Multi-Level Optimization of Material and Structural Layout

AJ de Wit, A Lipka, E Ramm, F van Keulen

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review


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.
Original languageUndefined/Unknown
Title of host publicationProceedings of the 3rd European Conference on Computational Mechanics, Lisbon, Portugal
Editors Mota Soares, C.A.
Place of PublicationDordrecht
Number of pages18
ISBN (Print)9781402049941
Publication statusPublished - 2006
Event3rd European Conference on Computational Mechanics - Lisbon, Portugal
Duration: 5 Jun 20069 Jun 2006

Publication series



Conference3rd European Conference on Computational Mechanics
Abbreviated titleECCOMAS CSMM 2006


  • conference contrib. refereed
  • Conf.proc. > 3 pag

Cite this

de Wit, AJ., Lipka, A., Ramm, E., & van Keulen, F. (2006). Multi-Level Optimization of Material and Structural Layout. In Mota Soares, C.A. (Ed.), Proceedings of the 3rd European Conference on Computational Mechanics, Lisbon, Portugal (pp. 1-18). Springer.