Some contributions to optimal design using explicit behaviour models

TLDR: For shape optimal design it is attempted to utilize the simple and efficient Lagrangian interpolation schemes and to restrict spline interpolation to the movable boundaries.

Abstract: The design of a strictly modular and flexible system for structural optimization is discussed. OPTIMA 2.0 uses advanced design oriented concepts and is provided for linear and nonlinear structural behaviour. For shape optimal design it is attempted to utilize the simple and efficient Lagrangian interpolation schemes and to restrict spline interpolation to the movable boundaries. A simple interpolation scheme for sizing variables allows the simultaneous handling of sizing and shaping. Some approximation models for the explicit approximation of implicit constraint functions are discussed and evaluated. The realm of this models is extended by introducing an exponential hybrid scheme. Applications are presented in shape optimal design. Objectives are minimum weight as well as minimum stress. Some special aspects of the minimum stress problem are discussed.