Hybrid level set phase field method for topology optimization of contact problems.

*(English)*Zbl 1363.35138The paper deals with the structural optimization contact problem with a Tresca type friction model on the boundary. In order to solve the optimization problem a combination of level-set technique within a phase field approach is developed and validated throughout a numerical example.

The paper focused in the analysis and numerical solution of the topology optimization of systems governed by elliptic variational inequalities. The aim of the optimization problem is to find the distribution of the material of the body in unilateral contact with the rigid foundation that minimizes the normal contact stress. The optimization problem is regularized using the Cahn-Hilliard interface energy term rather than a perimeter constraint. Also, for the topology optimization problem formulation a volume constraint is considered.

Comparing to the standard level set approach, the proposed hybrid methodology does not require to solve a Hamilton-Jacobi equation and to perform the reinitialization process of the signed distance function.

The paper focused in the analysis and numerical solution of the topology optimization of systems governed by elliptic variational inequalities. The aim of the optimization problem is to find the distribution of the material of the body in unilateral contact with the rigid foundation that minimizes the normal contact stress. The optimization problem is regularized using the Cahn-Hilliard interface energy term rather than a perimeter constraint. Also, for the topology optimization problem formulation a volume constraint is considered.

Comparing to the standard level set approach, the proposed hybrid methodology does not require to solve a Hamilton-Jacobi equation and to perform the reinitialization process of the signed distance function.

Reviewer: Sebastián M. Giusti (Córdoba)

##### MSC:

35J86 | Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators |

49K20 | Optimality conditions for problems involving partial differential equations |

49Q10 | Optimization of shapes other than minimal surfaces |

49Q12 | Sensitivity analysis for optimization problems on manifolds |

74N20 | Dynamics of phase boundaries in solids |

74P10 | Optimization of other properties in solid mechanics |