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THREE‐DIMENSIONAL DESIGN SENSITIVITY ANALYSIS USING A BOUNDARY INTEGRAL APPROACH
Author(s) -
ERMAN ZEKI,
FENNER ROGER T.
Publication year - 1997
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/(sici)1097-0207(19970228)40:4<637::aid-nme83>3.0.co;2-u
Subject(s) - sensitivity (control systems) , mathematics , discretization , boundary element method , boundary (topology) , mathematical analysis , subdivision , finite element method , finite difference , boundary value problem , geometry , structural engineering , engineering , civil engineering , electronic engineering
Abstract A general shape design sensitivity analysis approach, different from traditional sensitivity methods is developed for three‐dimensional elastostatic problems. The boundary integral design sensitivity formulation is given in order to obtain traction, displacement and equivalent stress sensitivities which are required for design optimization. Those integral equations are derived analytically by differentiation with respect to the normal to the surface at design variable points. Subdivision of boundary elements into sub‐elements and rigid body translation methods are employed to deal with singularities that occur during the numerical discretization of the domain. Four different examples are demonstrated to show the accuracy of the method. The boundary integral sensitivity results are compared with the finite difference sensitivity results. Excellent agreement is achieved between the two methods. © 1997 by John Wiley & Sons, Ltd.