Extension of APFEM to geometrical alterations and application to stochastic homogenisation
We recently proposed an efficient method facilitating the parametric study of a finite element mechanical simulation as a postprocessing step, i.e., without the need to run multiple simulations: the A Posteriori Finite Element Method (APFEM). APFEM only requires the knowledge of the vertices of the...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Wiley
2024
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| _version_ | 1817931403085479936 |
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| author | Ammouche, Y Jerusalem, A |
| author_facet | Ammouche, Y Jerusalem, A |
| author_sort | Ammouche, Y |
| collection | OXFORD |
| description | We recently proposed an efficient method facilitating the parametric study of a finite element mechanical simulation as a postprocessing step, i.e., without the need to run multiple simulations:
the A Posteriori Finite Element Method (APFEM). APFEM only requires the knowledge of the
vertices of the parameter space and is able to predict accurately how the degrees of freedom of a
simulation, i.e., nodal displacements, and other outputs of interests, e.g., element stress tensors,
evolve when simulation parameters vary within their predefined ranges. In our previous work,
these parameters were restricted to material properties and loading conditions. Here, we extend
the APFEM to additionally account for changes in the original geometry. This is achieved by
defining an intermediary reference frame whose mapping is defined stochastically in the weak
form. Subsequent deformation is then reached by correcting for this stochastic variation in the
reference frame through multiplicative decomposition of the deformation gradient tensor. The
resulting framework is shown here to provide accurate mechanical predictions for relevant applications of increasing complexity: i) quantifying the stress concentration factor of a plate under
uniaxial loading with one and two elliptical holes of varying eccentricities, and ii) performing the stochastic homogenisation of a composite plate with uncertain mechanical properties
and geometry inclusion. This extension of APFEM completes our original approach to account
parametrically for geometrical alterations, in addition to boundary conditions and material properties. The advantages of this approach in our original work in terms of stochastic prediction,
uncertainty quantification, structural and material optimisation and Bayesian inferences are all
naturally conserved. |
| first_indexed | 2024-03-07T08:25:26Z |
| format | Journal article |
| id | oxford-uuid:ebe7c2ec-12a4-4f4d-9957-ef010bb53a2a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:21:28Z |
| publishDate | 2024 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:ebe7c2ec-12a4-4f4d-9957-ef010bb53a2a2024-11-12T09:33:49ZExtension of APFEM to geometrical alterations and application to stochastic homogenisationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ebe7c2ec-12a4-4f4d-9957-ef010bb53a2aEnglishSymplectic ElementsWiley2024Ammouche, YJerusalem, AWe recently proposed an efficient method facilitating the parametric study of a finite element mechanical simulation as a postprocessing step, i.e., without the need to run multiple simulations: the A Posteriori Finite Element Method (APFEM). APFEM only requires the knowledge of the vertices of the parameter space and is able to predict accurately how the degrees of freedom of a simulation, i.e., nodal displacements, and other outputs of interests, e.g., element stress tensors, evolve when simulation parameters vary within their predefined ranges. In our previous work, these parameters were restricted to material properties and loading conditions. Here, we extend the APFEM to additionally account for changes in the original geometry. This is achieved by defining an intermediary reference frame whose mapping is defined stochastically in the weak form. Subsequent deformation is then reached by correcting for this stochastic variation in the reference frame through multiplicative decomposition of the deformation gradient tensor. The resulting framework is shown here to provide accurate mechanical predictions for relevant applications of increasing complexity: i) quantifying the stress concentration factor of a plate under uniaxial loading with one and two elliptical holes of varying eccentricities, and ii) performing the stochastic homogenisation of a composite plate with uncertain mechanical properties and geometry inclusion. This extension of APFEM completes our original approach to account parametrically for geometrical alterations, in addition to boundary conditions and material properties. The advantages of this approach in our original work in terms of stochastic prediction, uncertainty quantification, structural and material optimisation and Bayesian inferences are all naturally conserved. |
| spellingShingle | Ammouche, Y Jerusalem, A Extension of APFEM to geometrical alterations and application to stochastic homogenisation |
| title | Extension of APFEM to geometrical alterations and application to stochastic homogenisation |
| title_full | Extension of APFEM to geometrical alterations and application to stochastic homogenisation |
| title_fullStr | Extension of APFEM to geometrical alterations and application to stochastic homogenisation |
| title_full_unstemmed | Extension of APFEM to geometrical alterations and application to stochastic homogenisation |
| title_short | Extension of APFEM to geometrical alterations and application to stochastic homogenisation |
| title_sort | extension of apfem to geometrical alterations and application to stochastic homogenisation |
| work_keys_str_mv | AT ammouchey extensionofapfemtogeometricalalterationsandapplicationtostochastichomogenisation AT jerusalema extensionofapfemtogeometricalalterationsandapplicationtostochastichomogenisation |