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Nodal sensitivities as error estimates in computational mechanics

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Summary

This paper proposes the use of special sensitivities, called nodal sensitivities, as error indicators and estimators for numerical analysis in mechanics. Nodal sensitivities are defined as rates of change of response quantities with respect to nodal positions. Direct analytical differentiation is used to obtain the sensitivities, and the infinitesimal perturbations of the nodes are forced to lie along the elements. The idea proposed here can be used in conjunction with general purpose computational methods such as the Finite Element Method (FEM), the Boundary Element Method (BEM) or the Finite Difference Method (FDM); however, the BEM is the method of choice in this paper. The performance of the error indicators is evaluated through two numerical examples in linear elasticity.

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Author notes

  1. G. H. Paulino

    Present address: School of Civil and Environmental Engineering, Cornell University, Hollister Hall, 14853, Ithaca, N. Y., USA

  2. F. Shi &  S. Mukherjee

    Present address: Department of Theoretical and Applied Mechanics, Cornell University, Kimball Hall, 14853, Ithaca, N. Y., USA

  3. P. Ramesh

    Present address: Joseph C. Wilson Center for Research and Technology, Xerox Corporation, 800 Phillips Road, 14580, Webster, N.Y., USA

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    1. G. H. Paulino
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    2. F. Shi
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    3. S. Mukherjee
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    4. P. Ramesh
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    Paulino, G.H., Shi, F., Mukherjee, S. et al. Nodal sensitivities as error estimates in computational mechanics. Acta Mechanica 121, 191–213 (1997). https://doi.org/10.1007/BF01262532

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