Inverse membrane problems in elasticity
The inverse elasticity problem of determining the undeformed, deflated, configuration of a nonlinear elastic membrane, given the deformed configuration enclosing an incompressible fluid under known pressure, is considered. It is shown that, in practical cases, it is enough to determine only the unde...
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| Format: | Journal article |
| Language: | English |
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2009
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| _version_ | 1826284252852912128 |
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| author | Pathmanathan, P Chapman, S Gavaghan, D |
| author_facet | Pathmanathan, P Chapman, S Gavaghan, D |
| author_sort | Pathmanathan, P |
| collection | OXFORD |
| description | The inverse elasticity problem of determining the undeformed, deflated, configuration of a nonlinear elastic membrane, given the deformed configuration enclosing an incompressible fluid under known pressure, is considered. It is shown that, in practical cases, it is enough to determine only the undeformed metric tensor, and it is also shown how the two- and three-dimensional cases are fundamentally different. For the three-dimensional case, we set up and classify the partial differential equations to be solved, prove existence of an undeformed state given an undeformed metric and study the axisymmetric case in detail. © The author 2009. Published by Oxford University Press; all rights reserved. |
| first_indexed | 2024-03-07T01:11:05Z |
| format | Journal article |
| id | oxford-uuid:8d093044-cdc4-4508-b17f-17f21cceec6c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:11:05Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:8d093044-cdc4-4508-b17f-17f21cceec6c2022-03-26T22:48:36ZInverse membrane problems in elasticityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8d093044-cdc4-4508-b17f-17f21cceec6cEnglishSymplectic Elements at Oxford2009Pathmanathan, PChapman, SGavaghan, DThe inverse elasticity problem of determining the undeformed, deflated, configuration of a nonlinear elastic membrane, given the deformed configuration enclosing an incompressible fluid under known pressure, is considered. It is shown that, in practical cases, it is enough to determine only the undeformed metric tensor, and it is also shown how the two- and three-dimensional cases are fundamentally different. For the three-dimensional case, we set up and classify the partial differential equations to be solved, prove existence of an undeformed state given an undeformed metric and study the axisymmetric case in detail. © The author 2009. Published by Oxford University Press; all rights reserved. |
| spellingShingle | Pathmanathan, P Chapman, S Gavaghan, D Inverse membrane problems in elasticity |
| title | Inverse membrane problems in elasticity |
| title_full | Inverse membrane problems in elasticity |
| title_fullStr | Inverse membrane problems in elasticity |
| title_full_unstemmed | Inverse membrane problems in elasticity |
| title_short | Inverse membrane problems in elasticity |
| title_sort | inverse membrane problems in elasticity |
| work_keys_str_mv | AT pathmanathanp inversemembraneproblemsinelasticity AT chapmans inversemembraneproblemsinelasticity AT gavaghand inversemembraneproblemsinelasticity |