Topology optimization with implicit functions and regularization

By Ted Belytschko, Shaoping Xiao, Chandu Parimi. 2003

290 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/0fc96dca889037e7f90959cbb66974e7ddf07938

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Adaptive topology optimization with independent error control for separated displacement and density fields (2014, methodology): “Over the past two decades, many topology optimization methods have been developed, including the homogenization method [4], the SIMP (Solid Isotropic Material with Penalization) method [5,6], the level set method [7–9], the ESO (Evolutionary Structural Optimization) method [10] and other alternative”
A topology optimization method based on the level set method incorporating a fictitious interface energy (2010, methodology): “[56] proposed a topology optimization using an implicit function to represent structural boundaries and their method allows topological changes by introducing the concept of an active zone where the material properties such as Young’s modulus are smoothly distributed.”
The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “[30, 31], the level-set method is not only used to describe internal interfaces but also to describe the domain boundaries on a background mesh.”
Stress concentration minimization of 2D filets using X-FEM and level set description (2007, methodology): “For void inclu sions and holes, the displacement field is now approximated by: u(x) = ∑ i uiNi(x)V(x) (6)”
Radial basis functions and level set method for structural topology optimization (2006, methodology): “In practice, only low order approximations such as C shape functions [8,31,52] are used because of the polynomial snaking problem [53] that polynomial interpolation in high dimensions can easily lead to singular problems and cause derivative estimates to be very poor [45].”
An enhanced genetic algorithm for structural topology optimization (2006, methodology): “For structural topology optimization problems, an emerging family of methods is the one based on the optimization of implicit interfaces, which are used to define the exterior and interior boundaries of a structural topology, such as the level-set methods in [18–21] and implicit functions regulariza”
Explicit level‐set‐based topology optimization using an exact Heaviside function and consistent sensitivity analysis (2012, methodology): “The definition of an approximate Heaviside function is also used to approximate boundary integrals used in, for example, the sensitivities [23].”