Bi-material Topology Optimization Of Considering Graded Interface Properties Under Uncertainties

In the bi-material topology optimization,the material properties are general treated as discontinuous across the material interfaces.However,the material interfaces may be uncertain because of the interdiffusion or reactions between dissimilar materials.Thin transition zones are more appropriate to handle with the changes of material properties.In practice,the width of the transition zones always has some randomness due to uncertainties caused by the manufacturing techniques such as the development of multi-material additive manufacturing techniques.Hence an uncertain width that can be denoted by a random variable or random field is used to handle the transition material interface zones and smooth material property interpolation schemes are employed as materials going across their interface.As for the random field,the expansion optimal linear estimation(EOLE)method can be used.The topology optimization considering such uncertain width of the material interface(or called interface uncertainty)is solved by a level-set based method with polynomial chaos expansions(PCE)employed to analyze the stochastic response.Some 2d examples are given to show the robustness of considering interface uncertainty.