Abstract
A discrete model of a deformable elastic body in the form of an oriented graph is examined. The graph can be used as a nontraditional means of deriving resolvent equations, involving the transformation of systems of generalized coordinates describing elements of the sectioned body to a coordinate system that describes the body as a whole. It is shown that graphing (vertex and loop) laws can be interpreted as equilibrium and strain compatibility conditions that in the limit become the corresponding differential equations. With the use of a unit cell having eight degrees of freedom, the strain field is approximated by linear polynomials (which corresponds to approximation of the displacement fields by quadratic polynomials). The standard finite-element method requires 16 degrees of freedom (elements with eight nodes) for the same purpose. The proposed graphical approach thus reduces the number of equations that describe the model and the time and amount of memory needed to obtain a solution.
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Translated from Problemy Prochnosti, No. 12, pp. 60–70, December, 1993.
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Kuzovkov, E.G. Graphical model of an elastic medium in a cartesian coordinate system. Strength Mater 25, 906–914 (1993). https://doi.org/10.1007/BF00774638
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DOI: https://doi.org/10.1007/BF00774638