[23] A level-set based topology optimization using the element connectivity parameterization method
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N. Van Dijk, G. H. Yoon, F. Van Keulen, and M. Langelaar. Structural and Multidisciplinary Optimization 42 (2010): 269-282.
This contribution presents a novel and versatile approach to geometrically nonlinear topology optimization by combining the level-set method with the element con- nectivity parameterization method or ECP. The combined advantages of both methods open up the possibility to treat a wide range of optimization problems involving complex physical and/or geometrical nonlinearities in a general and elegant manner. The level-set method features shape opti- mization on a fixed mesh, leading to intrinsically black-and- white designs. This approach allows a clear description of location and orientation of the interface, whereas topologi- cal changes can still be handled easily. A popular concept used in conventional level-set methods is to map the level- set function to volume-fraction design variables for every element of a finite element mesh. The resulting element density variables are then used to scale the Young’s mod- ulus in each element using the Ersatz material approach. In this work we employ a modified material interpolation method, in which the element density variables, based on a per-element integration of a regularized Heaviside oper- ator applied to the level-set function, are used as element