ROBUST DYNAMIC TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURE SUBJECTED TO HARMONIC EXCITATION OF LOADING POSITION UNCERTAINTY

The robust topology optimization of an elastic continuum structure is performed under the loading position uncertainty of a dynamic excitation subject to the material volume constraint. The design purpose in this work is to minimize the structural dynamic compliance while reducing its sensitivity to the external load position perturbations in a certain region. First, on the basis of the non-probabilistic convex representation of an uncertainty, the stochastic variation of the loading position is indicated simply with an uncertain-but-bounded interval variable. Then, with the density variable method of the RAMP (rational approximation of material properties) model, the design sensitivity analyses of the structural dynamic compliance with respect to the topological variables are conducted according to the quadratic Taylor series expansion once the loading position moves locally. Finally, by using the gradient-based density approach of the standard MMA (method of moving asymptotes) upon the choice of the maximal absolute value of the design sensitivities over the uncertain position interval, the robust dynamic topology optimization designs can be implemented within a single-level optimization procedure for computational efficiency. The optimal configurations of two benchmark examples loaded with the harmonic excitation are compared comprehensively with those obtained under the fixed loading position of the excitation. Numerical results show that the present dynamic topology optimizations can essentially provide higher robustness to the loading point disturbances than the equivalent deterministic topology optimization solutions. As the material volume constraint is relaxed a little, the dynamic compliance of the robust topology optimization will be smaller than that of the deterministic topology optimization over the whole load uncertain interval.