ABSTRACT
The mass of a grid-point is calculated by summing the contributions from the surrounding zones. Hence, for a typical patch of zones (Fig. 5), the mass mg lumped at the common grid-point C is given by
in which the bracketed, superscripted letters refer to the adjoining zones. The establishment of the mass distribution scheme fixes the summation path in the momentum equation (eqn (21)). Conceptually, this path passes through the mid-points of the adjacent zone edges and the centres of mass of the surrounding zones (Fig. 7). In fact, because the stresses in each zone are assumed to be uniform, the actual path followed through
FIG. 7. Derivation of grid-point mass and summation path for force balance. (From Last and Harkness, 1989.)
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each individual zone is numerically unimportant — the main consideration is the points at which the path crosses into the next zone. To be consistent with the mass distribution, the mid-side points must be used, giving the numerically equivalent summation path indicated in Fig. 7. In applying eqn (21), the stress acting on each segment of the path is assumed to be equal to the uniform stress in the corresponding zone.
