# A level set method for topology optimization of continuum structures with bounded design domain

Article

Rong, Jian Hua and Liang, Qing Quan. 2008. "A level set method for topology optimization of continuum structures with bounded design domain." Computer Methods in Applied Mechanics and Engineering. 197 (17-18), pp. 1447-1465. https://doi.org/10.1016/j.cma.2007.11.026
Article Title A level set method for topology optimization of continuum structures with bounded design domain 4173 Article Rong, Jian Hua (Author) and Liang, Qing Quan (Author) Computer Methods in Applied Mechanics and Engineering 197 (17-18), pp. 1447-1465 19 2008 Netherlands 0045-7825 https://doi.org/10.1016/j.cma.2007.11.026 http://www.sciencedirect.com/science/journal/00457825 In practice, a continuum structure is usually designed to carry the traction applied to the boundary of the structure subject to prescribed displacements imposed on its boundary. The design domains of practical structures are often limited and significantly affect the final optimal design of the structures. Structural boundaries under traction and prescribed displacements should be treated as a zero level set in the level set methods. Firstly, to overcome the limitations of current level set methods and the stopping issue of structural boundary movements, this paper presents a set of new level set based optimization formulae for the optimal design of continuum structures with bounded design domains. A set of new normal velocities required by level set movements is given. A level set based optimization algorithm is developed and implemented with several robust and efficient numerical techniques, which include the level set regularization algorithm, gradient projection algorithm, nonlinear velocity mapping algorithm and return mapping algorithm. Secondly, in order to overcome the difficulty in nucleating holes in the design domain in the level set based optimization method, this paper introduces a new optimization strategy with a small possibility random topology mutations and crossovers. A mixed topology optimization algorithm is implemented and presented for the compliance minimization problems of continuum structures with material volume constraints. The validity and effectiveness of the proposed method are demonstrated with two examples. structural optimization; topology optimization; level set method; random mutation 400510. Structural engineering 490407. Mathematical logic, set theory, lattices and universal algebra 490412. Topology Files associated with this item cannot be displayed due to copyright restrictions. Changsha University of Science and Technology, China University of New South Wales

https://research.usq.edu.au/item/9yq4y/a-level-set-method-for-topology-optimization-of-continuum-structures-with-bounded-design-domain

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