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Implicit objective integration for sensitivity analysis in non‐linear solid mechanics
Author(s) -
Leu LiangJenq,
Mukherjee Subrata
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620372207
Subject(s) - viscoplasticity , numerical integration , isotropy , sensitivity (control systems) , mathematics , numerical analysis , constitutive equation , direct integration of a beam , computational mechanics , mathematical optimization , computer science , mathematical analysis , finite element method , structural engineering , physics , engineering , quantum mechanics , electronic engineering
Incrementally objective integration schemes are proposed for the accurate and efficient determination of design sensitivity coefficients (DSCs) for solid mechanics problems with both material and geometrical non‐linearities. The derivation of these schemes are based on the direct differentiation of objective schemes that are used in stress analysis for problems of this class. Two widely used objective stress rates, the Jaumann rate and the Green–Naghdi rate, are considered here within the same setting with only minor changes of the integration scheme. Numerical results are presented for a simple shear problem with different material constitutive laws, including a hypoelastic model and a unified isotropic viscoplastic model, for these two objective rates. The numerical results are compared with analytical solutions or direct integration solutions. The close agreement among these solutions demonstrates the accuracy and efficiency of the proposed scheme.