Integrated layout design of multi-component systems using XFEM and analytical sensitivity analysis

This study presents the integrated layout optimization of multi-component systems using a fixed mesh. The optimization formulation is established under the framework of the extended finite element method (XFEM). The level set method is used to represent components and is combined with the XFEM to describe material discontinuities across elements. Sensitivity analysis is proposed with respect to geometric variables of components and pseudo-densities of the basic structure. An analytical shape sensitivity analysis method with respect to positions and shapes of components is developed. Both solid and void components are considered to show the efficiency and accuracy of the proposed shape sensitivity analysis method. Furthermore, a revised finite circle method that adapts shape changes of elliptical components is proposed for the definition of non-overlapping constraints. Finally, numerical examples of maximizing the structural stiffness are tested to demonstrate the proposed method.

[1]  Michaël Bruyneel,et al.  A general and effective approach for the optimal design of fiber reinforced composite structures , 2006 .

[2]  Michael Yu Wang,et al.  A study on X-FEM in continuum structural optimization using a level set model , 2010, Comput. Aided Des..

[3]  T. Belytschko,et al.  Topology optimization with implicit functions and regularization , 2003 .

[4]  M. Wang,et al.  Level Set Based Structural Topology Optimization for Minimizing Frequency Response , 2011 .

[5]  M. Bendsøe,et al.  A geometry projection method for shape optimization , 2004 .

[6]  Takayuki Yamada,et al.  A topology optimization method based on the level set method incorporating a fictitious interface energy , 2010 .

[7]  Weihong Zhang,et al.  Integrated layout design of multi‐component system , 2009 .

[8]  Vadim Shapiro,et al.  Shape optimization with topological changes and parametric control , 2007 .

[9]  Xiaoming Wang,et al.  A level set method for structural topology optimization , 2003 .

[10]  Michael Yu Wang,et al.  Shape and topology optimization of compliant mechanisms using a parameterization level set method , 2007, J. Comput. Phys..

[11]  Jihong Zhu,et al.  Some Recent Advances in the Integrated Layout Design of Multicomponent Systems , 2011 .

[12]  G. K. Ananthasuresh,et al.  Optimal Embedding of Rigid Objects in the Topology Design of Structures , 2004 .

[13]  Weihong Zhang,et al.  Simultaneous design of components layout and supporting structures using coupled shape and topology optimization technique , 2008 .

[14]  Michael Yu Wang,et al.  Design of piezoelectric actuators using a multiphase level set method of piecewise constants , 2009, J. Comput. Phys..

[15]  M. Wang,et al.  A level set‐based parameterization method for structural shape and topology optimization , 2008 .

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

[17]  T. Belytschko,et al.  MODELING HOLES AND INCLUSIONS BY LEVEL SETS IN THE EXTENDED FINITE-ELEMENT METHOD , 2001 .

[18]  G. Allaire,et al.  Structural optimization using sensitivity analysis and a level-set method , 2004 .

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

[20]  R. Kanwal.  Generalized Functions: Theory and Applications , 2004 .

[21]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[22]  Weihong Zhang,et al.  Finite-circle method for component approximation and packing design optimization , 2009 .

[23]  Nam H. Kim,et al.  Eulerian shape design sensitivity analysis and optimization with a fixed grid , 2005 .

[24]  Y. Radovcic,et al.  BOSS QUATTRO: an open system for parametric design , 2002 .

[25]  Jihong Zhu,et al.  Integrated layout design of supports and structures , 2010 .

[26]  T. Belytschko,et al.  Arbitrary branched and intersecting cracks with the eXtended Finite Element Method , 2000 .

[27]  Jean-François Remacle,et al.  A computational approach to handle complex microstructure geometries , 2003 .

[28]  Xiaoming Wang,et al.  Color level sets: a multi-phase method for structural topology optimization with multiple materials , 2004 .

[29]  L. Van Miegroet,et al.  Stress concentration minimization of 2D filets using X-FEM and level set description , 2007 .

[30]  Patrick M. Knupp,et al.  Applications of mesh smoothing: copy, morph, and sweep on unstructured quadrilateral meshes , 1999 .

[31]  Stéphane Bordas,et al.  An extended finite element library , 2007 .

[32]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[33]  Vadim Shapiro,et al.  Theory of R-functions and Applications: A Primer , 1991 .

[34]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[35]  T. Belytschko,et al.  The extended/generalized finite element method: An overview of the method and its applications , 2010 .

[36]  C. Fleury,et al.  A family of MMA approximations for structural optimization , 2002 .

[37]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .