Propagation of uncertainties and multimodality in the impact problem of two elastic bodies

Autores
Buezas, Fernando Salvador; Rosales, Marta Beatriz; Sampaio, Rubens
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
An uncertainty quantification study is carried out for the problem of the frontal collision of two elastic bodies. The time of contact and the resultant force function involved during the collision are the quantities of interest. If the initial conditions and the mechanical and geometrical properties were known, the response prediction would be deterministic. However, if the data contains any uncertainty, a stochastic approach becomes appropriate. Based on the Principle of Maximum Entropy (PME), and under certain restrictions on the parameter values, we derive the probability density function (PDF) for each of the stochastic parameters to construct a probabilistic model. Two cases are dealt with: one of a collision involving two spheres and another of a collision of two discs. In the first case, a parameter involving geometry and material properties is assumed stochastic. Since a functional relationship exists, the propagation of the uncertainty of the time of contact can be done symbolically. However, the interaction force function can only be computed from the solution of a nonlinear ordinary differential equation. Given the PDF of the parameter, the problem of uncertainty propagation is tackled using Monte Carlo simulations. The comparison of both approaches yields an excellent agreement. With respect to the collision of two discs, first the small deformation problem, within the Hertz theory, is addressed with a Monte Carlo method. When the discs undergo large deformations, the problem is approximated using the equations of Finite Elasticity discretized by the finite element method (FEM) and combined with Monte Carlo simulations. In a first illustration, the modulus of elasticity is assumed stochastic with a gamma PDF. Further, the disc collision problem is analyzed when two parameters are stochastic: the modulus of elasticity and the Poisson's ratio. It is shown that under certain dispersion ranges, the PDF of the interaction force function undergoes a qualitatively change exhibiting bimodality.
Fil: Buezas, Fernando Salvador. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico - CONICET - Bahía Blanca. Instituto de Física del Sur; Argentina. Universidad Nacional del Sur. Departamento de Física; Argentina
Fil: Rosales, Marta Beatriz. Universidad Nacional del Sur. Departamento de Ingeniería. Area Estabilidad; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Sampaio, Rubens. Pontifícia Universidade Católica do Rio de Janeiro; Brasil
Materia
COLLISION
ELASTIC BODIES
MULTIMODALITY
UNCERTAINTY
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/2070

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network_name_str CONICET Digital (CONICET)
spelling Propagation of uncertainties and multimodality in the impact problem of two elastic bodiesBuezas, Fernando SalvadorRosales, Marta BeatrizSampaio, RubensCOLLISIONELASTIC BODIESMULTIMODALITYUNCERTAINTYhttps://purl.org/becyt/ford/2.3https://purl.org/becyt/ford/2An uncertainty quantification study is carried out for the problem of the frontal collision of two elastic bodies. The time of contact and the resultant force function involved during the collision are the quantities of interest. If the initial conditions and the mechanical and geometrical properties were known, the response prediction would be deterministic. However, if the data contains any uncertainty, a stochastic approach becomes appropriate. Based on the Principle of Maximum Entropy (PME), and under certain restrictions on the parameter values, we derive the probability density function (PDF) for each of the stochastic parameters to construct a probabilistic model. Two cases are dealt with: one of a collision involving two spheres and another of a collision of two discs. In the first case, a parameter involving geometry and material properties is assumed stochastic. Since a functional relationship exists, the propagation of the uncertainty of the time of contact can be done symbolically. However, the interaction force function can only be computed from the solution of a nonlinear ordinary differential equation. Given the PDF of the parameter, the problem of uncertainty propagation is tackled using Monte Carlo simulations. The comparison of both approaches yields an excellent agreement. With respect to the collision of two discs, first the small deformation problem, within the Hertz theory, is addressed with a Monte Carlo method. When the discs undergo large deformations, the problem is approximated using the equations of Finite Elasticity discretized by the finite element method (FEM) and combined with Monte Carlo simulations. In a first illustration, the modulus of elasticity is assumed stochastic with a gamma PDF. Further, the disc collision problem is analyzed when two parameters are stochastic: the modulus of elasticity and the Poisson's ratio. It is shown that under certain dispersion ranges, the PDF of the interaction force function undergoes a qualitatively change exhibiting bimodality.Fil: Buezas, Fernando Salvador. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico - CONICET - Bahía Blanca. Instituto de Física del Sur; Argentina. Universidad Nacional del Sur. Departamento de Física; ArgentinaFil: Rosales, Marta Beatriz. Universidad Nacional del Sur. Departamento de Ingeniería. Area Estabilidad; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Sampaio, Rubens. Pontifícia Universidade Católica do Rio de Janeiro; BrasilPergamon-Elsevier Science Ltd2013-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/2070Buezas, Fernando Salvador; Rosales, Marta Beatriz; Sampaio, Rubens; Propagation of uncertainties and multimodality in the impact problem of two elastic bodies; Pergamon-Elsevier Science Ltd; International Journal of Mechanical Sciences; 75; 10-2013; 145-1550020-7403enginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.ijmecsci.2013.05.009info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S002074031300163Xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:48:23Zoai:ri.conicet.gov.ar:11336/2070instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:48:24.277CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Propagation of uncertainties and multimodality in the impact problem of two elastic bodies
title Propagation of uncertainties and multimodality in the impact problem of two elastic bodies
spellingShingle Propagation of uncertainties and multimodality in the impact problem of two elastic bodies
Buezas, Fernando Salvador
COLLISION
ELASTIC BODIES
MULTIMODALITY
UNCERTAINTY
title_short Propagation of uncertainties and multimodality in the impact problem of two elastic bodies
title_full Propagation of uncertainties and multimodality in the impact problem of two elastic bodies
title_fullStr Propagation of uncertainties and multimodality in the impact problem of two elastic bodies
title_full_unstemmed Propagation of uncertainties and multimodality in the impact problem of two elastic bodies
title_sort Propagation of uncertainties and multimodality in the impact problem of two elastic bodies
dc.creator.none.fl_str_mv Buezas, Fernando Salvador
Rosales, Marta Beatriz
Sampaio, Rubens
author Buezas, Fernando Salvador
author_facet Buezas, Fernando Salvador
Rosales, Marta Beatriz
Sampaio, Rubens
author_role author
author2 Rosales, Marta Beatriz
Sampaio, Rubens
author2_role author
author
dc.subject.none.fl_str_mv COLLISION
ELASTIC BODIES
MULTIMODALITY
UNCERTAINTY
topic COLLISION
ELASTIC BODIES
MULTIMODALITY
UNCERTAINTY
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.3
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv An uncertainty quantification study is carried out for the problem of the frontal collision of two elastic bodies. The time of contact and the resultant force function involved during the collision are the quantities of interest. If the initial conditions and the mechanical and geometrical properties were known, the response prediction would be deterministic. However, if the data contains any uncertainty, a stochastic approach becomes appropriate. Based on the Principle of Maximum Entropy (PME), and under certain restrictions on the parameter values, we derive the probability density function (PDF) for each of the stochastic parameters to construct a probabilistic model. Two cases are dealt with: one of a collision involving two spheres and another of a collision of two discs. In the first case, a parameter involving geometry and material properties is assumed stochastic. Since a functional relationship exists, the propagation of the uncertainty of the time of contact can be done symbolically. However, the interaction force function can only be computed from the solution of a nonlinear ordinary differential equation. Given the PDF of the parameter, the problem of uncertainty propagation is tackled using Monte Carlo simulations. The comparison of both approaches yields an excellent agreement. With respect to the collision of two discs, first the small deformation problem, within the Hertz theory, is addressed with a Monte Carlo method. When the discs undergo large deformations, the problem is approximated using the equations of Finite Elasticity discretized by the finite element method (FEM) and combined with Monte Carlo simulations. In a first illustration, the modulus of elasticity is assumed stochastic with a gamma PDF. Further, the disc collision problem is analyzed when two parameters are stochastic: the modulus of elasticity and the Poisson's ratio. It is shown that under certain dispersion ranges, the PDF of the interaction force function undergoes a qualitatively change exhibiting bimodality.
Fil: Buezas, Fernando Salvador. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico - CONICET - Bahía Blanca. Instituto de Física del Sur; Argentina. Universidad Nacional del Sur. Departamento de Física; Argentina
Fil: Rosales, Marta Beatriz. Universidad Nacional del Sur. Departamento de Ingeniería. Area Estabilidad; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Sampaio, Rubens. Pontifícia Universidade Católica do Rio de Janeiro; Brasil
description An uncertainty quantification study is carried out for the problem of the frontal collision of two elastic bodies. The time of contact and the resultant force function involved during the collision are the quantities of interest. If the initial conditions and the mechanical and geometrical properties were known, the response prediction would be deterministic. However, if the data contains any uncertainty, a stochastic approach becomes appropriate. Based on the Principle of Maximum Entropy (PME), and under certain restrictions on the parameter values, we derive the probability density function (PDF) for each of the stochastic parameters to construct a probabilistic model. Two cases are dealt with: one of a collision involving two spheres and another of a collision of two discs. In the first case, a parameter involving geometry and material properties is assumed stochastic. Since a functional relationship exists, the propagation of the uncertainty of the time of contact can be done symbolically. However, the interaction force function can only be computed from the solution of a nonlinear ordinary differential equation. Given the PDF of the parameter, the problem of uncertainty propagation is tackled using Monte Carlo simulations. The comparison of both approaches yields an excellent agreement. With respect to the collision of two discs, first the small deformation problem, within the Hertz theory, is addressed with a Monte Carlo method. When the discs undergo large deformations, the problem is approximated using the equations of Finite Elasticity discretized by the finite element method (FEM) and combined with Monte Carlo simulations. In a first illustration, the modulus of elasticity is assumed stochastic with a gamma PDF. Further, the disc collision problem is analyzed when two parameters are stochastic: the modulus of elasticity and the Poisson's ratio. It is shown that under certain dispersion ranges, the PDF of the interaction force function undergoes a qualitatively change exhibiting bimodality.
publishDate 2013
dc.date.none.fl_str_mv 2013-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/2070
Buezas, Fernando Salvador; Rosales, Marta Beatriz; Sampaio, Rubens; Propagation of uncertainties and multimodality in the impact problem of two elastic bodies; Pergamon-Elsevier Science Ltd; International Journal of Mechanical Sciences; 75; 10-2013; 145-155
0020-7403
url http://hdl.handle.net/11336/2070
identifier_str_mv Buezas, Fernando Salvador; Rosales, Marta Beatriz; Sampaio, Rubens; Propagation of uncertainties and multimodality in the impact problem of two elastic bodies; Pergamon-Elsevier Science Ltd; International Journal of Mechanical Sciences; 75; 10-2013; 145-155
0020-7403
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ijmecsci.2013.05.009
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S002074031300163X
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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