A Novel Mesh Morphing Technique for Large Shape Deformation and Its Application to Optimal Design Problems

In the process of finding the optimal solution by parameter sweeping analysis for optimal shape design problems, the silhouette of the device to be optimized usually needs to be changed many times. To avoid the tedious and time-consuming mesh regeneration process when the shape parameters change, a parameterized mesh technique is adopted in this paper. In the proposed method, the new coordinates of the nodes and their displacement vectors can be obtained instantly because all nodes are associated with the design parameters. To eliminate inverted elements in case of large shape deformation, a smart edge swapping technique is proposed. The edge swapping process is based on the nodal displacement vectors and the edge facing the displacement vector of the node is to be swapped. The parameterized mesh technique is fully described and examples are also given to showcase the effectiveness of the proposed method.

[1]  S. L. Ho,et al.  A Moving Mesh Embedded Algorithm in Finite Element Method for Optimal Design of Electromagnetic Devices , 2011, IEEE Transactions on Magnetics.

[2]  L. Freitag,et al.  Tetrahedral mesh improvement via optimization of the element condition number , 2002 .

[3]  Wolfgang Ring,et al.  Shape design with great geometrical deformations using continuously moving finite element nodes , 1998 .

[4]  O. C. Zienkiewicz,et al.  A simple error estimator and adaptive procedure for practical engineerng analysis , 1987 .

[5]  Maurizio Repetto,et al.  Stochastic algorithms in electromagnetic optimization , 1998 .

[6]  K. Yamazaki,et al.  An Adaptive Finite Element Method for Minor Shape Modification in Optimization Algorithms , 2008, IEEE Transactions on Magnetics.

[7]  Shuangxia Niu,et al.  A Parameterized Mesh Generation and Refinement Method for Finite Element Parameter Sweeping Analysis of Electromagnetic Devices , 2012, IEEE Transactions on Magnetics.

[8]  María Cecilia Rivara,et al.  Automatic LEFM crack propagation method based on local Lepp-Delaunay mesh refinement , 2010, Adv. Eng. Softw..

[9]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[10]  Scott W. Sloan,et al.  An implementation of Watson's algorithm for computing 2-dimensional delaunay triangulations , 1984 .

[11]  Hua Su,et al.  Applying response surface methodology in the design and optimization of electromagnetic devices , 1997 .

[12]  Emmanuel Lefrançois.  A simple mesh deformation technique for fluid-structure interaction based on a submesh approach , 2008 .

[13]  S.R.H. Hoole,et al.  Geometric parametrization and constrained optimization techniques in the design of salient pole synchronous machines , 1992 .