Material tailoring in three-dimensional flexural deformations of functionally graded material beams
Soft materials such as rubberlike and biological tissues are usually modeled as incompressible. Mechanical properties of polymeric materials can be controlled either by exposing them to ultraviolet light for different time durations or by changing their molecular structure. A challenge is to find th...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Batra, R.C. [verfasserIn] |
|---|
| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
3-Dimensional flexural deformations |
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| Übergeordnetes Werk: |
Enthalten in: Composite structures - Amsterdam : Elsevier, 1983, 259 |
|---|---|
| Übergeordnetes Werk: |
volume:259 |
| DOI / URN: |
10.1016/j.compstruct.2020.113232 |
|---|
| Katalog-ID: |
ELV005364698 |
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| 520 | |a Soft materials such as rubberlike and biological tissues are usually modeled as incompressible. Mechanical properties of polymeric materials can be controlled either by exposing them to ultraviolet light for different time durations or by changing their molecular structure. A challenge is to find the spatial variation of the moduli to fully utilize the material. One way to achieve this is to have a uniform distribution of the stress component likely to cause their failure. To achieve this, we analytically analyze 3-dimensional infinitesimal flexural deformations of a functionally graded (FG) and linearly elastic beam of rectangular cross-section with Young’s modulus a continuous function of the thickness coordinate. The problem is first studied for an incompressible material and then for a compressible material for which Poisson’s ratio is assumed to be a constant. It is found that when Young’s modulus at a point is inversely proportional to its distance from the neutral axis, then the magnitude of the bending stress is uniform over beam’s cross-section, the beam is the lightest possible and its deflections are 2/3rd of that of the corresponding beam of a homogeneous material that has the same maximum bending stress as the FG beam. Noting that Young’s modulus cannot be infinity at the neutral axis, we avoid this by assuming that it is a constant over a small region around the neutral axis. For a transversely isotropic incompressible material beam, it is shown that (2μ1 + μ2) determines beam’s flexural stiffness where μ1 and μ2 are, respectively, the shear moduli along and perpendicular to the axis of transverse isotropy. Beams of homogeneous materials having the same geometry as the FG beam have different shear moduli depending upon whether the FG and the homogeneous material beams have the same maximum deflection, the same maximum bending stress or the same total strain energy of deformation. | ||
| 650 | 4 | |a 3-Dimensional flexural deformations | |
| 650 | 4 | |a Functionally graded material beam | |
| 650 | 4 | |a Equivalent homogeneous material beam | |
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10.1016/j.compstruct.2020.113232 doi (DE-627)ELV005364698 (ELSEVIER)S0263-8223(20)33158-5 DE-627 ger DE-627 rda eng 670 DE-600 51.75 bkl Batra, R.C. verfasserin aut Material tailoring in three-dimensional flexural deformations of functionally graded material beams 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Soft materials such as rubberlike and biological tissues are usually modeled as incompressible. Mechanical properties of polymeric materials can be controlled either by exposing them to ultraviolet light for different time durations or by changing their molecular structure. A challenge is to find the spatial variation of the moduli to fully utilize the material. One way to achieve this is to have a uniform distribution of the stress component likely to cause their failure. To achieve this, we analytically analyze 3-dimensional infinitesimal flexural deformations of a functionally graded (FG) and linearly elastic beam of rectangular cross-section with Young’s modulus a continuous function of the thickness coordinate. The problem is first studied for an incompressible material and then for a compressible material for which Poisson’s ratio is assumed to be a constant. It is found that when Young’s modulus at a point is inversely proportional to its distance from the neutral axis, then the magnitude of the bending stress is uniform over beam’s cross-section, the beam is the lightest possible and its deflections are 2/3rd of that of the corresponding beam of a homogeneous material that has the same maximum bending stress as the FG beam. Noting that Young’s modulus cannot be infinity at the neutral axis, we avoid this by assuming that it is a constant over a small region around the neutral axis. For a transversely isotropic incompressible material beam, it is shown that (2μ1 + μ2) determines beam’s flexural stiffness where μ1 and μ2 are, respectively, the shear moduli along and perpendicular to the axis of transverse isotropy. Beams of homogeneous materials having the same geometry as the FG beam have different shear moduli depending upon whether the FG and the homogeneous material beams have the same maximum deflection, the same maximum bending stress or the same total strain energy of deformation. 3-Dimensional flexural deformations Functionally graded material beam Equivalent homogeneous material beam Enthalten in Composite structures Amsterdam : Elsevier, 1983 259 (DE-627)320509044 (DE-600)2013177-X (DE-576)094531447 0263-8223 nnns volume:259 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 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_4338 GBV_ILN_4393 51.75 Verbundwerkstoffe Schichtstoffe AR 259 |
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10.1016/j.compstruct.2020.113232 doi (DE-627)ELV005364698 (ELSEVIER)S0263-8223(20)33158-5 DE-627 ger DE-627 rda eng 670 DE-600 51.75 bkl Batra, R.C. verfasserin aut Material tailoring in three-dimensional flexural deformations of functionally graded material beams 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Soft materials such as rubberlike and biological tissues are usually modeled as incompressible. Mechanical properties of polymeric materials can be controlled either by exposing them to ultraviolet light for different time durations or by changing their molecular structure. A challenge is to find the spatial variation of the moduli to fully utilize the material. One way to achieve this is to have a uniform distribution of the stress component likely to cause their failure. To achieve this, we analytically analyze 3-dimensional infinitesimal flexural deformations of a functionally graded (FG) and linearly elastic beam of rectangular cross-section with Young’s modulus a continuous function of the thickness coordinate. The problem is first studied for an incompressible material and then for a compressible material for which Poisson’s ratio is assumed to be a constant. It is found that when Young’s modulus at a point is inversely proportional to its distance from the neutral axis, then the magnitude of the bending stress is uniform over beam’s cross-section, the beam is the lightest possible and its deflections are 2/3rd of that of the corresponding beam of a homogeneous material that has the same maximum bending stress as the FG beam. Noting that Young’s modulus cannot be infinity at the neutral axis, we avoid this by assuming that it is a constant over a small region around the neutral axis. For a transversely isotropic incompressible material beam, it is shown that (2μ1 + μ2) determines beam’s flexural stiffness where μ1 and μ2 are, respectively, the shear moduli along and perpendicular to the axis of transverse isotropy. Beams of homogeneous materials having the same geometry as the FG beam have different shear moduli depending upon whether the FG and the homogeneous material beams have the same maximum deflection, the same maximum bending stress or the same total strain energy of deformation. 3-Dimensional flexural deformations Functionally graded material beam Equivalent homogeneous material beam Enthalten in Composite structures Amsterdam : Elsevier, 1983 259 (DE-627)320509044 (DE-600)2013177-X (DE-576)094531447 0263-8223 nnns volume:259 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 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_4338 GBV_ILN_4393 51.75 Verbundwerkstoffe Schichtstoffe AR 259 |
| allfields_unstemmed |
10.1016/j.compstruct.2020.113232 doi (DE-627)ELV005364698 (ELSEVIER)S0263-8223(20)33158-5 DE-627 ger DE-627 rda eng 670 DE-600 51.75 bkl Batra, R.C. verfasserin aut Material tailoring in three-dimensional flexural deformations of functionally graded material beams 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Soft materials such as rubberlike and biological tissues are usually modeled as incompressible. Mechanical properties of polymeric materials can be controlled either by exposing them to ultraviolet light for different time durations or by changing their molecular structure. A challenge is to find the spatial variation of the moduli to fully utilize the material. One way to achieve this is to have a uniform distribution of the stress component likely to cause their failure. To achieve this, we analytically analyze 3-dimensional infinitesimal flexural deformations of a functionally graded (FG) and linearly elastic beam of rectangular cross-section with Young’s modulus a continuous function of the thickness coordinate. The problem is first studied for an incompressible material and then for a compressible material for which Poisson’s ratio is assumed to be a constant. It is found that when Young’s modulus at a point is inversely proportional to its distance from the neutral axis, then the magnitude of the bending stress is uniform over beam’s cross-section, the beam is the lightest possible and its deflections are 2/3rd of that of the corresponding beam of a homogeneous material that has the same maximum bending stress as the FG beam. Noting that Young’s modulus cannot be infinity at the neutral axis, we avoid this by assuming that it is a constant over a small region around the neutral axis. For a transversely isotropic incompressible material beam, it is shown that (2μ1 + μ2) determines beam’s flexural stiffness where μ1 and μ2 are, respectively, the shear moduli along and perpendicular to the axis of transverse isotropy. Beams of homogeneous materials having the same geometry as the FG beam have different shear moduli depending upon whether the FG and the homogeneous material beams have the same maximum deflection, the same maximum bending stress or the same total strain energy of deformation. 3-Dimensional flexural deformations Functionally graded material beam Equivalent homogeneous material beam Enthalten in Composite structures Amsterdam : Elsevier, 1983 259 (DE-627)320509044 (DE-600)2013177-X (DE-576)094531447 0263-8223 nnns volume:259 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 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_4338 GBV_ILN_4393 51.75 Verbundwerkstoffe Schichtstoffe AR 259 |
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10.1016/j.compstruct.2020.113232 doi (DE-627)ELV005364698 (ELSEVIER)S0263-8223(20)33158-5 DE-627 ger DE-627 rda eng 670 DE-600 51.75 bkl Batra, R.C. verfasserin aut Material tailoring in three-dimensional flexural deformations of functionally graded material beams 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Soft materials such as rubberlike and biological tissues are usually modeled as incompressible. Mechanical properties of polymeric materials can be controlled either by exposing them to ultraviolet light for different time durations or by changing their molecular structure. A challenge is to find the spatial variation of the moduli to fully utilize the material. One way to achieve this is to have a uniform distribution of the stress component likely to cause their failure. To achieve this, we analytically analyze 3-dimensional infinitesimal flexural deformations of a functionally graded (FG) and linearly elastic beam of rectangular cross-section with Young’s modulus a continuous function of the thickness coordinate. The problem is first studied for an incompressible material and then for a compressible material for which Poisson’s ratio is assumed to be a constant. It is found that when Young’s modulus at a point is inversely proportional to its distance from the neutral axis, then the magnitude of the bending stress is uniform over beam’s cross-section, the beam is the lightest possible and its deflections are 2/3rd of that of the corresponding beam of a homogeneous material that has the same maximum bending stress as the FG beam. Noting that Young’s modulus cannot be infinity at the neutral axis, we avoid this by assuming that it is a constant over a small region around the neutral axis. For a transversely isotropic incompressible material beam, it is shown that (2μ1 + μ2) determines beam’s flexural stiffness where μ1 and μ2 are, respectively, the shear moduli along and perpendicular to the axis of transverse isotropy. Beams of homogeneous materials having the same geometry as the FG beam have different shear moduli depending upon whether the FG and the homogeneous material beams have the same maximum deflection, the same maximum bending stress or the same total strain energy of deformation. 3-Dimensional flexural deformations Functionally graded material beam Equivalent homogeneous material beam Enthalten in Composite structures Amsterdam : Elsevier, 1983 259 (DE-627)320509044 (DE-600)2013177-X (DE-576)094531447 0263-8223 nnns volume:259 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 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_4338 GBV_ILN_4393 51.75 Verbundwerkstoffe Schichtstoffe AR 259 |
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Material tailoring in three-dimensional flexural deformations of functionally graded material beams |
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| title_full |
Material tailoring in three-dimensional flexural deformations of functionally graded material beams |
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Batra, R.C. |
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Composite structures |
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Composite structures |
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eng |
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600 - Technology |
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2020 |
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Batra, R.C. |
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Elektronische Aufsätze |
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Batra, R.C. |
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10.1016/j.compstruct.2020.113232 |
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670 |
| title_sort |
material tailoring in three-dimensional flexural deformations of functionally graded material beams |
| title_auth |
Material tailoring in three-dimensional flexural deformations of functionally graded material beams |
| abstract |
Soft materials such as rubberlike and biological tissues are usually modeled as incompressible. Mechanical properties of polymeric materials can be controlled either by exposing them to ultraviolet light for different time durations or by changing their molecular structure. A challenge is to find the spatial variation of the moduli to fully utilize the material. One way to achieve this is to have a uniform distribution of the stress component likely to cause their failure. To achieve this, we analytically analyze 3-dimensional infinitesimal flexural deformations of a functionally graded (FG) and linearly elastic beam of rectangular cross-section with Young’s modulus a continuous function of the thickness coordinate. The problem is first studied for an incompressible material and then for a compressible material for which Poisson’s ratio is assumed to be a constant. It is found that when Young’s modulus at a point is inversely proportional to its distance from the neutral axis, then the magnitude of the bending stress is uniform over beam’s cross-section, the beam is the lightest possible and its deflections are 2/3rd of that of the corresponding beam of a homogeneous material that has the same maximum bending stress as the FG beam. Noting that Young’s modulus cannot be infinity at the neutral axis, we avoid this by assuming that it is a constant over a small region around the neutral axis. For a transversely isotropic incompressible material beam, it is shown that (2μ1 + μ2) determines beam’s flexural stiffness where μ1 and μ2 are, respectively, the shear moduli along and perpendicular to the axis of transverse isotropy. Beams of homogeneous materials having the same geometry as the FG beam have different shear moduli depending upon whether the FG and the homogeneous material beams have the same maximum deflection, the same maximum bending stress or the same total strain energy of deformation. |
| abstractGer |
Soft materials such as rubberlike and biological tissues are usually modeled as incompressible. Mechanical properties of polymeric materials can be controlled either by exposing them to ultraviolet light for different time durations or by changing their molecular structure. A challenge is to find the spatial variation of the moduli to fully utilize the material. One way to achieve this is to have a uniform distribution of the stress component likely to cause their failure. To achieve this, we analytically analyze 3-dimensional infinitesimal flexural deformations of a functionally graded (FG) and linearly elastic beam of rectangular cross-section with Young’s modulus a continuous function of the thickness coordinate. The problem is first studied for an incompressible material and then for a compressible material for which Poisson’s ratio is assumed to be a constant. It is found that when Young’s modulus at a point is inversely proportional to its distance from the neutral axis, then the magnitude of the bending stress is uniform over beam’s cross-section, the beam is the lightest possible and its deflections are 2/3rd of that of the corresponding beam of a homogeneous material that has the same maximum bending stress as the FG beam. Noting that Young’s modulus cannot be infinity at the neutral axis, we avoid this by assuming that it is a constant over a small region around the neutral axis. For a transversely isotropic incompressible material beam, it is shown that (2μ1 + μ2) determines beam’s flexural stiffness where μ1 and μ2 are, respectively, the shear moduli along and perpendicular to the axis of transverse isotropy. Beams of homogeneous materials having the same geometry as the FG beam have different shear moduli depending upon whether the FG and the homogeneous material beams have the same maximum deflection, the same maximum bending stress or the same total strain energy of deformation. |
| abstract_unstemmed |
Soft materials such as rubberlike and biological tissues are usually modeled as incompressible. Mechanical properties of polymeric materials can be controlled either by exposing them to ultraviolet light for different time durations or by changing their molecular structure. A challenge is to find the spatial variation of the moduli to fully utilize the material. One way to achieve this is to have a uniform distribution of the stress component likely to cause their failure. To achieve this, we analytically analyze 3-dimensional infinitesimal flexural deformations of a functionally graded (FG) and linearly elastic beam of rectangular cross-section with Young’s modulus a continuous function of the thickness coordinate. The problem is first studied for an incompressible material and then for a compressible material for which Poisson’s ratio is assumed to be a constant. It is found that when Young’s modulus at a point is inversely proportional to its distance from the neutral axis, then the magnitude of the bending stress is uniform over beam’s cross-section, the beam is the lightest possible and its deflections are 2/3rd of that of the corresponding beam of a homogeneous material that has the same maximum bending stress as the FG beam. Noting that Young’s modulus cannot be infinity at the neutral axis, we avoid this by assuming that it is a constant over a small region around the neutral axis. For a transversely isotropic incompressible material beam, it is shown that (2μ1 + μ2) determines beam’s flexural stiffness where μ1 and μ2 are, respectively, the shear moduli along and perpendicular to the axis of transverse isotropy. Beams of homogeneous materials having the same geometry as the FG beam have different shear moduli depending upon whether the FG and the homogeneous material beams have the same maximum deflection, the same maximum bending stress or the same total strain energy of deformation. |
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| title_short |
Material tailoring in three-dimensional flexural deformations of functionally graded material beams |
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