Analytical formulation of the stiffness method for 2d reticular structures using green functions
Green functions (F.G.) are defined as the response of a medium to a unit point load and are widely used to solve boundary value problems. Unfortunately, in structural analysis, its use is limited and they are only used indirectly and with another name in the calculation of influence lines and in the...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad de Medellín
- Repositorio:
- Repositorio UDEM
- Idioma:
- spa
- OAI Identifier:
- oai:repository.udem.edu.co:11407/5918
- Acceso en línea:
- http://hdl.handle.net/11407/5918
- Palabra clave:
- Finite element method
Green functions
Mixed finite elements
Stiffness method
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- License
- http://purl.org/coar/access_right/c_16ec
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Analytical formulation of the stiffness method for 2d reticular structures using green functions |
| title |
Analytical formulation of the stiffness method for 2d reticular structures using green functions |
| spellingShingle |
Analytical formulation of the stiffness method for 2d reticular structures using green functions Finite element method Green functions Mixed finite elements Stiffness method |
| title_short |
Analytical formulation of the stiffness method for 2d reticular structures using green functions |
| title_full |
Analytical formulation of the stiffness method for 2d reticular structures using green functions |
| title_fullStr |
Analytical formulation of the stiffness method for 2d reticular structures using green functions |
| title_full_unstemmed |
Analytical formulation of the stiffness method for 2d reticular structures using green functions |
| title_sort |
Analytical formulation of the stiffness method for 2d reticular structures using green functions |
| dc.subject.spa.fl_str_mv |
Finite element method Green functions Mixed finite elements Stiffness method |
| topic |
Finite element method Green functions Mixed finite elements Stiffness method |
| description |
Green functions (F.G.) are defined as the response of a medium to a unit point load and are widely used to solve boundary value problems. Unfortunately, in structural analysis, its use is limited and they are only used indirectly and with another name in the calculation of influence lines and in the formulation of the virtual work method. This article presents the Green functions stiffness method, which is a novel methodology to obtain the analytical or exact response of two dimensional frames, which mixes the stiffnes method and the Green functions, the latter used for the calculation of displacement fields. In particular, the formulation will be carried out for bar elements (subjected to axial force), beam elements (subjected to shear force and bending moment), beam over flexible foundation elements (subjected to shear force and bending moment) and two dimensional frames (subjected to axial force, cutting force and bending moment). This formulation has as its main property that it can be used to compute the analytic reponse for any external load distribution and minimizes the number of elements to be used in discretizations. In addition, the equivalence of this formulation with that obtained by an “exact” implementation of the finite element method is presented. © 2020, Scipedia S.L. All rights reserved. |
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2020 |
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2021-02-05T14:57:54Z |
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2021-02-05T14:57:54Z |
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2020 |
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Article |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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2131315 |
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http://hdl.handle.net/11407/5918 |
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10.23967/J.RIMNI.2020.09.004 |
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2131315 10.23967/J.RIMNI.2020.09.004 |
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http://hdl.handle.net/11407/5918 |
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spa |
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spa |
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https://www.scopus.com/inward/record.uri?eid=2-s2.0-85092524795&doi=10.23967%2fJ.RIMNI.2020.09.004&partnerID=40&md5=fce7c5d0549e50f1528aaaac2f4d3cf5 |
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36 |
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3 |
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1 |
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52 |
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Challis, Lawrie, Sheard, Fred, The green of Green functions (2003) Physics Today, 56 (12), pp. 41-46 Duffy, Dean G., (2015) Green’s functions with applications, , Chapman and Hall/CRC Banerjee, PK, Butterfield, R., (1981) Boundary Element Methods in Engineering Science, , McGraw-Hill, New York Sánchez-Sesma, F. J., Ramos-Martínez, J., Campillo, M., An indirect boundary element method applied to simulate the seismic response of alluvial valleys for incident P, S and Rayleigh waves (1993) Earthquake engineering & structural dynamics, 22 (4), pp. 279-295 Fairweather, G., Karageorghis, A., Martin, P.A., The method of fundamental solutions for scattering and radiation problems (2003) Engineering Analysis with Boundary Elements, 27 (7), pp. 759-769 Thomson, William T., Transmission of elastic waves through a stratified solid medium (1950) Journal of applied Physics, 21 (2), pp. 89-93 Boussinesq, Joseph, (1885) Application des potentiels a l'étude de l'équilibre et du mouvement des solides élastiques, , Gauthier-Villars Cerruti, Valentino, Ricerche intorno all'equilibrio de'corpi elastici isotropi: memoria (1882), Coi tipi del Salviucci Mindlin, R.D., Force at a Point in the Interior of a Semi-Infinite Solid (1936) Physics, 7 (5), pp. 195-202 Stokes, George Gebriel, On dynamical theory of diffraction (1849) Transactions of the Cambridge Philosophical Society, 9, pp. 1-48 Lamb, H., On the propagation of tremors over the surface of an elastic solid (1904) Philosophical Transactions of the Royal Society of London, 203, pp. 1-42 Chao, C.C., Dynamical response of an elastic half-space to tangential surface loadings (1960) Journal of Applied Mechanics, 27, p. 559 Kausel, E., (2006) Fundamental solutions in elastodynamics: a compendium, , Cambridge University Press Aki, K., Richards, P.G., (2002) Quantitative seismology, , Univ Science Books Colunga, Arturo Tena, (2007) Análisis de estructuras con métodos matriciales, , Limusa McCormac, Jack C., (2007) Structural Analysis: using classical and matrix methods, , Wiley Hoboken, NJ Kassimali, Aslam, (2012) Matrix analysis of structures SI version, , Cengage Learning Reddy, J.N., (2006) An introduction to the finite element method, , McGrawHill Bathe, K.J., (2006) Finite element procedures, , McGrawHill Hetényi, Miklós, (1971) Beams on elastic foundation: theory with applications in the fields of civil and mechanical engineering, , University of Michigan Eisemberger, M., Yankelevsky, D.Z., Exact stiffness matrix for beams on elastic foundation (1985) Computer & Structures, 21 (6), pp. 1355-1359 |
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Scipedia S.L. |
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Ingeniería Civil |
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Facultad de Ingenierías |
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Scipedia S.L. |
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Revista Internacional de Metodos Numericos para Calculo y Diseno en Ingenieria |
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Universidad de Medellín |
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Repositorio Institucional Universidad de Medellin |
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repositorio@udem.edu.co |
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1814159210477256704 |
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20202021-02-05T14:57:54Z2021-02-05T14:57:54Z2131315http://hdl.handle.net/11407/591810.23967/J.RIMNI.2020.09.004Green functions (F.G.) are defined as the response of a medium to a unit point load and are widely used to solve boundary value problems. Unfortunately, in structural analysis, its use is limited and they are only used indirectly and with another name in the calculation of influence lines and in the formulation of the virtual work method. This article presents the Green functions stiffness method, which is a novel methodology to obtain the analytical or exact response of two dimensional frames, which mixes the stiffnes method and the Green functions, the latter used for the calculation of displacement fields. In particular, the formulation will be carried out for bar elements (subjected to axial force), beam elements (subjected to shear force and bending moment), beam over flexible foundation elements (subjected to shear force and bending moment) and two dimensional frames (subjected to axial force, cutting force and bending moment). This formulation has as its main property that it can be used to compute the analytic reponse for any external load distribution and minimizes the number of elements to be used in discretizations. In addition, the equivalence of this formulation with that obtained by an “exact” implementation of the finite element method is presented. © 2020, Scipedia S.L. All rights reserved.spaScipedia S.L.Ingeniería CivilFacultad de Ingenieríashttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85092524795&doi=10.23967%2fJ.RIMNI.2020.09.004&partnerID=40&md5=fce7c5d0549e50f1528aaaac2f4d3cf5363152Challis, Lawrie, Sheard, Fred, The green of Green functions (2003) Physics Today, 56 (12), pp. 41-46Duffy, Dean G., (2015) Green’s functions with applications, , Chapman and Hall/CRCBanerjee, PK, Butterfield, R., (1981) Boundary Element Methods in Engineering Science, , McGraw-Hill, New YorkSánchez-Sesma, F. J., Ramos-Martínez, J., Campillo, M., An indirect boundary element method applied to simulate the seismic response of alluvial valleys for incident P, S and Rayleigh waves (1993) Earthquake engineering & structural dynamics, 22 (4), pp. 279-295Fairweather, G., Karageorghis, A., Martin, P.A., The method of fundamental solutions for scattering and radiation problems (2003) Engineering Analysis with Boundary Elements, 27 (7), pp. 759-769Thomson, William T., Transmission of elastic waves through a stratified solid medium (1950) Journal of applied Physics, 21 (2), pp. 89-93Boussinesq, Joseph, (1885) Application des potentiels a l'étude de l'équilibre et du mouvement des solides élastiques, , Gauthier-VillarsCerruti, Valentino, Ricerche intorno all'equilibrio de'corpi elastici isotropi: memoria (1882), Coi tipi del SalviucciMindlin, R.D., Force at a Point in the Interior of a Semi-Infinite Solid (1936) Physics, 7 (5), pp. 195-202Stokes, George Gebriel, On dynamical theory of diffraction (1849) Transactions of the Cambridge Philosophical Society, 9, pp. 1-48Lamb, H., On the propagation of tremors over the surface of an elastic solid (1904) Philosophical Transactions of the Royal Society of London, 203, pp. 1-42Chao, C.C., Dynamical response of an elastic half-space to tangential surface loadings (1960) Journal of Applied Mechanics, 27, p. 559Kausel, E., (2006) Fundamental solutions in elastodynamics: a compendium, , Cambridge University PressAki, K., Richards, P.G., (2002) Quantitative seismology, , Univ Science BooksColunga, Arturo Tena, (2007) Análisis de estructuras con métodos matriciales, , LimusaMcCormac, Jack C., (2007) Structural Analysis: using classical and matrix methods, , Wiley Hoboken, NJKassimali, Aslam, (2012) Matrix analysis of structures SI version, , Cengage LearningReddy, J.N., (2006) An introduction to the finite element method, , McGrawHillBathe, K.J., (2006) Finite element procedures, , McGrawHillHetényi, Miklós, (1971) Beams on elastic foundation: theory with applications in the fields of civil and mechanical engineering, , University of MichiganEisemberger, M., Yankelevsky, D.Z., Exact stiffness matrix for beams on elastic foundation (1985) Computer & Structures, 21 (6), pp. 1355-1359Revista Internacional de Metodos Numericos para Calculo y Diseno en IngenieriaFinite element methodGreen functionsMixed finite elementsStiffness methodAnalytical formulation of the stiffness method for 2d reticular structures using green functionsArticleinfo:eu-repo/semantics/articlehttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Molina-Villegas, J.C., Universidad de Medellín, Universidad Nacional de Colombia, ColombiaGiraldo, H.N.D., Departamento de Ingeniería Civil, Universidad Nacional de Colombia, Facultad de Minas, ColombiaOchoa, A.F.A., Departamento de Ingeniería Civil, Universidad Nacional de Colombia, Facultad de Minas, Colombiahttp://purl.org/coar/access_right/c_16ecMolina-Villegas J.C.Giraldo H.N.D.Ochoa A.F.A.11407/5918oai:repository.udem.edu.co:11407/59182021-02-05 09:57:54.361Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co |