeaa)DE-He213 Elastica (dpeaa)DE-He213 Virgin, Lawrence N. aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 43(2010), 5 vom: 24. Dez., Seite 657-664 (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:43 year:2010 number:5 day:24 month:12 pages:657-664 https://dx.doi.org/10.1007/s00158-010-0611-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 43 2010 5 24 12 657-664 |
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Enthalten in Structural and multidisciplinary optimization 43(2010), 5 vom: 24. Dez., Seite 657-664 volume:43 year:2010 number:5 day:24 month:12 pages:657-664 |
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Enthalten in Structural and multidisciplinary optimization 43(2010), 5 vom: 24. Dez., Seite 657-664 volume:43 year:2010 number:5 day:24 month:12 pages:657-664 |
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Plaut, Raymond H. @@aut@@ Virgin, Lawrence N. @@aut@@ |
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Plaut, Raymond H. |
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Plaut, Raymond H. misc Optimal beam misc Cantilever misc Self-weight misc Minimum deflection misc Large deflections misc Elastica Optimal design of cantilevered elastica for minimum tip deflection under self-weight |
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Optimal design of cantilevered elastica for minimum tip deflection under self-weight Optimal beam (dpeaa)DE-He213 Cantilever (dpeaa)DE-He213 Self-weight (dpeaa)DE-He213 Minimum deflection (dpeaa)DE-He213 Large deflections (dpeaa)DE-He213 Elastica (dpeaa)DE-He213 |
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Optimal design of cantilevered elastica for minimum tip deflection under self-weight |
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optimal design of cantilevered elastica for minimum tip deflection under self-weight |
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Optimal design of cantilevered elastica for minimum tip deflection under self-weight |
| abstract |
Abstract The optimal distribution of material to minimize the vertical deflection of the free end of a horizontal cantilever is determined. The beam is only subjected to its own weight. Large deflections are considered, and the structure is modeled as an inextensible elastica. A minimum-area constraint is included, and is active in a region near the tip. After the problem is formulated, numerical results are obtained with the use of a shooting method. The moment of inertia is assumed to be proportional to the area or its square or cube. The results depend on this relationship, the minimum-area constraint, and a nondimensional parameter depending on the beam’s density, length, and modulus of elasticity. In the numerical results presented, if the minimum area is 1/20 of the area of the uniform beam, the tip deflection for the optimal design is 78–89% smaller than that for the uniform beam. An experiment is conducted and the data are in close agreement with the numerical results. © Springer-Verlag 2010 |
| abstractGer |
Abstract The optimal distribution of material to minimize the vertical deflection of the free end of a horizontal cantilever is determined. The beam is only subjected to its own weight. Large deflections are considered, and the structure is modeled as an inextensible elastica. A minimum-area constraint is included, and is active in a region near the tip. After the problem is formulated, numerical results are obtained with the use of a shooting method. The moment of inertia is assumed to be proportional to the area or its square or cube. The results depend on this relationship, the minimum-area constraint, and a nondimensional parameter depending on the beam’s density, length, and modulus of elasticity. In the numerical results presented, if the minimum area is 1/20 of the area of the uniform beam, the tip deflection for the optimal design is 78–89% smaller than that for the uniform beam. An experiment is conducted and the data are in close agreement with the numerical results. © Springer-Verlag 2010 |
| abstract_unstemmed |
Abstract The optimal distribution of material to minimize the vertical deflection of the free end of a horizontal cantilever is determined. The beam is only subjected to its own weight. Large deflections are considered, and the structure is modeled as an inextensible elastica. A minimum-area constraint is included, and is active in a region near the tip. After the problem is formulated, numerical results are obtained with the use of a shooting method. The moment of inertia is assumed to be proportional to the area or its square or cube. The results depend on this relationship, the minimum-area constraint, and a nondimensional parameter depending on the beam’s density, length, and modulus of elasticity. In the numerical results presented, if the minimum area is 1/20 of the area of the uniform beam, the tip deflection for the optimal design is 78–89% smaller than that for the uniform beam. An experiment is conducted and the data are in close agreement with the numerical results. © Springer-Verlag 2010 |
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Optimal design of cantilevered elastica for minimum tip deflection under self-weight |
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https://dx.doi.org/10.1007/s00158-010-0611-x |
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Virgin, Lawrence N. |
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