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Shape design sensitivity analysis via material derivative‐adjoint variable technique for 3‐D and 2‐D curved boundary elements
Author(s) -
Burczyński T.,
Kane J. H.,
Balakrishna C.
Publication year - 1995
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.1620381702
Subject(s) - quadrilateral , boundary (topology) , material derivative , discretization , mathematics , sensitivity (control systems) , boundary element method , mathematical analysis , boundary value problem , singular boundary method , boundary knot method , finite element method , quadratic equation , adjoint equation , mixed boundary condition , geometry , physics , partial differential equation , electronic engineering , engineering , thermodynamics
A general approach to shape design sensitivity analysis of three‐ and two‐dimensional elastic solid objects is developed using the material derivative‐adjoint variable technique and boundary element method. The formulation of the problem is general and first‐order sensitivities in the form of boundary integrals for the effect of boundary shape variations are derived for an arbitrary performance functional. Second‐order quadrilateral surface elements (for 3‐D problems) and quadratic boundary elements (for 2‐D problems) are employed in the solution of primary and adjoint systems and discretization of the boundary integral expressions for sensitivities. The accuracy of sensitivity information is studied for selected global performance functionals and also for boundary state fields at discrete points. Numerical results are presented to demonstrate the accuracy and efficiency of this approach.