The Efficient Computation of Bounds for Functionals of Finite Element Solutions in Large Strain Elasticity
We present an implicit a-posteriori finite element procedure to compute bounds for functional outputs of finite element solutions in large strain elasticity. The method proposed relies on the existence of a potential energy functional whose local minima, over a space of suitably chosen continuous fu...
| Main Authors: | , , |
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| Format: | Article |
| Language: | en_US |
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2003
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| Online Access: | http://hdl.handle.net/1721.1/4000 |
| _version_ | 1826206248711749632 |
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| author | Bonet, J. Huerta, A. Peraire, Jaime |
| author_facet | Bonet, J. Huerta, A. Peraire, Jaime |
| author_sort | Bonet, J. |
| collection | MIT |
| description | We present an implicit a-posteriori finite element procedure to compute bounds for functional outputs of finite element solutions in large strain elasticity. The method proposed relies on the existence of a potential energy functional whose local minima, over a space of suitably chosen continuous functions, corresponds to the problem solution. The output of interest is cast as a constrained minimization problem over an enlarged discontinuous finite element space. A Lagrangian is formed were the multipliers are an adjoint solution, which enforces equilibrium, and hybrid fluxes, which constrain the solution to be continuous. By computing approximate values for the multipliers on a coarse mesh, strict upper and lower bounds for the output of interest on a suitably refined mesh, are obtained. This requires a minimization over a discontinuous space, which can be carried out locally at low cost. The computed bounds are uniformly valid regardless of the size of the underlying coarse discretization. The method is demonstrated with two applications involving large strain plane stress incompressible neo-hookean hyperelasticity. |
| first_indexed | 2024-09-23T13:26:26Z |
| format | Article |
| id | mit-1721.1/4000 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:26:26Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | mit-1721.1/40002019-04-10T08:59:55Z The Efficient Computation of Bounds for Functionals of Finite Element Solutions in Large Strain Elasticity Bonet, J. Huerta, A. Peraire, Jaime large strain elasticity efficient bounds computation finite element solutions functional outputs We present an implicit a-posteriori finite element procedure to compute bounds for functional outputs of finite element solutions in large strain elasticity. The method proposed relies on the existence of a potential energy functional whose local minima, over a space of suitably chosen continuous functions, corresponds to the problem solution. The output of interest is cast as a constrained minimization problem over an enlarged discontinuous finite element space. A Lagrangian is formed were the multipliers are an adjoint solution, which enforces equilibrium, and hybrid fluxes, which constrain the solution to be continuous. By computing approximate values for the multipliers on a coarse mesh, strict upper and lower bounds for the output of interest on a suitably refined mesh, are obtained. This requires a minimization over a discontinuous space, which can be carried out locally at low cost. The computed bounds are uniformly valid regardless of the size of the underlying coarse discretization. The method is demonstrated with two applications involving large strain plane stress incompressible neo-hookean hyperelasticity. Singapore-MIT Alliance (SMA) 2003-12-23T02:20:51Z 2003-12-23T02:20:51Z 2002-01 Article http://hdl.handle.net/1721.1/4000 en_US High Performance Computation for Engineered Systems (HPCES); 562584 bytes application/pdf application/pdf |
| spellingShingle | large strain elasticity efficient bounds computation finite element solutions functional outputs Bonet, J. Huerta, A. Peraire, Jaime The Efficient Computation of Bounds for Functionals of Finite Element Solutions in Large Strain Elasticity |
| title | The Efficient Computation of Bounds for Functionals of Finite Element Solutions in Large Strain Elasticity |
| title_full | The Efficient Computation of Bounds for Functionals of Finite Element Solutions in Large Strain Elasticity |
| title_fullStr | The Efficient Computation of Bounds for Functionals of Finite Element Solutions in Large Strain Elasticity |
| title_full_unstemmed | The Efficient Computation of Bounds for Functionals of Finite Element Solutions in Large Strain Elasticity |
| title_short | The Efficient Computation of Bounds for Functionals of Finite Element Solutions in Large Strain Elasticity |
| title_sort | efficient computation of bounds for functionals of finite element solutions in large strain elasticity |
| topic | large strain elasticity efficient bounds computation finite element solutions functional outputs |
| url | http://hdl.handle.net/1721.1/4000 |
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