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Shape optimization of shell structures based on NURBS description using automatic differentiation
Author(s) -
Espath L. F. R.,
Linn R. V.,
Awruch A. M.
Publication year - 2011
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.3183
Subject(s) - sequential quadratic programming , finite element method , shape optimization , shell (structure) , automatic differentiation , mathematics , mathematical optimization , computer science , b spline , algorithm , quadratic programming , computation , mathematical analysis , structural engineering , mechanical engineering , engineering
The consolidation of the link among four fields in computational mathematics and mechanics is the main objective of this work. Surfaces based on NURBS (non‐uniform rational B‐spline), mathematical optimization, the finite element method (FEM) in structural analysis, and automatic differentiation (AD) are applied in shape optimization of shells. This problem is performed taking into account the fact that material and mechanical characteristics influence both, the structural shape and the thickness variation, in order to obtain the best performance with respect to a specific criterium. Some techniques were implemented to modify the shell geometry conserving the same parameterization without a new finite element mesh generation. The shape modification is carried out using an optimization code based on the data obtained by a finite element analysis and gradients evaluation. In this work the optimization procedure is performed using an SQP (Sequential Quadratic Programming) algorithm, where the variables are the control points in homogeneous coordinates, the knot vectors, and the thickness. The functional value is determined by the FEM and gradients are evaluated using AD. Some examples are analyzed and discussed. As a consequence of the shape optimization, shells with high structural performance and aesthetically beautiful shapes can be obtained. Copyright © 2011 John Wiley & Sons, Ltd.