A level set method for structural topology optimization based on topology random mutations

The level set method was firstly introduced into the structuraltopology optimization by Sethian et al. Wang et al. studied structuraltopology optimization by incorporating the shape derivative or sensitivityanalysis with the level set model. In essence, the method employs theimplicit moving material interface models or the level set vector torepresent complex interfaces, and the movement of the material interfaces isgoverned by a Hamilton--Jacobi type partial differential equation, whoserobust numerical algorithm can handle topology merging or breaking naturallyduring the topology optimization process. In order to consider limitedmaximum design domain etc. practical requirements, Rong proposed an improvedlevel set method for topology optimization of continuum structures. However,the level set based topology optimization method is unable to nucleate holeswithin the structural material, which is far from the structural boundaries.In order to overcome the difficulty generating new material holes, thematerial topological derivative analysis was incorporated into the level setmethod.The level set method based on topological derivatives employs topologicalderivative information and the structural volume reduction quantity toidentify hole nucleation sites. And the initial structure must be set to themaximum design domain structure for this method. Moreover, it is not fit tosolving the topology optimization problem with an equality volumeconstraint. In order to solve this problem and overcome the difficulty ofthat the level set based topology optimization method is unable to nucleateholes within the structural material, this paper proposes a new level setmethod for structural topology optimization based on random topologymutations. At first, this paper introduces a new optimization scheme withtopology mutations in the optimization iteration process in a smallpossibility random way. Second, a mutation operator is given and theproposed algorithm convergence is discussed. Finally, a new topologyoptimization method, which incorporates topology mutations into the levelset method for structural topology optimization with maximum design domainlimits, is proposed. The algorithm of the objective function of the problembeing the strain energy with a material volume constraint is implemented.The benefit and advantages of the proposed method are illustrated withexamples.