Reliability-based topology optimization of continuum structures under uncertain harmonic excitations
WANG Xuan1,2，SHI Yuankun1，CHEN Xiang1，LONG Kai2
1.College of Civil Engineering, Hefei University of Technology, Hefei 230009, China; 2.School of Mechanical Engineering, Tianjin University, Tianjin 300072, China; 3.State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China
Abstract：An effective reliability-based topology optimization method is proposed for the design problem of continuum structure considering the uncertainty of load amplitude and frequency of harmonic excitation. A reliability design optimization model of minimizing structural volume ratio under probabilistic reliability constraint is established, in which the limit state function is the sum of the amplitude squares of the degrees of freedom concerned. The analytic sensitivity formulations of limit state function with respect to design variables and random variables are derived using adjoint variable method. The Performance Measure Approach (PMA) is used to achieve reliability analysis, and the method of moving asymptotes (MMA) is used to update design variables. Finally, three numerical examples and Monte Carlo simulation are tested to verify the effectiveness and stability of the proposed method for the design problem of continuum structure under uncertain harmonic excitation. The influences of the uncertainty of amplitude and frequency of harmonic excitation, reliability index, and coefficient of variations on the optimization results are also discussed.
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