Closed-form solution of Euler–Bernoulli frames in the frequency domain
This paper presents the frequency domain formulation of the Green’s Functions Stiffness Method (GFSM) for plane Euler–Bernoulli frames subjected to arbitrary external loads (forces and bending moments). The GFSM is a generalization of the Stiffness Method (SM) or the Finite Element Method (FEM) that...
Ausführliche Beschreibung
Autor*in: |
Molina-Villegas, Juan Camilo [verfasserIn] Ballesteros Ortega, Jorge Eliecer [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2023 |
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Schlagwörter: |
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Übergeordnetes Werk: |
Enthalten in: Engineering analysis with boundary elements - Amsterdam [u.a.] : Elsevier Science, 1989, 155, Seite 682-695 |
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Übergeordnetes Werk: |
volume:155 ; pages:682-695 |
DOI / URN: |
10.1016/j.enganabound.2023.06.027 |
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Katalog-ID: |
ELV061739472 |
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520 | |a This paper presents the frequency domain formulation of the Green’s Functions Stiffness Method (GFSM) for plane Euler–Bernoulli frames subjected to arbitrary external loads (forces and bending moments). The GFSM is a generalization of the Stiffness Method (SM) or the Finite Element Method (FEM) that computes the closed-form analytical structural response by decomposing it into a homogeneous and a fixed or particular responses. The homogeneous response is obtained from the displacements at the element ends in the absence of external loads, while the fixed response is calculated using the Green’s functions of fixed elements through a superposition integral that includes the external loads. The GFSM can be categorized as a mesh reduction method that generalizes the Spectral Element Method (SEM), in which the structural response is first obtained in the frequency domain and then converted to the time domain using the Fast Fourier Transform algorithm. Compared to the SEM, the significant advantage of the GFSM is that the frequency domain structural response is exact and avoids the need for dense meshes when external loads have complex patterns. Three examples are presented to demonstrate the effectiveness of the GFSM, each of which shows excellent agreement when compared to the FEM solution even using far fewer elements. | ||
650 | 4 | |a Green’s Functions Stiffness method | |
650 | 4 | |a Green’s functions | |
650 | 4 | |a Finite Element Method | |
650 | 4 | |a Spectral Element Method | |
650 | 4 | |a Dynamics of structures | |
650 | 4 | |a Frequency domain analysis | |
650 | 4 | |a Closed-form solution | |
650 | 4 | |a Mesh reduction method | |
700 | 1 | |a Ballesteros Ortega, Jorge Eliecer |e verfasserin |0 (orcid)0000-0003-0956-0365 |4 aut | |
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10.1016/j.enganabound.2023.06.027 doi (DE-627)ELV061739472 (ELSEVIER)S0955-7997(23)00343-0 DE-627 ger DE-627 rda eng 690 620 VZ 50.03 bkl Molina-Villegas, Juan Camilo verfasserin aut Closed-form solution of Euler–Bernoulli frames in the frequency domain 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper presents the frequency domain formulation of the Green’s Functions Stiffness Method (GFSM) for plane Euler–Bernoulli frames subjected to arbitrary external loads (forces and bending moments). The GFSM is a generalization of the Stiffness Method (SM) or the Finite Element Method (FEM) that computes the closed-form analytical structural response by decomposing it into a homogeneous and a fixed or particular responses. The homogeneous response is obtained from the displacements at the element ends in the absence of external loads, while the fixed response is calculated using the Green’s functions of fixed elements through a superposition integral that includes the external loads. The GFSM can be categorized as a mesh reduction method that generalizes the Spectral Element Method (SEM), in which the structural response is first obtained in the frequency domain and then converted to the time domain using the Fast Fourier Transform algorithm. Compared to the SEM, the significant advantage of the GFSM is that the frequency domain structural response is exact and avoids the need for dense meshes when external loads have complex patterns. Three examples are presented to demonstrate the effectiveness of the GFSM, each of which shows excellent agreement when compared to the FEM solution even using far fewer elements. Green’s Functions Stiffness method Green’s functions Finite Element Method Spectral Element Method Dynamics of structures Frequency domain analysis Closed-form solution Mesh reduction method Ballesteros Ortega, Jorge Eliecer verfasserin (orcid)0000-0003-0956-0365 aut Enthalten in Engineering analysis with boundary elements Amsterdam [u.a.] : Elsevier Science, 1989 155, Seite 682-695 Online-Ressource (DE-627)320515486 (DE-600)2013898-2 (DE-576)259271462 0955-7997 nnns volume:155 pages:682-695 GBV_USEFLAG_U GBV_ELV SYSFLAG_U 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_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_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 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_4338 GBV_ILN_4393 GBV_ILN_4700 50.03 Methoden und Techniken der Ingenieurwissenschaften VZ AR 155 682-695 |
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10.1016/j.enganabound.2023.06.027 doi (DE-627)ELV061739472 (ELSEVIER)S0955-7997(23)00343-0 DE-627 ger DE-627 rda eng 690 620 VZ 50.03 bkl Molina-Villegas, Juan Camilo verfasserin aut Closed-form solution of Euler–Bernoulli frames in the frequency domain 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper presents the frequency domain formulation of the Green’s Functions Stiffness Method (GFSM) for plane Euler–Bernoulli frames subjected to arbitrary external loads (forces and bending moments). The GFSM is a generalization of the Stiffness Method (SM) or the Finite Element Method (FEM) that computes the closed-form analytical structural response by decomposing it into a homogeneous and a fixed or particular responses. The homogeneous response is obtained from the displacements at the element ends in the absence of external loads, while the fixed response is calculated using the Green’s functions of fixed elements through a superposition integral that includes the external loads. The GFSM can be categorized as a mesh reduction method that generalizes the Spectral Element Method (SEM), in which the structural response is first obtained in the frequency domain and then converted to the time domain using the Fast Fourier Transform algorithm. Compared to the SEM, the significant advantage of the GFSM is that the frequency domain structural response is exact and avoids the need for dense meshes when external loads have complex patterns. Three examples are presented to demonstrate the effectiveness of the GFSM, each of which shows excellent agreement when compared to the FEM solution even using far fewer elements. Green’s Functions Stiffness method Green’s functions Finite Element Method Spectral Element Method Dynamics of structures Frequency domain analysis Closed-form solution Mesh reduction method Ballesteros Ortega, Jorge Eliecer verfasserin (orcid)0000-0003-0956-0365 aut Enthalten in Engineering analysis with boundary elements Amsterdam [u.a.] : Elsevier Science, 1989 155, Seite 682-695 Online-Ressource (DE-627)320515486 (DE-600)2013898-2 (DE-576)259271462 0955-7997 nnns volume:155 pages:682-695 GBV_USEFLAG_U GBV_ELV SYSFLAG_U 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_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_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 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_4338 GBV_ILN_4393 GBV_ILN_4700 50.03 Methoden und Techniken der Ingenieurwissenschaften VZ AR 155 682-695 |
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10.1016/j.enganabound.2023.06.027 doi (DE-627)ELV061739472 (ELSEVIER)S0955-7997(23)00343-0 DE-627 ger DE-627 rda eng 690 620 VZ 50.03 bkl Molina-Villegas, Juan Camilo verfasserin aut Closed-form solution of Euler–Bernoulli frames in the frequency domain 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper presents the frequency domain formulation of the Green’s Functions Stiffness Method (GFSM) for plane Euler–Bernoulli frames subjected to arbitrary external loads (forces and bending moments). The GFSM is a generalization of the Stiffness Method (SM) or the Finite Element Method (FEM) that computes the closed-form analytical structural response by decomposing it into a homogeneous and a fixed or particular responses. The homogeneous response is obtained from the displacements at the element ends in the absence of external loads, while the fixed response is calculated using the Green’s functions of fixed elements through a superposition integral that includes the external loads. The GFSM can be categorized as a mesh reduction method that generalizes the Spectral Element Method (SEM), in which the structural response is first obtained in the frequency domain and then converted to the time domain using the Fast Fourier Transform algorithm. Compared to the SEM, the significant advantage of the GFSM is that the frequency domain structural response is exact and avoids the need for dense meshes when external loads have complex patterns. Three examples are presented to demonstrate the effectiveness of the GFSM, each of which shows excellent agreement when compared to the FEM solution even using far fewer elements. Green’s Functions Stiffness method Green’s functions Finite Element Method Spectral Element Method Dynamics of structures Frequency domain analysis Closed-form solution Mesh reduction method Ballesteros Ortega, Jorge Eliecer verfasserin (orcid)0000-0003-0956-0365 aut Enthalten in Engineering analysis with boundary elements Amsterdam [u.a.] : Elsevier Science, 1989 155, Seite 682-695 Online-Ressource (DE-627)320515486 (DE-600)2013898-2 (DE-576)259271462 0955-7997 nnns volume:155 pages:682-695 GBV_USEFLAG_U GBV_ELV SYSFLAG_U 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_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_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 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_4338 GBV_ILN_4393 GBV_ILN_4700 50.03 Methoden und Techniken der Ingenieurwissenschaften VZ AR 155 682-695 |
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10.1016/j.enganabound.2023.06.027 doi (DE-627)ELV061739472 (ELSEVIER)S0955-7997(23)00343-0 DE-627 ger DE-627 rda eng 690 620 VZ 50.03 bkl Molina-Villegas, Juan Camilo verfasserin aut Closed-form solution of Euler–Bernoulli frames in the frequency domain 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper presents the frequency domain formulation of the Green’s Functions Stiffness Method (GFSM) for plane Euler–Bernoulli frames subjected to arbitrary external loads (forces and bending moments). The GFSM is a generalization of the Stiffness Method (SM) or the Finite Element Method (FEM) that computes the closed-form analytical structural response by decomposing it into a homogeneous and a fixed or particular responses. The homogeneous response is obtained from the displacements at the element ends in the absence of external loads, while the fixed response is calculated using the Green’s functions of fixed elements through a superposition integral that includes the external loads. The GFSM can be categorized as a mesh reduction method that generalizes the Spectral Element Method (SEM), in which the structural response is first obtained in the frequency domain and then converted to the time domain using the Fast Fourier Transform algorithm. Compared to the SEM, the significant advantage of the GFSM is that the frequency domain structural response is exact and avoids the need for dense meshes when external loads have complex patterns. Three examples are presented to demonstrate the effectiveness of the GFSM, each of which shows excellent agreement when compared to the FEM solution even using far fewer elements. Green’s Functions Stiffness method Green’s functions Finite Element Method Spectral Element Method Dynamics of structures Frequency domain analysis Closed-form solution Mesh reduction method Ballesteros Ortega, Jorge Eliecer verfasserin (orcid)0000-0003-0956-0365 aut Enthalten in Engineering analysis with boundary elements Amsterdam [u.a.] : Elsevier Science, 1989 155, Seite 682-695 Online-Ressource (DE-627)320515486 (DE-600)2013898-2 (DE-576)259271462 0955-7997 nnns volume:155 pages:682-695 GBV_USEFLAG_U GBV_ELV SYSFLAG_U 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_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_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 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_4338 GBV_ILN_4393 GBV_ILN_4700 50.03 Methoden und Techniken der Ingenieurwissenschaften VZ AR 155 682-695 |
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10.1016/j.enganabound.2023.06.027 doi (DE-627)ELV061739472 (ELSEVIER)S0955-7997(23)00343-0 DE-627 ger DE-627 rda eng 690 620 VZ 50.03 bkl Molina-Villegas, Juan Camilo verfasserin aut Closed-form solution of Euler–Bernoulli frames in the frequency domain 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper presents the frequency domain formulation of the Green’s Functions Stiffness Method (GFSM) for plane Euler–Bernoulli frames subjected to arbitrary external loads (forces and bending moments). The GFSM is a generalization of the Stiffness Method (SM) or the Finite Element Method (FEM) that computes the closed-form analytical structural response by decomposing it into a homogeneous and a fixed or particular responses. The homogeneous response is obtained from the displacements at the element ends in the absence of external loads, while the fixed response is calculated using the Green’s functions of fixed elements through a superposition integral that includes the external loads. The GFSM can be categorized as a mesh reduction method that generalizes the Spectral Element Method (SEM), in which the structural response is first obtained in the frequency domain and then converted to the time domain using the Fast Fourier Transform algorithm. Compared to the SEM, the significant advantage of the GFSM is that the frequency domain structural response is exact and avoids the need for dense meshes when external loads have complex patterns. Three examples are presented to demonstrate the effectiveness of the GFSM, each of which shows excellent agreement when compared to the FEM solution even using far fewer elements. Green’s Functions Stiffness method Green’s functions Finite Element Method Spectral Element Method Dynamics of structures Frequency domain analysis Closed-form solution Mesh reduction method Ballesteros Ortega, Jorge Eliecer verfasserin (orcid)0000-0003-0956-0365 aut Enthalten in Engineering analysis with boundary elements Amsterdam [u.a.] : Elsevier Science, 1989 155, Seite 682-695 Online-Ressource (DE-627)320515486 (DE-600)2013898-2 (DE-576)259271462 0955-7997 nnns volume:155 pages:682-695 GBV_USEFLAG_U GBV_ELV SYSFLAG_U 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_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_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 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_4338 GBV_ILN_4393 GBV_ILN_4700 50.03 Methoden und Techniken der Ingenieurwissenschaften VZ AR 155 682-695 |
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690 620 VZ 50.03 bkl Closed-form solution of Euler–Bernoulli frames in the frequency domain Green’s Functions Stiffness method Green’s functions Finite Element Method Spectral Element Method Dynamics of structures Frequency domain analysis Closed-form solution Mesh reduction method |
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Closed-form solution of Euler–Bernoulli frames in the frequency domain |
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Closed-form solution of Euler–Bernoulli frames in the frequency domain |
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Molina-Villegas, Juan Camilo |
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Molina-Villegas, Juan Camilo Ballesteros Ortega, Jorge Eliecer |
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closed-form solution of euler–bernoulli frames in the frequency domain |
title_auth |
Closed-form solution of Euler–Bernoulli frames in the frequency domain |
abstract |
This paper presents the frequency domain formulation of the Green’s Functions Stiffness Method (GFSM) for plane Euler–Bernoulli frames subjected to arbitrary external loads (forces and bending moments). The GFSM is a generalization of the Stiffness Method (SM) or the Finite Element Method (FEM) that computes the closed-form analytical structural response by decomposing it into a homogeneous and a fixed or particular responses. The homogeneous response is obtained from the displacements at the element ends in the absence of external loads, while the fixed response is calculated using the Green’s functions of fixed elements through a superposition integral that includes the external loads. The GFSM can be categorized as a mesh reduction method that generalizes the Spectral Element Method (SEM), in which the structural response is first obtained in the frequency domain and then converted to the time domain using the Fast Fourier Transform algorithm. Compared to the SEM, the significant advantage of the GFSM is that the frequency domain structural response is exact and avoids the need for dense meshes when external loads have complex patterns. Three examples are presented to demonstrate the effectiveness of the GFSM, each of which shows excellent agreement when compared to the FEM solution even using far fewer elements. |
abstractGer |
This paper presents the frequency domain formulation of the Green’s Functions Stiffness Method (GFSM) for plane Euler–Bernoulli frames subjected to arbitrary external loads (forces and bending moments). The GFSM is a generalization of the Stiffness Method (SM) or the Finite Element Method (FEM) that computes the closed-form analytical structural response by decomposing it into a homogeneous and a fixed or particular responses. The homogeneous response is obtained from the displacements at the element ends in the absence of external loads, while the fixed response is calculated using the Green’s functions of fixed elements through a superposition integral that includes the external loads. The GFSM can be categorized as a mesh reduction method that generalizes the Spectral Element Method (SEM), in which the structural response is first obtained in the frequency domain and then converted to the time domain using the Fast Fourier Transform algorithm. Compared to the SEM, the significant advantage of the GFSM is that the frequency domain structural response is exact and avoids the need for dense meshes when external loads have complex patterns. Three examples are presented to demonstrate the effectiveness of the GFSM, each of which shows excellent agreement when compared to the FEM solution even using far fewer elements. |
abstract_unstemmed |
This paper presents the frequency domain formulation of the Green’s Functions Stiffness Method (GFSM) for plane Euler–Bernoulli frames subjected to arbitrary external loads (forces and bending moments). The GFSM is a generalization of the Stiffness Method (SM) or the Finite Element Method (FEM) that computes the closed-form analytical structural response by decomposing it into a homogeneous and a fixed or particular responses. The homogeneous response is obtained from the displacements at the element ends in the absence of external loads, while the fixed response is calculated using the Green’s functions of fixed elements through a superposition integral that includes the external loads. The GFSM can be categorized as a mesh reduction method that generalizes the Spectral Element Method (SEM), in which the structural response is first obtained in the frequency domain and then converted to the time domain using the Fast Fourier Transform algorithm. Compared to the SEM, the significant advantage of the GFSM is that the frequency domain structural response is exact and avoids the need for dense meshes when external loads have complex patterns. Three examples are presented to demonstrate the effectiveness of the GFSM, each of which shows excellent agreement when compared to the FEM solution even using far fewer elements. |
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Closed-form solution of Euler–Bernoulli frames in the frequency domain |
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