TY - GEN

T1 - Level set-based topology optimization using an immersed boundary element method

AU - Yamasaki, Shintaro

AU - Yamada, Takayuki

AU - Matsumoto, Toshiro

PY - 2012

Y1 - 2012

N2 - In this presentation, we propose a new immersed boundary element method (BEM) targeting level set-based topology optimization and construct a concrete topology optimization method using the immersed BEM. The key idea of the immersed BEM is replacing the nodal coordinates of the boundary element mesh with the nodal level set function values and the nodal coordinates of the Eulerian mesh maintaining the level set function. By this replacement, the boundary element mesh seems to be immersed in the Eulerian mesh. The relationship between the nodal coordinates of the boundary element mesh and the nodal level set function of the Eulerian mesh is clearly given in the immersed BEM, therefore, we can strictly derive the sensitivities of the nodal coordinates of the boundary element mesh with respect to the nodal level set function of the Eulerian mesh. That is, we can strictly derive the sensitivities of the objective function with respect to the nodal level set function, by using the immersed BEM. In the constructed topology optimization method, optimization is therefore performed using the strictly derived sensitivities while completely eliminating grayscale elements. The usefulness of the immersed BEM and the constructed topology optimization method is confirmed using a numerical example.

AB - In this presentation, we propose a new immersed boundary element method (BEM) targeting level set-based topology optimization and construct a concrete topology optimization method using the immersed BEM. The key idea of the immersed BEM is replacing the nodal coordinates of the boundary element mesh with the nodal level set function values and the nodal coordinates of the Eulerian mesh maintaining the level set function. By this replacement, the boundary element mesh seems to be immersed in the Eulerian mesh. The relationship between the nodal coordinates of the boundary element mesh and the nodal level set function of the Eulerian mesh is clearly given in the immersed BEM, therefore, we can strictly derive the sensitivities of the nodal coordinates of the boundary element mesh with respect to the nodal level set function of the Eulerian mesh. That is, we can strictly derive the sensitivities of the objective function with respect to the nodal level set function, by using the immersed BEM. In the constructed topology optimization method, optimization is therefore performed using the strictly derived sensitivities while completely eliminating grayscale elements. The usefulness of the immersed BEM and the constructed topology optimization method is confirmed using a numerical example.

KW - Boundary element method

KW - Level set method

KW - Topology optimization

UR - http://www.scopus.com/inward/record.url?scp=84871633707&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871633707&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84871633707

SN - 9783950353709

T3 - ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers

SP - 5182

EP - 5194

BT - ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers

T2 - 6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012

Y2 - 10 September 2012 through 14 September 2012

ER -