Developing and Investigation the Numerical Efficiency of Modified Energy Method in Solid Mechanics With Geometric Nonlinearity and Bifurcation Points

Geometric nonlinear analyses are used in many structural problems, such as the determination of failure load, as well as the study of buckling mechanism. Nevertheless, due to the complex nature of this type of problems and the absence of a comprehensive analytical solution for them, numerical method...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Ahmad Razaghi, Jafar Asgari Marnani, Mohammad Sadegh Rohanimanesh
Formato: article
Lenguaje:FA
Publicado: Iranian Society of Structrual Engineering (ISSE) 2021
Materias:
Acceso en línea:https://doaj.org/article/eceb10d03b2d46eb92cdb55fbde2db10
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
id oai:doaj.org-article:eceb10d03b2d46eb92cdb55fbde2db10
record_format dspace
spelling oai:doaj.org-article:eceb10d03b2d46eb92cdb55fbde2db102021-11-08T15:54:55ZDeveloping and Investigation the Numerical Efficiency of Modified Energy Method in Solid Mechanics With Geometric Nonlinearity and Bifurcation Points2476-39772538-261610.22065/jsce.2019.163823.1746https://doaj.org/article/eceb10d03b2d46eb92cdb55fbde2db102021-07-01T00:00:00Zhttps://www.jsce.ir/article_96675_02a04a7abd73a16f5ff85226177cddda.pdfhttps://doaj.org/toc/2476-3977https://doaj.org/toc/2538-2616Geometric nonlinear analyses are used in many structural problems, such as the determination of failure load, as well as the study of buckling mechanism. Nevertheless, due to the complex nature of this type of problems and the absence of a comprehensive analytical solution for them, numerical methods are utilized in practice to approximate the exact response of these systems. In the application of numerical methods, there are also some difficulties such as divergence or finding the correct path of equilibrium, especially in the case of bifurcation points. Hence, the main purpose of this research is to apply the modified energy method (introduced in the dynamics of structures) in quasi-static problems with geometric nonlinearity and bifurcation points so that the efficiency of this method can be compared to others, such as Newtonian numerical techniques and force-displacement-constraint approaches. To achieve the objectives of this research, after briefly reviewing the current force-based computational methods in practice, the energy method is described for such problems, and then the step-by-step process of its computer implementation will be presented. Afterward, by coding in MATLAB software and applying the method to numerical examples employed by other researchers such as truss and frame structures, the numerical results are verified by analytical solution as well as those obtained by other methods, such as Newton-Raphson and Arc Length techniques. Generally, the interpretation of the results obtained from performed simulations has shown that the presented numerical method in analyzing nonlinear geometric problems has better accuracy compared to the Arc Length method; moreover, it can well pass through bifurcation points in the force-displacement curve without divergence in comparison with the Newton-Raphson method.Ahmad RazaghiJafar Asgari MarnaniMohammad Sadegh RohanimaneshIranian Society of Structrual Engineering (ISSE)articlenumerical studymodified energy methodsolid mechanicsgeometric nonlinearitybifurcation pointsBridge engineeringTG1-470Building constructionTH1-9745FAJournal of Structural and Construction Engineering, Vol 8, Iss 5, Pp 83-109 (2021)
institution DOAJ
collection DOAJ
language FA
topic numerical study
modified energy method
solid mechanics
geometric nonlinearity
bifurcation points
Bridge engineering
TG1-470
Building construction
TH1-9745
spellingShingle numerical study
modified energy method
solid mechanics
geometric nonlinearity
bifurcation points
Bridge engineering
TG1-470
Building construction
TH1-9745
Ahmad Razaghi
Jafar Asgari Marnani
Mohammad Sadegh Rohanimanesh
Developing and Investigation the Numerical Efficiency of Modified Energy Method in Solid Mechanics With Geometric Nonlinearity and Bifurcation Points
description Geometric nonlinear analyses are used in many structural problems, such as the determination of failure load, as well as the study of buckling mechanism. Nevertheless, due to the complex nature of this type of problems and the absence of a comprehensive analytical solution for them, numerical methods are utilized in practice to approximate the exact response of these systems. In the application of numerical methods, there are also some difficulties such as divergence or finding the correct path of equilibrium, especially in the case of bifurcation points. Hence, the main purpose of this research is to apply the modified energy method (introduced in the dynamics of structures) in quasi-static problems with geometric nonlinearity and bifurcation points so that the efficiency of this method can be compared to others, such as Newtonian numerical techniques and force-displacement-constraint approaches. To achieve the objectives of this research, after briefly reviewing the current force-based computational methods in practice, the energy method is described for such problems, and then the step-by-step process of its computer implementation will be presented. Afterward, by coding in MATLAB software and applying the method to numerical examples employed by other researchers such as truss and frame structures, the numerical results are verified by analytical solution as well as those obtained by other methods, such as Newton-Raphson and Arc Length techniques. Generally, the interpretation of the results obtained from performed simulations has shown that the presented numerical method in analyzing nonlinear geometric problems has better accuracy compared to the Arc Length method; moreover, it can well pass through bifurcation points in the force-displacement curve without divergence in comparison with the Newton-Raphson method.
format article
author Ahmad Razaghi
Jafar Asgari Marnani
Mohammad Sadegh Rohanimanesh
author_facet Ahmad Razaghi
Jafar Asgari Marnani
Mohammad Sadegh Rohanimanesh
author_sort Ahmad Razaghi
title Developing and Investigation the Numerical Efficiency of Modified Energy Method in Solid Mechanics With Geometric Nonlinearity and Bifurcation Points
title_short Developing and Investigation the Numerical Efficiency of Modified Energy Method in Solid Mechanics With Geometric Nonlinearity and Bifurcation Points
title_full Developing and Investigation the Numerical Efficiency of Modified Energy Method in Solid Mechanics With Geometric Nonlinearity and Bifurcation Points
title_fullStr Developing and Investigation the Numerical Efficiency of Modified Energy Method in Solid Mechanics With Geometric Nonlinearity and Bifurcation Points
title_full_unstemmed Developing and Investigation the Numerical Efficiency of Modified Energy Method in Solid Mechanics With Geometric Nonlinearity and Bifurcation Points
title_sort developing and investigation the numerical efficiency of modified energy method in solid mechanics with geometric nonlinearity and bifurcation points
publisher Iranian Society of Structrual Engineering (ISSE)
publishDate 2021
url https://doaj.org/article/eceb10d03b2d46eb92cdb55fbde2db10
work_keys_str_mv AT ahmadrazaghi developingandinvestigationthenumericalefficiencyofmodifiedenergymethodinsolidmechanicswithgeometricnonlinearityandbifurcationpoints
AT jafarasgarimarnani developingandinvestigationthenumericalefficiencyofmodifiedenergymethodinsolidmechanicswithgeometricnonlinearityandbifurcationpoints
AT mohammadsadeghrohanimanesh developingandinvestigationthenumericalefficiencyofmodifiedenergymethodinsolidmechanicswithgeometricnonlinearityandbifurcationpoints
_version_ 1718441623003594752