Robust topology optimization of multi-material structures considering uncertain graded interface

Material interface-related uncertainties induced by inter-diffusion or reactions between two different materials may deteriorate the actual performance of a structural design achieved by topology optimization. Thus a rational methodology is needed to address this issue in the design of hybrid-material engineering products implemented by some novel fabrication techniques such as additive manufacturing. This paper presents a robust shape and topology optimization method accounting for uncertain graded interface properties of multi-material structures. A level set function is used to track the evolving material interfaces during the optimization process, and the material interface uncertainties is modeled by introducing an intermediate zone with graded properties represented by a random field. On the basis of discretizing the input random field by means of the Expansion Optimal Linear Estimation (EOLE) method, the uncertain propagation analysis is implemented with the Polynomial Chaos expansion (PCE) to predict the stochastic response. Then the robust shape and topology optimization problem is stated as a multi-criteria optimization problem, in which the expected value and the standard deviation of the performance function of interest are to be minimized under a given material volume constraint. The shape derivative of the stochastic response is derived in the context of Eulerian description, and then used to advance the evolution of the level set function through the Hamilton-Jacobi equation. In the numerical examples, the proposed robust design method is exemplified by the mean compliance minimization problems.