A gradient-based, parameter-free approach to shape optimization

[1]  Erik Lund,et al.  A Method of “Exact” Numerical Differentiation for Error Elimination in Finite-Element-Based Semi-Analytical Shape Sensitivity Analyses* , 1993 .

[2]  Pauli Pedersen,et al.  Shapes of orthotropic plates for minimum energy concentration , 1992 .

[3]  Xiangmin Jiao,et al.  Face offsetting: A unified approach for explicit moving interfaces , 2007, J. Comput. Phys..

[4]  O. Pironneau.  Optimal Shape Design for Elliptic Systems , 1983 .

[5]  Ole Sigmund,et al.  New Developments in Handling Stress Constraints in Optimal Material Distributions , 1998 .

[6]  Denise Chenais,et al.  On the existence of a solution in a domain identification problem , 1975 .

[7]  C. S. Jog,et al.  A new approach to variable-topology shape design using a constraint on perimeter , 1996 .

[8]  Yutaka Ohtake,et al.  Mesh regularization and adaptive smoothing , 2001, Comput. Aided Des..

[9]  E. Schnack,et al.  Nonparametric gradient-less shape optimization for real-world applications , 2005 .

[10]  E. Lund,et al.  Structural natural-frequency shape-sensitivity analysis: a fixed-basis-function finite-element approach , 2003 .

[11]  R. Haftka,et al.  Elements of Structural Optimization , 1984 .

[12]  Julián A. Norato,et al.  Stress-based topology optimization for continua , 2010 .

[13]  George I. N. Rozvany,et al.  Shape and layout optimization of structural systems and optimality criteria methods , 1992 .

[14]  Duong Hien Tran,et al.  Parameter Sensitivity in Nonlinear Mechanics: Theory and Finite Element Computations , 1997 .

[15]  Pascal Frey.  Generation and adaptation of computational surface meshes from discrete anatomical data , 2004 .

[16]  J. Zolésio,et al.  Introduction to shape optimization : shape sensitivity analysis , 1992 .

[17]  Daniel A. Tortorelli,et al.  A systematic approach to shape sensitivity analysis , 1993 .

[18]  M. Imam.  Three‐dimensional shape optimization , 1982 .

[19]  N. V. Banichuk,et al.  Optimality conditions in the problem of seeking the hole shapes in elastic bodies: PMM vol. 41, n≗ 5, 1977, pp. 920–925 , 1977 .

[20]  Frithiof I. Niordson,et al.  Optimal design of elastic plates with a constraint on the slope of the thickness function , 1983 .

[21]  Jahau Lewis Chen,et al.  Shape Optimization by Growth Using Simulated Biological Approaches , 1993 .

[22]  Edward J. Haug,et al.  Design Sensitivity Analysis of Structural Systems , 1986 .

[23]  M. Zhou,et al.  Checkerboard and minimum member size control in topology optimization , 2001 .

[24]  B. Bourdin.  Filters in topology optimization , 2001 .

[25]  Sunil Saigal,et al.  Boundary-element shape optimization system for aircraft structural components , 1990 .

[26]  J. Petersson,et al.  Topology optimization using regularized intermediate density control , 2001 .

[27]  Eckart Schnack,et al.  An optimization procedure for stress concentrations by the finite element technique , 1979 .

[28]  Noboru Kikuchi,et al.  Adaptive finite element methods for shape optimization of linearly elastic structures , 1986 .

[29]  N. Olhoff,et al.  Shape design sensitivity analysis of eigenvalues using “exact” numerical differentiation of finite element matrices , 1994 .

[30]  T. E. Bruns,et al.  Topology optimization of non-linear elastic structures and compliant mechanisms , 2001 .

[31]  D. Tortorelli,et al.  Tangent operators and design sensitivity formulations for transient non‐linear coupled problems with applications to elastoplasticity , 1994 .

[32]  Daniel A. Tortorelli,et al.  A Geometric Representation Scheme Suitable for Shape Optimization , 1993 .

[33]  A. Lee,et al.  Shape optimization of connecting rod pin end using a generic model , 1992 .

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

[35]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[36]  F. van Keulen,et al.  Rigorous improvement of semi-analytical design sensitivities by exact differentiation of rigid body motions , 1998 .

[37]  J. Samareh.  Survey of Shape Parameterization Techniques for High-Fidelity Multidisciplinary Shape Optimization , 2001 .

[38]  Frédo Durand,et al.  Non-iterative, feature-preserving mesh smoothing , 2003, ACM Trans. Graph..

[39]  Gabriel Taubin,et al.  Curve and surface smoothing without shrinkage , 1995, Proceedings of IEEE International Conference on Computer Vision.

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

[41]  Daniel A. Tortorelli,et al.  Optimal design of nonlinear parabolic systems. Part II: Variable spatial domain with applications to casting optimization , 1994 .

[42]  Lizhuang Ma,et al.  SUSAN structure preserving filtering for mesh denoising , 2006, The Visual Computer.

[43]  Daniel Cohen-Or,et al.  Bilateral mesh denoising , 2003 .

[44]  P. Pedersen.  On optimal shapes in materials and structures , 2000 .

[45]  Niels Olhoff,et al.  Shape sensitivity analysis using a fixed basis function finite element approach , 2001 .

[46]  Cecil Armstrong,et al.  Sensitivity-based optimization of parameterized CAD geometries , 2009 .

[47]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[48]  A. Belegundu,et al.  A shape optimization approach based on natural design variables and shape functions , 1988 .

[49]  N. Olhoff,et al.  An investigation concerning optimal design of solid elastic plates , 1981 .

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

[51]  S. Chen,et al.  Three-dimensional shape optimization with variational geometry , 1997 .

[52]  Ole Sigmund,et al.  On the Design of Compliant Mechanisms Using Topology Optimization , 1997 .

[53]  Ren-Jye Yang,et al.  Stress-based topology optimization , 1996 .

[54]  G. P. Cherepanov.  Inverse problems of the plane theory of elasticity: PMM vol. 38, n≗ 6, 1974, pp. 963–979 , 1974 .

[55]  O. Sigmund,et al.  Checkerboard patterns in layout optimization , 1995 .

[56]  Hideyuki Azegami,et al.  A SMOOTHING METHOD FOR SHAPE OPTIMIZATION: TRACTION METHOD USING THE ROBIN CONDITION , 2006 .

[57]  R. Haftka,et al.  Structural shape optimization — a survey , 1986 .

[58]  Yury Grabovsky,et al.  The cavity of the optimal shape under the shear stresses , 1998 .

[59]  Katsushi Ikeuchi,et al.  Iterative Smoothed Residuals: A Low-Pass Filter for Smoothing With Controlled Shrinkage , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[60]  Roland Wüchner,et al.  Optimal shapes of mechanically motivated surfaces , 2010 .

[61]  S. Zhang,et al.  A systematic approach for generating velocity fields in shape optimization , 1992 .

[62]  Martin Berggren,et al.  Shape optimization of an acoustic horn , 2003 .

[63]  G. N. Vanderplaats,et al.  Structural Design Optimization Status and Direction , 1997 .

[64]  Kyung K. Choi,et al.  A CAD-based design parameterization for shape optimization of elastic solids , 1999 .

[65]  C. Mattheck,et al.  A new method of structural shape optimization based on biological growth , 1990 .

[66]  P. Pedersen.  Suggested benchmarks for shape optimization for minimum stress concentration , 2008 .

[67]  Kai-Uwe Bletzinger,et al.  Approximation of derivatives in semi-analytical structural optimization , 2008 .