Large deflections of nonlinear elastic and viscoelastic columns with follower loads: The elastica and viscoelastica problems part I: The nonlinear elastic column

Harry H. Hilton; Daniel M. De Albuquerque

Large deflections of nonlinear elastic and viscoelastic columns with follower loads: The elastica and viscoelastica problems part I: The nonlinear elastic column

Harry H. Hilton, Daniel M. De Albuquerque

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

Abstract

Large deection analyses of nonhomogeneous nonlinear elastic or viscoelastic columns (elastica and viscoelastica) with initial curvature and with deection dependent cross sectional areas subjected to follower loads is formulated. Column end shortening due to both curvature and compressive loads is taken into account and the governing coupled nonlinear differential equations are solved by successive approximation methods (SAM) and numerically by a double Runge-Kutta iterative shooting approach. Various solution protocols are analyzed and evaluated. The effects of end shortening and follower load angle on elastic and viscoelastic columns are discussed.

Original language	English (US)
Title of host publication	58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017
Publisher	American Institute of Aeronautics and Astronautics Inc. (AIAA)
ISBN (Print)	9781624104534
State	Published - 2017
Event	58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017 - Grapevine, United States Duration: Jan 9 2017 → Jan 13 2017

Publication series

Name	58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017

Conference

Conference	58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017
Country/Territory	United States
City	Grapevine
Period	1/9/17 → 1/13/17

Keywords

Buckling criteria
Elastica
Follower loads
Large deformations
Nonlinear elasticity
Nonlinear viscoelasticity
Starting transients
Viscoelastica

ASJC Scopus subject areas

Mechanics of Materials
Architecture
Civil and Structural Engineering
Building and Construction

Library availability

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Hilton, H. H., & De Albuquerque, D. M. (2017). Large deflections of nonlinear elastic and viscoelastic columns with follower loads: The elastica and viscoelastica problems part I: The nonlinear elastic column. In 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017 Article AIAA 2545270 (58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017). American Institute of Aeronautics and Astronautics Inc. (AIAA).

Large deflections of nonlinear elastic and viscoelastic columns with follower loads: The elastica and viscoelastica problems part I: The nonlinear elastic column. / Hilton, Harry H.; De Albuquerque, Daniel M.
58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017. American Institute of Aeronautics and Astronautics Inc. (AIAA), 2017. AIAA 2545270 (58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017).

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

Hilton, HH & De Albuquerque, DM 2017, Large deflections of nonlinear elastic and viscoelastic columns with follower loads: The elastica and viscoelastica problems part I: The nonlinear elastic column. in 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017., AIAA 2545270, 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017, American Institute of Aeronautics and Astronautics Inc. (AIAA), 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017, Grapevine, United States, 1/9/17.

Hilton HH, De Albuquerque DM. Large deflections of nonlinear elastic and viscoelastic columns with follower loads: The elastica and viscoelastica problems part I: The nonlinear elastic column. In 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017. American Institute of Aeronautics and Astronautics Inc. (AIAA). 2017. AIAA 2545270. (58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017).

Hilton, Harry H. ; De Albuquerque, Daniel M. / Large deflections of nonlinear elastic and viscoelastic columns with follower loads : The elastica and viscoelastica problems part I: The nonlinear elastic column. 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017. American Institute of Aeronautics and Astronautics Inc. (AIAA), 2017. (58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017).

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abstract = "Large deection analyses of nonhomogeneous nonlinear elastic or viscoelastic columns (elastica and viscoelastica) with initial curvature and with deection dependent cross sectional areas subjected to follower loads is formulated. Column end shortening due to both curvature and compressive loads is taken into account and the governing coupled nonlinear differential equations are solved by successive approximation methods (SAM) and numerically by a double Runge-Kutta iterative shooting approach. Various solution protocols are analyzed and evaluated. The effects of end shortening and follower load angle on elastic and viscoelastic columns are discussed.",

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note = "Funding Information: Support for HHH by the Private Sector Program Division (PSP) of the National Center for Supercomputing Applications (NCSA) at the University of Illinois at Urbana-Champaign (UIUC) and for DMdeA by the Brazilian Scientific Mobility Program is gratefully acknowledged. The latter made possible DMdeA?s internship at UIUC. Publisher Copyright: {\textcopyright} 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.; 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017 ; Conference date: 09-01-2017 Through 13-01-2017",

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N1 - Funding Information: Support for HHH by the Private Sector Program Division (PSP) of the National Center for Supercomputing Applications (NCSA) at the University of Illinois at Urbana-Champaign (UIUC) and for DMdeA by the Brazilian Scientific Mobility Program is gratefully acknowledged. The latter made possible DMdeA?s internship at UIUC. Publisher Copyright: © 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

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N2 - Large deection analyses of nonhomogeneous nonlinear elastic or viscoelastic columns (elastica and viscoelastica) with initial curvature and with deection dependent cross sectional areas subjected to follower loads is formulated. Column end shortening due to both curvature and compressive loads is taken into account and the governing coupled nonlinear differential equations are solved by successive approximation methods (SAM) and numerically by a double Runge-Kutta iterative shooting approach. Various solution protocols are analyzed and evaluated. The effects of end shortening and follower load angle on elastic and viscoelastic columns are discussed.

AB - Large deection analyses of nonhomogeneous nonlinear elastic or viscoelastic columns (elastica and viscoelastica) with initial curvature and with deection dependent cross sectional areas subjected to follower loads is formulated. Column end shortening due to both curvature and compressive loads is taken into account and the governing coupled nonlinear differential equations are solved by successive approximation methods (SAM) and numerically by a double Runge-Kutta iterative shooting approach. Various solution protocols are analyzed and evaluated. The effects of end shortening and follower load angle on elastic and viscoelastic columns are discussed.

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KW - Nonlinear viscoelasticity

KW - Starting transients

KW - Viscoelastica

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Large deflections of nonlinear elastic and viscoelastic columns with follower loads: The elastica and viscoelastica problems part I: The nonlinear elastic column

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

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