Derechos de autor 2021 Investigación e Innovación en Ingenierías
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Análisis No-lineal de estructuras compuestas por cables
Corresponding Author(s) : Daniel Ricardo Salinas Guayacundo
daniel.salinas@uniminuto.edu.co
Investigación e Innovación en Ingenierías,
Vol. 9 Núm. 2 (2021): Julio - Diciembre
Resumen
Objetivo: Desarrollar una metodología basada en una versión ajustada del Método de Densidad de Fuerza (MDF) para realizar el análisis no-lineal de estructuras tridimensionales conformadas por cables sometidas a cargas estáticas implementada en MathCAD que no presente problemas en la obtención de la solución numérica y que provea una forma eficiente y estable de convergencia numérica. Metodología: Lo primero es presentar un marco teórico asociado a las estructuras conformadas por cables y al método de analysis basado en el MDF. Seguidamente, las rutinas o funciones en MathCAD son creadas para realizar el análisis no-lineal de estructuras compuestas por cables. Finalmente, los resultados entregados por las rutinas son validados a través de la comparación de los mismos con los resultados presentados en el artículo de investigación tomado como referencia y los resultados provistos por un software de estructuras conformadas por cables. Resultados: Se demostró que las rutinas creadas proveen resultados adecuados y confiables del análisis estructural no-lineal de estructuras compuestas por cables sometidos a cargas estáticas verticales y horizontales. Conclusiones: Las rutinas desarrolladas en MathCAD proveen resultados consistentes en función a lo encontrado con los resultados obtenidos y los hallados en el artículo tomado como referencia y a los provistos por el programa utilizado. En los ejemplos analizados en este artículo de investigación, no se encontraron problemas numéricos que pudieran generar inestabilidad. Las rutinas proveen una forma sencilla de visualizar las consideraciones, procedimiento y resultados importantes obtenidos en el proceso de realizar análisis que involucre no-linealidad geométrica de estructuras compuestas por cables.
Palabras clave
Mathcad, sistema de cables, método de densidad de fuerza
[1]
D. R. Salinas Guayacundo y E. A. Marmolejo Otero, «Análisis No-lineal de estructuras compuestas por cables», Investigación e Innovación en Ingenierías, vol. 9, n.º 2, pp. 142–156, sep. 2021.
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Referencias
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[1] M. Crusells-Girona, F.C. Filippou, and R.L. Taylor, “A mixed formulation for nonlinear analysis of cable structures”, Computers and Structures, 18650-61, 2017. https://doi.org/10.1016/j.compstruc.2017.03.011
[2] X. Feng, S. Guo, “Geometrical nonlinear elasto-plastic analysis of tensegrity systems via the co-rotational method”, Mech Res Commun, Vol., 79, pp. 32-42, 2017. https://doi.org/10.1016/j.mechrescom.2016.12.003
[3] R. Liu, H. Guo, R. Liu, D. Tang, H. Wang, and Z. Deng, “Design and form finding of cable net for a large cable–rib tension antenna with flexible deployable structures”, Eng Struct, 199, p. 109662, 2019 https://doi.org/10.1016/j.engstruct.2019.109662
[4] X. Feng, “The optimal initial self-stress design for tensegrity grid structures”, Comput. Struct, Vol., 193, No. 21–30, 2017. https://doi.org/10.1016/j.compstruc.2017.07.029
[5] M.A. Fernández-Ruiz, E. Hernández-Montes, J.F. Carbonell-Márquez, and L.M. Gil-Martín, “Octahedron family: the double-expanded octahedron tensegrity”, Int. J. Solids Struct., 165 (15), pp. 1-13, 2019. https://doi.org/10.1016/j.ijsolstr.2019.01.017
[6] K, Linkwitz, and H. J. Schek, “Einige Bemerkungen zur Berechnung vorgespannten Seilnetzkonstruktionen”, Ingenieur Archiv, Vol. 40, pp. 145-158. 1971.
[7] H.J. Schek, “The force density method for form finding and computation of general network”, Computer Methods in Applied Mechanics and Engineering, Vol., 3, pp. 115-134, 1974 https://doi.org/10.1016/0045-7825(74)90045-0
[8] Y, Dementiev, L. Burulko, and E. Suvorkova, “Pedagogical aspects of applied software packages and computer technologies use in student’s education”, Social and Behavioral Sciences, 206(1), pp. 289-294, 2015. https://doi.org/10.1016/j.sbspro.2015.10.050
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[10] A.A. Cuadri, J.E. Martín-Alfonso, and J. Urbano, “A teaching methodology based on Mathcad for improving the calculation of pumping power”, Education for Chemical Engineers, Vol., 28, Pages 68-78, ISSN 1749-7728, 2019 https://doi.org/10.1016/j.ece.2018.11.007
[11] J.Y. Zhang, and M. Ohsaki, “Adaptive force density method for form-finding problem of tensegrity structures”, International Journal of Solids and Structures (43), pp. 5658-5673, 2006. https://doi.org/10.1016/j.ijsolstr.2005.10.011
[12] S. Lee, J. Lee, “A novel method for topology design of tensegrity structures”, Compos. Struct., Vol., 152, pp. 11-19, 2016 https://doi.org/10.1016/j.compstruct.2016.05.009
[13] S. Lee, B.S. Gan, and J. Lee, “A fully automatic group selection for form-finding process of truncated tetrahedral tensegrity structures via a double-loop genetic algorithm”, Compos. Part B, 106, pp. 308 315, 2016, https://doi.org/10.1016/j.compositesb.2016.09.018
[14] D.T.T. Do, S. Lee, and J. Lee, “A modified differential evolution algorithm for tensegrity structures”, Compos. Struct., Vol., 158, pp. 11-19, 2016. https://doi.org/10.1016/j.compstruct.2016.08.039
[15] S. Yuan, and B. Yang, “The fixed nodal position method for form finding of high-precision lightweight truss structures”, Int J Solids Struct, 161, pp. 82-95, 2019. https://doi.org/10.1016/j.ijsolstr.2018.11.011
[16] Y.Q. Tang, and T.J. Li, “Equivalent-force density method as a shape-finding tool for cable-membrane structures”, Eng Struct, Vol., 151, pp. 11-19, 2017. https://doi.org/10.1016/j.engstruct.2017.08.010
[17] M. Bruggi, “A constrained force density method for the funicular analysis and design of arches, domes and vaults”, Int J Solids Struct, 193-194, pp. 251-269, 2020. https://doi.org/10.1016/j.ijsolstr.2020.02.030
[18] C. Cercadillo-García, and J.L. Fernández-Cabo, “Analytical and numerical funicular analysis by means of the parametric force density method”, J. Appl. Res. Technol., 14 (2), pp. 108-124, 2016. https://doi.org/10.1016/j.jart.2016.03.001
[19] A. Liew, D. Pagonakis, T.V. Mele, and P. Block, “Load-path optimisation of funicular networks”, Meccanica, Vol., 53 (1-2), pp. 279-294, 2018. http://dx.doi.org/10.1007/s11012-017-0714-1
[20] S. Belov, M. Pavlov, V. Ponomarev, S. Ponomarev, and A. Zhukov, “Calculation method for cable-beam shell structures”. AIP Conference Proceedings, 1772, 060006, 2016. https://doi.org/10.1063/1.4964586
[21] S. Hansen, “Extended Active Learning as a Means to Learn Syntax in Programming Languages”, Proceedings of the 2008 Annual ASEE Conference, Pittsburgh, PA, 2008. https://doi.org/10.18260/1-2--4280
[22] F. Charney, “A Transformational Approach to Teaching Matrix Structural Analysis, and Visual Implementation using Mathcad”, Proceedings of the 18th Analysis and Computation Specialty Conference at Structures Congress, ASCE, April 24-26, Vancouver, British Columbia, Canada, 2008. https://doi.org/10.1061/41000(315)9
[23] C.H. Thornton, and C. Birnstiel, “Three-dimensional suspension structures”. J. Structural Div. ASCE, pp 247-270, 1967.
[24] G.R. Monforton, and N.M, El-Hakim, “Analysis of truss-cable structures”, Comput. Struct., 11: 327-335, 1980. https://doi.org/10.1016/0045-7949(80)90082-6
[25] F. Charney, Nonlinear Analysis, pp. 78-118, Blacksburg, Virginia, 1996.
[26] A. Nuhoglu, “Nonlinear analysis of cable systems with point based iterative procedure”, Scientific Research and Essays, Vol. 6(6), 2010. https://doi.org/10.5897/SRE10.384
[27] K.G. Park, and D.W. Lee, “Mechanical Characteristics of Cable Truss Roof Systems”, Journal of Korean Association for Spatial Structures, Vol., 6; pp.89-96, 2016. http://dx.doi.org/10.9712/KASS.2016.16.3.047
[28] F. Charney, “CABNET, Cable net structures software”, Blacksburg, Virginia, 1996.
Referencias
[1] M. Crusells-Girona, F.C. Filippou, and R.L. Taylor, “A mixed formulation for nonlinear analysis of cable structures”, Computers and Structures, 18650-61, 2017. https://doi.org/10.1016/j.compstruc.2017.03.011
[2] X. Feng, S. Guo, “Geometrical nonlinear elasto-plastic analysis of tensegrity systems via the co-rotational method”, Mech Res Commun, Vol., 79, pp. 32-42, 2017. https://doi.org/10.1016/j.mechrescom.2016.12.003
[3] R. Liu, H. Guo, R. Liu, D. Tang, H. Wang, and Z. Deng, “Design and form finding of cable net for a large cable–rib tension antenna with flexible deployable structures”, Eng Struct, 199, p. 109662, 2019 https://doi.org/10.1016/j.engstruct.2019.109662
[4] X. Feng, “The optimal initial self-stress design for tensegrity grid structures”, Comput. Struct, Vol., 193, No. 21–30, 2017. https://doi.org/10.1016/j.compstruc.2017.07.029
[5] M.A. Fernández-Ruiz, E. Hernández-Montes, J.F. Carbonell-Márquez, and L.M. Gil-Martín, “Octahedron family: the double-expanded octahedron tensegrity”, Int. J. Solids Struct., 165 (15), pp. 1-13, 2019. https://doi.org/10.1016/j.ijsolstr.2019.01.017
[6] K, Linkwitz, and H. J. Schek, “Einige Bemerkungen zur Berechnung vorgespannten Seilnetzkonstruktionen”, Ingenieur Archiv, Vol. 40, pp. 145-158. 1971.
[7] H.J. Schek, “The force density method for form finding and computation of general network”, Computer Methods in Applied Mechanics and Engineering, Vol., 3, pp. 115-134, 1974 https://doi.org/10.1016/0045-7825(74)90045-0
[8] Y, Dementiev, L. Burulko, and E. Suvorkova, “Pedagogical aspects of applied software packages and computer technologies use in student’s education”, Social and Behavioral Sciences, 206(1), pp. 289-294, 2015. https://doi.org/10.1016/j.sbspro.2015.10.050
[9] R. R. Bradshaw, “History of the Analysis of Cable Net Structures”, Structures Congress 2005, April 20-24, New York, New York, United States, 2005. https://doi.org/10.1061/40753(171)70
[10] A.A. Cuadri, J.E. Martín-Alfonso, and J. Urbano, “A teaching methodology based on Mathcad for improving the calculation of pumping power”, Education for Chemical Engineers, Vol., 28, Pages 68-78, ISSN 1749-7728, 2019 https://doi.org/10.1016/j.ece.2018.11.007
[11] J.Y. Zhang, and M. Ohsaki, “Adaptive force density method for form-finding problem of tensegrity structures”, International Journal of Solids and Structures (43), pp. 5658-5673, 2006. https://doi.org/10.1016/j.ijsolstr.2005.10.011
[12] S. Lee, J. Lee, “A novel method for topology design of tensegrity structures”, Compos. Struct., Vol., 152, pp. 11-19, 2016 https://doi.org/10.1016/j.compstruct.2016.05.009
[13] S. Lee, B.S. Gan, and J. Lee, “A fully automatic group selection for form-finding process of truncated tetrahedral tensegrity structures via a double-loop genetic algorithm”, Compos. Part B, 106, pp. 308 315, 2016, https://doi.org/10.1016/j.compositesb.2016.09.018
[14] D.T.T. Do, S. Lee, and J. Lee, “A modified differential evolution algorithm for tensegrity structures”, Compos. Struct., Vol., 158, pp. 11-19, 2016. https://doi.org/10.1016/j.compstruct.2016.08.039
[15] S. Yuan, and B. Yang, “The fixed nodal position method for form finding of high-precision lightweight truss structures”, Int J Solids Struct, 161, pp. 82-95, 2019. https://doi.org/10.1016/j.ijsolstr.2018.11.011
[16] Y.Q. Tang, and T.J. Li, “Equivalent-force density method as a shape-finding tool for cable-membrane structures”, Eng Struct, Vol., 151, pp. 11-19, 2017. https://doi.org/10.1016/j.engstruct.2017.08.010
[17] M. Bruggi, “A constrained force density method for the funicular analysis and design of arches, domes and vaults”, Int J Solids Struct, 193-194, pp. 251-269, 2020. https://doi.org/10.1016/j.ijsolstr.2020.02.030
[18] C. Cercadillo-García, and J.L. Fernández-Cabo, “Analytical and numerical funicular analysis by means of the parametric force density method”, J. Appl. Res. Technol., 14 (2), pp. 108-124, 2016. https://doi.org/10.1016/j.jart.2016.03.001
[19] A. Liew, D. Pagonakis, T.V. Mele, and P. Block, “Load-path optimisation of funicular networks”, Meccanica, Vol., 53 (1-2), pp. 279-294, 2018. http://dx.doi.org/10.1007/s11012-017-0714-1
[20] S. Belov, M. Pavlov, V. Ponomarev, S. Ponomarev, and A. Zhukov, “Calculation method for cable-beam shell structures”. AIP Conference Proceedings, 1772, 060006, 2016. https://doi.org/10.1063/1.4964586
[21] S. Hansen, “Extended Active Learning as a Means to Learn Syntax in Programming Languages”, Proceedings of the 2008 Annual ASEE Conference, Pittsburgh, PA, 2008. https://doi.org/10.18260/1-2--4280
[22] F. Charney, “A Transformational Approach to Teaching Matrix Structural Analysis, and Visual Implementation using Mathcad”, Proceedings of the 18th Analysis and Computation Specialty Conference at Structures Congress, ASCE, April 24-26, Vancouver, British Columbia, Canada, 2008. https://doi.org/10.1061/41000(315)9
[23] C.H. Thornton, and C. Birnstiel, “Three-dimensional suspension structures”. J. Structural Div. ASCE, pp 247-270, 1967.
[24] G.R. Monforton, and N.M, El-Hakim, “Analysis of truss-cable structures”, Comput. Struct., 11: 327-335, 1980. https://doi.org/10.1016/0045-7949(80)90082-6
[25] F. Charney, Nonlinear Analysis, pp. 78-118, Blacksburg, Virginia, 1996.
[26] A. Nuhoglu, “Nonlinear analysis of cable systems with point based iterative procedure”, Scientific Research and Essays, Vol. 6(6), 2010. https://doi.org/10.5897/SRE10.384
[27] K.G. Park, and D.W. Lee, “Mechanical Characteristics of Cable Truss Roof Systems”, Journal of Korean Association for Spatial Structures, Vol., 6; pp.89-96, 2016. http://dx.doi.org/10.9712/KASS.2016.16.3.047
[28] F. Charney, “CABNET, Cable net structures software”, Blacksburg, Virginia, 1996.
[2] X. Feng, S. Guo, “Geometrical nonlinear elasto-plastic analysis of tensegrity systems via the co-rotational method”, Mech Res Commun, Vol., 79, pp. 32-42, 2017. https://doi.org/10.1016/j.mechrescom.2016.12.003
[3] R. Liu, H. Guo, R. Liu, D. Tang, H. Wang, and Z. Deng, “Design and form finding of cable net for a large cable–rib tension antenna with flexible deployable structures”, Eng Struct, 199, p. 109662, 2019 https://doi.org/10.1016/j.engstruct.2019.109662
[4] X. Feng, “The optimal initial self-stress design for tensegrity grid structures”, Comput. Struct, Vol., 193, No. 21–30, 2017. https://doi.org/10.1016/j.compstruc.2017.07.029
[5] M.A. Fernández-Ruiz, E. Hernández-Montes, J.F. Carbonell-Márquez, and L.M. Gil-Martín, “Octahedron family: the double-expanded octahedron tensegrity”, Int. J. Solids Struct., 165 (15), pp. 1-13, 2019. https://doi.org/10.1016/j.ijsolstr.2019.01.017
[6] K, Linkwitz, and H. J. Schek, “Einige Bemerkungen zur Berechnung vorgespannten Seilnetzkonstruktionen”, Ingenieur Archiv, Vol. 40, pp. 145-158. 1971.
[7] H.J. Schek, “The force density method for form finding and computation of general network”, Computer Methods in Applied Mechanics and Engineering, Vol., 3, pp. 115-134, 1974 https://doi.org/10.1016/0045-7825(74)90045-0
[8] Y, Dementiev, L. Burulko, and E. Suvorkova, “Pedagogical aspects of applied software packages and computer technologies use in student’s education”, Social and Behavioral Sciences, 206(1), pp. 289-294, 2015. https://doi.org/10.1016/j.sbspro.2015.10.050
[9] R. R. Bradshaw, “History of the Analysis of Cable Net Structures”, Structures Congress 2005, April 20-24, New York, New York, United States, 2005. https://doi.org/10.1061/40753(171)70
[10] A.A. Cuadri, J.E. Martín-Alfonso, and J. Urbano, “A teaching methodology based on Mathcad for improving the calculation of pumping power”, Education for Chemical Engineers, Vol., 28, Pages 68-78, ISSN 1749-7728, 2019 https://doi.org/10.1016/j.ece.2018.11.007
[11] J.Y. Zhang, and M. Ohsaki, “Adaptive force density method for form-finding problem of tensegrity structures”, International Journal of Solids and Structures (43), pp. 5658-5673, 2006. https://doi.org/10.1016/j.ijsolstr.2005.10.011
[12] S. Lee, J. Lee, “A novel method for topology design of tensegrity structures”, Compos. Struct., Vol., 152, pp. 11-19, 2016 https://doi.org/10.1016/j.compstruct.2016.05.009
[13] S. Lee, B.S. Gan, and J. Lee, “A fully automatic group selection for form-finding process of truncated tetrahedral tensegrity structures via a double-loop genetic algorithm”, Compos. Part B, 106, pp. 308 315, 2016, https://doi.org/10.1016/j.compositesb.2016.09.018
[14] D.T.T. Do, S. Lee, and J. Lee, “A modified differential evolution algorithm for tensegrity structures”, Compos. Struct., Vol., 158, pp. 11-19, 2016. https://doi.org/10.1016/j.compstruct.2016.08.039
[15] S. Yuan, and B. Yang, “The fixed nodal position method for form finding of high-precision lightweight truss structures”, Int J Solids Struct, 161, pp. 82-95, 2019. https://doi.org/10.1016/j.ijsolstr.2018.11.011
[16] Y.Q. Tang, and T.J. Li, “Equivalent-force density method as a shape-finding tool for cable-membrane structures”, Eng Struct, Vol., 151, pp. 11-19, 2017. https://doi.org/10.1016/j.engstruct.2017.08.010
[17] M. Bruggi, “A constrained force density method for the funicular analysis and design of arches, domes and vaults”, Int J Solids Struct, 193-194, pp. 251-269, 2020. https://doi.org/10.1016/j.ijsolstr.2020.02.030
[18] C. Cercadillo-García, and J.L. Fernández-Cabo, “Analytical and numerical funicular analysis by means of the parametric force density method”, J. Appl. Res. Technol., 14 (2), pp. 108-124, 2016. https://doi.org/10.1016/j.jart.2016.03.001
[19] A. Liew, D. Pagonakis, T.V. Mele, and P. Block, “Load-path optimisation of funicular networks”, Meccanica, Vol., 53 (1-2), pp. 279-294, 2018. http://dx.doi.org/10.1007/s11012-017-0714-1
[20] S. Belov, M. Pavlov, V. Ponomarev, S. Ponomarev, and A. Zhukov, “Calculation method for cable-beam shell structures”. AIP Conference Proceedings, 1772, 060006, 2016. https://doi.org/10.1063/1.4964586
[21] S. Hansen, “Extended Active Learning as a Means to Learn Syntax in Programming Languages”, Proceedings of the 2008 Annual ASEE Conference, Pittsburgh, PA, 2008. https://doi.org/10.18260/1-2--4280
[22] F. Charney, “A Transformational Approach to Teaching Matrix Structural Analysis, and Visual Implementation using Mathcad”, Proceedings of the 18th Analysis and Computation Specialty Conference at Structures Congress, ASCE, April 24-26, Vancouver, British Columbia, Canada, 2008. https://doi.org/10.1061/41000(315)9
[23] C.H. Thornton, and C. Birnstiel, “Three-dimensional suspension structures”. J. Structural Div. ASCE, pp 247-270, 1967.
[24] G.R. Monforton, and N.M, El-Hakim, “Analysis of truss-cable structures”, Comput. Struct., 11: 327-335, 1980. https://doi.org/10.1016/0045-7949(80)90082-6
[25] F. Charney, Nonlinear Analysis, pp. 78-118, Blacksburg, Virginia, 1996.
[26] A. Nuhoglu, “Nonlinear analysis of cable systems with point based iterative procedure”, Scientific Research and Essays, Vol. 6(6), 2010. https://doi.org/10.5897/SRE10.384
[27] K.G. Park, and D.W. Lee, “Mechanical Characteristics of Cable Truss Roof Systems”, Journal of Korean Association for Spatial Structures, Vol., 6; pp.89-96, 2016. http://dx.doi.org/10.9712/KASS.2016.16.3.047
[28] F. Charney, “CABNET, Cable net structures software”, Blacksburg, Virginia, 1996.