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...

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Autores principales:	Ahmad Razaghi, Jafar Asgari Marnani, Mohammad Sadegh Rohanimanesh
Formato:	article
Lenguaje:	FA
Publicado:	Iranian Society of Structrual Engineering (ISSE) 2021
Materias:	numerical study modified energy method solid mechanics geometric nonlinearity bifurcation points Bridge engineering TG1-470 Building construction TH1-9745
Acceso en línea:	https://doaj.org/article/eceb10d03b2d46eb92cdb55fbde2db10
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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
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Developing and Investigation the Numerical Efficiency of Modified Energy Method in Solid Mechanics With Geometric Nonlinearity and Bifurcation Points

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