The simulation-based design of nonlinear systems is hampered by several hurdles such as high CPU times, the difficulty to evaluate gradients, and the acute sensitivity of responses to loading and design uncertainties. In addition, the system's responses might be discontinuous due to the presence of numerous limit and bifurcation points. This considerably limits the blind use of traditional optimization and probabilistic methods. Typical examples of problems with discontinuous behaviors are structural impacts and nonlinear aeroelasticity with limit cycle oscillations (LCO).

This seminar will describe a methodology which facilitates the probabilistic (optimal) simulation-based design of nonlinear problems. The approach, referred to as explicit design space decomposition, is based on data mining and machine learning techniques. The main feature of this approach lies in the explicit definition of limit state functions (or constraints) constructed from a design of experiments (DOE). A method to adaptatively update the limit state function and refine the DOE will be presented.

Several test examples will demonstrate the efficiency of the approach in the case of the reliability-based optimization of nonlinear structures and LCO problems.