Optimal shape design for thin-walled beam cross-sections

✍ Scribed by Uwe Schramm; Walter D. Pilkey

• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 866 KB
• Volume: 37
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620372307

✦ Synopsis

Abstract

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.