Implementation of combined approximations in structural optimization

Some approximation concepts, intended to reduce the computational effort during optimization of structural systems, are presented. High quality approximations of the response functions are introduced and used to evaluate both the constraint values and constraint derivatives. The various approximations are then integrated into an effective procedure for structural optimization. The solution is carried out by selecting a sequence of direction vectors in the design space. For each selected direction, optimization is carried out in a corresponding two-dimensional design plane, with only a single independent variable. As a result, the number of directions needed to reach the optimum, and the overall computational effort involved in the solution process are significantly reduced. Assuming second-order approximations in some typical examples, it has been found that only two to three exact analyses are needed to achieve the optimum. Moreover, for higher-order approximations, a single exact analysis is sufficient for the whole design process.