ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
The NONSS method for numerically integrating time-dependent constitutive equations requires evaluation of the partial derivatives of the constitutive equations. A numerical method for evaluating these partial derivatives has been developed, thus avoiding the cumbersome task of analytically re-deriving the partial derivatives when improvements to the constitutive model are evaluated. This method is based upon the adaptive finite-difference algorithm published by Stepleman and Winarsky. Modifications of their algorithm are described that allow its efficient use within an extended version of NONSS, called NONSS-ND.Using the MATMOD constitutive equations, the capabilities of NONSS-ND are demonstrated by comparing the results of a wide variety of deformation simulations with those of NONSS, for which the derivatives are computed from analytical solutions. The numerical differentiation within NONSS-ND is shown to be sufficiently accurate for use in integrating time-dependent constitutive equations, but results in a 30-100 per cent increase in computation time. Multi-element structural calculations are therefore found to be uneconomical, but NONSS-ND is well suited for testing alternative constitutive models owing to its accuracy and its general applicability to highly non-linear systems of differential equations.
Additional Material:
11 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620280509
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