We present an a-posteriori method for computing rigorous upper and lower bounds of the J-integral in two dimensional linear elasticity. The J-integral, which is typically expressed as a contour integral, is recast as a surface integral which yields a quadratic continuous functional of the displacement. By expanding the quadratic output about an approximate finite element solution, the output is expressed as a known computable quantity plus linear and quadratic functionals of the solution error. The quadratic component is bounded by the energy norm of the error scaled by a continuity constant, which is determined explicitly. The linear component is expressed as an inner product of the errors in the displacement and in a computed adjoint solution, and bounded using standard a-posteriori error estimation techniques. The method is illustrated with two fracture problems in plane strain elasticity. / Singapore-MIT Alliance (SMA)
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/3881 |
| Date | 01 1900 |
| Creators | Xuan, Z.C., Lee, Kwok Hong, Patera, Anthony T., Peraire, Jaime |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Article |
| Format | 1986710 bytes, application/pdf |
| Relation | High Performance Computation for Engineered Systems (HPCES); |
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