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Optimal shape design for thin‐walled beam cross‐sections
Author(s) -
Schramm Uwe,
Pilkey Walter D.
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.1620372307
Subject(s) - image warping , finite element method , shape optimization , mathematics , b spline , spline (mechanical) , beam (structure) , connection (principal bundle) , regular polygon , optimal design , geometry , mathematical analysis , mathematical optimization , structural engineering , computer science , engineering , statistics , artificial intelligence
Problems of shape optimization for thin‐walled beam cross‐sections are investigated. In particular, shape optimization under torsional loading is treated. The shape of the beam cross‐section is described by non‐uniform rational B ‐splines (NURBs). Biquadratic and p ‐version finite elements are used to calculate the warping function. The definition of the element geometry is carried out by isoparametric and B ‐spline mappings. Both methods are discussed and compared. For structural shape optimization the B ‐spline mapping in connection with the p ‐version finite elements is very efficient. The optimization is implemented using convex linearisation and a dual method of mathematical programming. Sensitivity analysis is performed analytically. Sample calculations are included.