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On implementation of the extended interior penalty function
Author(s) -
Cassis Juan H.,
Schmit Lucien A.
Publication year - 1976
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.1620100102
Subject(s) - penalty method , taylor series , mathematical optimization , parametric statistics , constraint (computer aided design) , context (archaeology) , set (abstract data type) , mathematics , function (biology) , variable (mathematics) , series (stratigraphy) , interval (graph theory) , interval arithmetic , planar , computer science , algorithm , mathematical analysis , geometry , paleontology , statistics , computer graphics (images) , combinatorics , evolutionary biology , bounded function , biology , programming language
The extended interior penalty function formulation is implemented. A rational method for determining the transition between the interior and extended parts is set forth. The formulation includes a straightforward method for avoiding design points with some negative components, which are physically meaningless in structural analysis. The technique, when extended to problems involving parametric constraints, can facilitate closed form integration of the penalty terms over the most important parts of the parameter interval. The method lends itself well to the use of approximation concepts, such as design variable linking, constraint deletion and Taylor series expansions of response quantities in terms of design variables. Examples demonstrating the algorithm, in the context of planar orthogonal frames subjected to ground motion, are included.