Isogeometric shape optimization of three dimensional problems

Shape optimization of 3-D structures is a challenging task. The newly developed isogeometrical analysis is a more suitable approach, in comparison with other numerical methods, to address the problem. Apart from the ability of defining the boundaries of the problem by more precision which cannot be easily achieved by other techniques, such as finite element and mesh-free methods, this method takes burden of several remeshings that are needed in the conventional approaches to structural shape optimization.

[1]  Claude Fleury,et al.  Shape Optimal Design - An Approach Matching C.A.D. and Optimization Concepts , 1985 .

[2]  O. C. Zienkiewicz,et al.  Optimization of shape to minimize stress concentration , 1975 .

[3]  Niels Olhoff,et al.  On CAD-integrated structural topology and design optimization , 1991 .

[4]  بهروز حسنی,et al.  Homogenization and Structural Topology Optimization, Theory, Practice and Software , 1999 .

[5]  R. Haftka,et al.  Structural shape optimization - A survey , 1985 .

[6]  Ekkehard Ramm,et al.  Efficient modeling in shape optimal design , 1991 .

[7]  E. Ramm,et al.  Structural optimization and form finding of light weight structures , 2001 .

[8]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[9]  Seung-Hyun Ha,et al.  Isogeometric shape design optimization: exact geometry and enhanced sensitivity , 2009 .

[10]  Alessandro Reali,et al.  Isogeometric Analysis of Structural Vibrations , 2006 .

[11]  E. Hinton,et al.  Homogenization and Structural Topology Optimization: Theory, Practice and Software , 2011 .

[12]  Ekkehard Ramm,et al.  A General Finite Element Approach to the form Finding of Tensile Structures by the Updated Reference Strategy , 1999 .

[13]  T. Hughes,et al.  Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows , 2007 .

[14]  W. Wall,et al.  Isogeometric structural shape optimization , 2008 .

[15]  L. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communications.

[16]  V. Braibant,et al.  Shape optimal design using B-splines , 1984 .

[17]  T. Hughes,et al.  ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES , 2006 .

[18]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[19]  Jasbir S. Arora,et al.  Introduction to Optimum Design , 1988 .

[20]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[21]  T. Hughes,et al.  Isogeometric Fluid–structure Interaction Analysis with Applications to Arterial Blood Flow , 2006 .