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Shakedown analysis with multidimensional loading spaces

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Abstract

A numerical method for the computation of shakedown loads of structures subjected to varying thermal and mechanical loading is proposed for the case of multidimensional loading spaces. The shakedown loading factors are determined based on the lower bound direct method using the von Mises yield criterion. The resulting nonlinear convex optimization problem is solved by use of the interior-point method. Although the underlying theory allows for the consideration of arbitrary numbers of loadings in principle, until now applications have been restricted to special cases, where either one or two loads vary independently. In this article, former formulations of the optimization problem are generalized for the case of arbitrary numbers of loadings. The method is implemented into an interior-point algorithm specially designed for this method. For illustration, numerical results are presented for a three-dimensional loading space applied to a square plate with a central circular hole.

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  1. Institute of General Mechanics, RWTH Aachen University, Templergraben 64, 52056, Aachen, Germany

    Jaan-Willem Simon & Dieter Weichert

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  1. Jaan-Willem Simon
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  2. Dieter Weichert
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Correspondence to Jaan-Willem Simon.

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Simon, JW., Weichert, D. Shakedown analysis with multidimensional loading spaces. Comput Mech 49, 477–485 (2012). https://doi.org/10.1007/s00466-011-0656-8

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