The Reliability of the Arc-Length Method in the Analysis of Mode-Jumping Problems

Marco Cerini; Brian G. Falzon

doi:10.2514/6.2003-1621

The Reliability of the Arc-Length Method in the Analysis of Mode-Jumping Problems

Marco Cerini, Brian G. Falzon

School of Mechanical and Aerospace Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The Arc-Length Method is a solution procedure that enables a generic non-linear problem to pass limit points. Some examples are provided of mode-jumping problems solutions using a commercial nite element package, and other investigations are carried out on a simple structure of which the numerical solution can be compared with an analytical one. It is shown that Arc-Length Method is not reliable when bifurcations are present in the primary equilibrium path; also the presence of very sharp snap-backs or special boundary conditions may cause convergence diÆculty at limit points. An improvement to the predictor used in the incremental procedure is suggested, together with a reliable criteria for selecting either solution of the quadratic arc-length constraint. The gap that is sometimes observed between the experimantal load level of mode-jumping and its arc-length prediction is explained through an example.

Original language	English
Title of host publication	44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
Publisher	Aerospace Research Council
Number of pages	10
ISBN (Electronic)	9781624101007
DOIs	https://doi.org/10.2514/6.2003-1621
Publication status	Published - 08 Apr 2003
Event	AIAA/ASME/AHS/ASC 44th Structures, Structural Dynamics and Materials Conference - Norfolk, United States Duration: 07 Apr 2003 → 10 Apr 2003

Conference

Conference	AIAA/ASME/AHS/ASC 44th Structures, Structural Dynamics and Materials Conference
Country	United States
City	Norfolk
Period	07/04/2003 → 10/04/2003

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10.2514/6.2003-1621

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Cerini, M., & Falzon, B. G. (2003). The Reliability of the Arc-Length Method in the Analysis of Mode-Jumping Problems. In 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference Aerospace Research Council. https://doi.org/10.2514/6.2003-1621

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abstract = "The Arc-Length Method is a solution procedure that enables a generic non-linear problem to pass limit points. Some examples are provided of mode-jumping problems solutions using a commercial nite element package, and other investigations are carried out on a simple structure of which the numerical solution can be compared with an analytical one. It is shown that Arc-Length Method is not reliable when bifurcations are present in the primary equilibrium path; also the presence of very sharp snap-backs or special boundary conditions may cause convergence di{\AE}culty at limit points. An improvement to the predictor used in the incremental procedure is suggested, together with a reliable criteria for selecting either solution of the quadratic arc-length constraint. The gap that is sometimes observed between the experimantal load level of mode-jumping and its arc-length prediction is explained through an example.",

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doi = "10.2514/6.2003-1621",

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booktitle = "44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference",

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Cerini, M & Falzon, BG 2003, The Reliability of the Arc-Length Method in the Analysis of Mode-Jumping Problems. in 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Aerospace Research Council, AIAA/ASME/AHS/ASC 44th Structures, Structural Dynamics and Materials Conference, Norfolk, United States, 07/04/2003. https://doi.org/10.2514/6.2003-1621

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AU - Cerini, Marco

AU - Falzon, Brian G.

PY - 2003/4/8

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N2 - The Arc-Length Method is a solution procedure that enables a generic non-linear problem to pass limit points. Some examples are provided of mode-jumping problems solutions using a commercial nite element package, and other investigations are carried out on a simple structure of which the numerical solution can be compared with an analytical one. It is shown that Arc-Length Method is not reliable when bifurcations are present in the primary equilibrium path; also the presence of very sharp snap-backs or special boundary conditions may cause convergence diÆculty at limit points. An improvement to the predictor used in the incremental procedure is suggested, together with a reliable criteria for selecting either solution of the quadratic arc-length constraint. The gap that is sometimes observed between the experimantal load level of mode-jumping and its arc-length prediction is explained through an example.

AB - The Arc-Length Method is a solution procedure that enables a generic non-linear problem to pass limit points. Some examples are provided of mode-jumping problems solutions using a commercial nite element package, and other investigations are carried out on a simple structure of which the numerical solution can be compared with an analytical one. It is shown that Arc-Length Method is not reliable when bifurcations are present in the primary equilibrium path; also the presence of very sharp snap-backs or special boundary conditions may cause convergence diÆculty at limit points. An improvement to the predictor used in the incremental procedure is suggested, together with a reliable criteria for selecting either solution of the quadratic arc-length constraint. The gap that is sometimes observed between the experimantal load level of mode-jumping and its arc-length prediction is explained through an example.

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DO - 10.2514/6.2003-1621

M3 - Conference contribution

BT - 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Y2 - 7 April 2003 through 10 April 2003

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