Investigation and improvement of sensitivity computation using the area-fraction weighted fixed grid FEM and structural optimization

Boundary based structural optimization methods often employ a fixed grid FEM to compute sensitivities for efficiency and simplicity. A simple and popular fixed grid approach is to modify the stiffness of elements intersected by the boundary by an area-fraction weighting. However, poor sensitivities and numerical instabilities can occur when using this method. Sensitivity computation for a compliance objective is investigated and the results are used to develop a weighted least squares scheme to improve sensitivities computed by the area-fraction approach. This is implemented together with a numerically stable structural topology optimization using the level set method with no additional filtering or regularization. The performance of the proposed scheme is demonstrated by classic benchmark examples of topology optimization.

[1]  Byung Man Kwak,et al.  Smooth boundary topology optimization for eigenvalue performance and its application to the design of a flexural stage , 2008 .

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

[3]  H. A. Kim,et al.  Smooth Boundary Based Optimisation Using Fixed Grid , 2007 .

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

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

[6]  Liping Chen,et al.  A semi-implicit level set method for structural shape and topology optimization , 2008, J. Comput. Phys..

[7]  Grant P. Steven,et al.  Fixed grid finite elements in elasticity problems , 1999 .

[8]  James A. Sethian,et al.  The Fast Construction of Extension Velocities in Level Set Methods , 1999 .

[9]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods , 1999 .

[10]  M. Wang,et al.  A moving superimposed finite element method for structural topology optimization , 2006 .

[11]  Grant P. Steven,et al.  On improving the GA step-wise shape optimization method through the application of the Fixed Grid FEA paradigm , 2003 .

[12]  Y. Xie,et al.  Improving efficiency of evolutionary structural optimization by implementing fixed grid mesh , 2002 .

[13]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[14]  S. Y. Wang,et al.  An extended level set method for shape and topology optimization , 2007, J. Comput. Phys..

[15]  Kyung K. Choi,et al.  Remesh-free shape optimization using the wavelet-Galerkin method , 2004 .

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

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

[18]  Danping Peng,et al.  Weighted ENO Schemes for Hamilton-Jacobi Equations , 1999, SIAM J. Sci. Comput..