Shape optimization of shell structures based on NURBS description using automatic differentiation

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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:International journal for numerical methods in engineering Jg. 88; H. 7; S. 613 - 636
Hauptverfasser: Espath, L. F. R., Linn, R. V., Awruch, A. M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Chichester, UK John Wiley & Sons, Ltd 18.11.2011
Wiley
Schlagworte:
automatic differentiation
Differentiation
Exact sciences and technology
Finite element method
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematical models
mathematical optimization
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
NURBS
Optimization
Parametrization
Physics
Sciences and techniques of general use
Shape optimization
Shells
Solid mechanics
Static elasticity (thermoelasticity...)
structural analysis
Structural and continuum mechanics
B spline
Performance evaluation
Shell structure
Program optimization
Form defect
Parameterization
Automatic mesh generation
Modeling
Spline approximation
NURBS
Finite element method
Shell
Non uniform rational B spline
Sequential method
Mesh generation
Geometrical shape
High performance
Gradient
mathematical optimization
Mechanical properties
Quadratic programming
automatic differentiation
Differentiation
Control point
Structural analysis
ISSN:0029-5981, 1097-0207, 1097-0207
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
Bibliographie:istex:3A972202EEC8C033083355407A138203E596B31F
ark:/67375/WNG-P3NP2NJ3-C
ArticleID:NME3183
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0029-5981
1097-0207
1097-0207
DOI:10.1002/nme.3183