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Computing Upper and Lower Bounds for the J-Integral in Two-Dimensional Linear Elasticity

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)

Identiferoai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/3881
Date01 1900
CreatorsXuan, Z.C., Lee, Kwok Hong, Patera, Anthony T., Peraire, Jaime
Source SetsM.I.T. Theses and Dissertation
Languageen_US
Detected LanguageEnglish
TypeArticle
Format1986710 bytes, application/pdf
RelationHigh Performance Computation for Engineered Systems (HPCES);

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