Level-set based topology optimization using an interface-enriched finite element method

Immersed boundary analysis and level set based topology optimization

Sanne van den Boom (PhD candidate), Alejandro M. Aragón (supervisor), and Fred van Keulen (supervisor)

Standard density-based topology optimization results in topologies with a staircased boundary description that often also contains intermediate densities. For problems that are sensitive to the way interfaces are resolved, a smoother description of the boundary during optimization is desired. A level set-based topology optimization approach, combined with the Interface-enriched Generalized Finite Element Method (IGFEM) provides such a smooth boundary description throughout the optimization procedure. Radial Basis Functions (RBFs), used to construct the level set function, offer control of the complexity of the design, similar to filters in density-based topology optimization. In this work, analytical sensitivities for IGFEM are derived and the method is tested on well-known compliance minimization problems.

Comparison to a density based method for different mesh sizes.
Increased complexity in the design as a function of the number of radial basis functions.
3-D topology optimization of a cantilever beam.

References 

  • van den Boom, SJ, Zhang, J, van Keulen, F, Aragón, AM. An interface-enriched generalized finite element method for level set-based topology optimization. Struct Multidiscip Optim, 2020 (In Press) arXiv:2003.13751
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