ABSTRACT
With the ever-increasing complexities in engineering applications, it is almost impossible to obtain the exact analytical solutions. As a consequence, numerical methods have been widely employed taking advantage of modern supercomputers and parallel computing. Such a computational or simulation tool functions as a black box that generates a set of output (or responses) for a given set of input (or design variables) without knowing the explicit input-output relationships. By combining a simulation tool with some mathematical procedure, optimization can be carried out to improve the system design. Th is simulation-based design optimization has been seen in a wide range of engineering applications. However, for many large-scale simulations such as dynamic contact problems (e.g., crash), the computational cost is still high even with parallel computing and supercomputers. Th is makes it very diffi cult to perform simulation-based design optimization, because an optimization procedure typically requires hundreds
or even millions of simulation runs. It is highly desirable to have explicit functions that are both inexpensive and accurate for the input-output relationships to replace the computational tool. Th is leads to the wide adoption of the metamodeling approach.
