Algorithm to maintain linear element in 3D level set topology optimization

Reference:

Brampton, C. J., Kim, A. H. and Cunningham, J. L., 2012. Algorithm to maintain linear element in 3D level set topology optimization. In: ICPRAM 2012 - Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods. , pp. 341-350.

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Abstract

In level set topology optimization the boundary of the structure is defined by level set function values stored at the nodes of a regular gird of simple bilinear elements. By changing the level set function values according to optimization sensitivities the boundary of the structure is moved to create an optimal structure. However it is possible for the boundary to cut an element more than once; violating the linear element assumptions resulting in insufficient nodal information for the optimization sensitivity calculations. To resolve this the local boundary of the structure is moved so that each element is only cut once. In 2D where a square element mesh is used an element cut twice times is altered by moving one of the boundaries within the element to intercept the node closest to it removing the extra cut from the element. In 3D where a voxel mesh is used the process of moving the boundary within an element is more complicated due to the greater number of boundary cuts possible and the effect that it can have on neighbouring elements. An algorithm is developed which allows the boundary within a 3D element to be moved with these considerations taken into account.

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