Designing robust structures – A nonlinear simulation based approach

https://doi.org/10.1016/j.compstruc.2007.05.037Get rights and content

Abstract

This paper presents a generally applicable numerical procedure for designing robust structures under uncertainty, which can be coupled with any arbitrary nonlinear computational model for statical or dynamic structural analysis. Based on the results from an uncertain structural analysis several permissible design domains are determined with the aid of cluster analysis methods instead of traditionally computing only one particular set of crisp design parameter values; these represent design alternatives. To identify a preference solution, a discrete three-criteria optimization problem is formulated, which is focused on maximum structural robustness and includes a safety component. A measure for the global robustness of the design alternatives is introduced based on an analog to Shannon’s entropy. The goal of the resulting design is that the structural behavior is only marginally affected by uncertainty and by changes in the design parameters, which further provides comfortable decision margins to the construction engineer.

The proposed procedure is demonstrated by means of a numerical example and of an example from engineering practice in vehicle crashworthiness design.

Section snippets

Problem specification

Robustness is one of the primary requirements to ensure a structure to operate faultless over a period of time and must thus be incorporated in the design process, already. This involves, on one hand, accounting for considerable uncertainty in the problem specification and, on the other hand, appropriately assessing the robustness of a structure.

For the robustness of a structure no general definition exists. In the past decades two different points of view have been developed regarding the

Robustness assessment

Robust structural design generally aims at an optimum adjustment of the design parameters with respect to defined design preferences for the mean and regarding fluctuations of structural responses. The method proposed herein focuses on the latter, which refers to structural robustness. Structural robustness is introduced as a global measure for the degree of independence between changes in the whole set of structural parameters and the associated fluctuations in structural responses. This

General scheme

The general scheme of designing robust structures may be summarized with the flowchart in Fig. 2. The particular procedure components are elucidated in the following subsections. Some background information regarding the employed numerical methodologies is provided in Appendix A.

Initial situation

The procedure of robust structural design starts with the specification and the quantification of all structural and design parameters. At this point a distinction is made between two types of uncertain input parameters

Steel girder under dynamic loading

The procedure of designing robust structures is demonstrated by means of the simple steel girder shown in Fig. 9. The girder is excited to vibrate by a harmonic loading that consists of two components. This affects node 1 transverse to the bar axis and causes time-dependent displacements v(1, t) in load direction and rotations φ(1, t) of this node, which are summarized in the displacement vectorv̲(1,t)=v(1,t)φ(1,t).A displacement norm is then calculated with v(1, t) in m and φ(1, t) in rad and with

Conclusions

The presented method for designing robust structures may provide a viable tool to derive a proper structural design. It is capable of processing the results from any uncertain structural analysis and is independent of the computational model. In the result the construction engineer is provided with design parameter ranges, from which the final design vector can be selected in view of subjective preferences without a need for additional verifications by structural analysis. In contrast to the

Acknowledgements

The authors gratefully acknowledge the support of the German Research Foundation (DFG).

References (58)

  • I. Doltsinis et al.

    Robust design of structures using optimization methods

    Comput Methods Appl Mech Eng

    (2004)
  • B. Rai et al.

    Robust design of an interior hard trim to improve occupant safety in a vehicle crash

    Reliab Eng Syst Safety

    (2005)
  • Y.K. Wen

    Reliability and performance-based design

    Struct Safety

    (2001)
  • R.O. Foschi et al.

    Reliability and performance-based design: a computational approach and applications

    Struct Safety

    (2002)
  • J. Zhang et al.

    Performance-based design and seismic reliability analysis using designed experiments and neural networks

    Probab Eng Mech

    (2004)
  • S. Saha et al.

    Inverse reliability based structural design for system dependent critical earthquake loads

    Probab Eng Mech

    (2005)
  • J.O. Royset et al.

    Reliability-based optimal design using sample average approximations

    Probab Eng Mech

    (2004)
  • S.K. Au

    Reliability-based design sensitivity by efficient simulation

    Comput Struct

    (2005)
  • B. Möller et al.

    Engineering computation under uncertainty – capabilities of non-traditional models

    Comput Struct

    (2008)
  • Y. Ben-Haim

    Uncertainty, probability and information-gaps

    Reliab Eng Syst Safety

    (2004)
  • F.T.K. Au et al.

    Robust design of structures using convex models

    Comput Struct

    (2003)
  • C.M. Rocco et al.

    Robust design using a hybrid-cellular-evolutionary and interval-arithmetic approach: a reliability application

    Reliab Eng Syst Safety

    (2003)
  • L. Zadeh

    Fuzzy sets

    Information Control

    (1965)
  • W.L. Oberkampf et al.

    Error and uncertainty in modeling and simulation

    Reliab Eng Syst Safety

    (2002)
  • E.H. Ruspini

    A new approach to clustering

    Informat Control

    (1969)
  • J.C. Bezdek et al.

    FCM: The fuzzy c-means clustering algorithmn

    Comput Geosci

    (1984)
  • F. Knoll

    Risk, structural engineering and human error

    (1984)
  • M. Pötzl et al.

    Robust concrete bridges without bearings and joints

    Struct Eng Int (IABSE)

    (1996)
  • Harding G. Robustness: A historical perspective and the future – a regulators view. In: Workshop on Robustness of...
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