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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/2070
Ver los metadatos del registro completo
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oai:ri.conicet.gov.ar:11336/2070 |
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network_name_str |
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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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1844613504129040384 |
score |
13.070432 |