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Nonlinear reanalysis for structural modifications based on residual increment approximations

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Abstract

This paper presents a reanalysis method for nonlinear problems. The main objective is to predict the changes in the state variables due to given design modifications, e.g. changes in the cross-sections, the geometry, material parameters etc. The approach is based on residual increment approximations, which are used within an iterative algorithm. The reanalysis method requires only the evaluation of residual vectors, which can be done very fast and efficient. Moreover, the validity of the approach is extended by using a rational approximation method. In contrast to other existing reanalysis methods, which are based on the evaluation of changed stiffness matrices, only residual vectors have to be computed and stored. The approach is general and can be applied to linear and nonlinear problems with different kind of design modifications. Furthermore, the proposed reanalysis method is easy to implement in existing finite element programs, because no derivatives with respect to the design variables are necessary. The capability of the proposed framework is demonstrated by means of several computational examples from nonlinear elasticity.

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Acknowledgments

The authors gratefully acknowledge the support of this work by the German Research Foundation (DFG) under grant number MA 4004/3-1.

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Authors and Affiliations

  1. Department of Civil Engineering, Ostwestfalen-Lippe University of Applied Sciences, 32756, Detmold, Germany

    Daniel Materna

  2. Department of Materials Science & Engineering, University of Ioannina, 45110, Ioannina, Greece

    Vassilios K. Kalpakides

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  1. Daniel Materna
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  2. Vassilios K. Kalpakides
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Correspondence to Daniel Materna.

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Materna, D., Kalpakides, V.K. Nonlinear reanalysis for structural modifications based on residual increment approximations. Comput Mech 57, 1–18 (2016). https://doi.org/10.1007/s00466-015-1209-3

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  • DOI: https://doi.org/10.1007/s00466-015-1209-3

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