An equivalent loads method for non-probabilistic reliability-based topology optimization of geometrically nonlinear structures

摘要

A novel method for geometrically nonlinear non-probabilistic reliability-based topology optimization is proposed based on equivalent loads for uncertainties. Different from the original definition of equivalent loads, the equivalent loads are redefined to consider geometrically nonlinearities and uncertainties. In the new definition, equivalent loads for uncertainties can generate the same interval displacement response field in linear static analysis as actual loads of nonlinear static analysis. Based on the interval non-probabilistic reliability index, the linear reliability optimization model is formulated using the new equivalent loads for uncertainties. In order to avoid directly solving the nested double-loop reliability optimization problem, the performance measure approach is utilized to convert constraints on the reliability index into constraints on the concerned performance. A couple of standard examples are presented to validate the proposed method.