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

An efficient method is proposed in this paper to study the dynamic robust topology optimization of a continuum structure under the loading direction uncertainty of a harmonic excitation. The design purpose is to reduce the sensitivity of the structural steady-state response of the topological layout to the external load direction perturbations. Firstly, on the basis of the probability representation of an uncertainty, the stochastic variation of the loading direction is described reasonably by a normal distribution, and the external excitation is decomposed along the two essential axes. Then, both the mean and variance of the structural dynamic compliance under the load direction variation are represented efficiently through the quadratic Taylor series expansions with respect to the nominal loading state. Furthermore, the design sensitivity analyses of those stochastic characteristics to a topological variable are performed readily upon the quadratic Taylor expressions such that the explicit formulae are achieved without any extra implementations. Finally, the weighted sum of the mean and standard deviation of the dynamic structural compliance is accordingly defined as the objective function and the coefficient of variation of the dynamic compliance is introduced as the measurement of the structural robustness. Then the robust dynamic topology optimization can be performed with a gradient-based density approach on the RAMP (rational approximation of material properties) model. Both the robust and deterministic topology optimizations of two benchmark examples loaded with the harmonic excitation are conducted respectively, and the structural layouts are compared comprehensively. Numerical results show that the robust dynamic topology optimal configurations can essentially provide a higher robustness against the load direction disturbances than the corresponding deterministic ones and exhibit much stronger resilience. 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 variation range.