Multi-Level Optimization of Material and Structural Layout

Within the classical design of, for example, bridges and airplane structures, optimization approaches generally focus primarily on adjusting large-scale (macroscopic) parameters and are therefore neglecting the influence of small-scale (microscopic) parameters on the large-scale behavior. The main reason is because of numerical efficiency. In literature various multi-level optimization appproaches are described in which six main approaches can be distinguished, Optimization by Linear Decomposition, Collaborative Optimization, Concurrent SubSpace Optimization, Bi-Level Integrated System Synthesis, Analytical Target Cascading and the method of Quasi-separable Subsystem Decomposition. This paper provides an overview of these methods, where the main interest lies in how these methods handle coupled analysis between the levels of the hierarchy. In this paper a multi-level notation is introduced, in order to make a clear distinction between the aspects of optimization and analysis of multi-level design. It emphasizes the handling of inconsistencies between subsystems and their solution. The proposed notation enables a clear comparison of the multi-level methods on the basis of their treatment of interdisciplinary consistency contraints. Furthermore, the multi-level optimization framework is illustrated for structural optimization by applying the notations to a classical two bar truss example. The work here is part of a larger ongoing effort towards integrating multi-scale mechanics and multi-level optimization. The two bar truss example is in this context a suited example. It contains relevant characteristics of multi-scale mechanics and multi-level optimization and its simplicity helps to capture the essence of multi-level design approaches. In future work we aim to describe multi-scale mechanics in a similar fashion, which is expected to open up possibilities of exploiting synergy effects through further integration of the two formulations.