By Chandra A., Mukherjee S.

This publication specializes in research of producing techniques, and its integration into the layout cycle of those techniques utilizing the boundary aspect procedure (BEM) because the computational version of selection.

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128) by T (V) to get (Hill 1978) where (n • Vv), • = nk vk ,. 118) since they already contain T' V) . 130) appear, among other places, in Chen and Ji (1990). 118)] is sometimes referred to as "load correction" and is a consequence of the change in the area of a surface element and the rotation of a unit normal, at a point on it, during the large-deformation process. 1 18). 118). This matter is discussed further later in this chapter. 89) in terms of velocity gradients, and dvjlds\ and dvjds-i are tangential derivatives of the velocity field at P along two surface directions given by the unit vectors j' 1 -* and t^2\ Once the velocity field is known, these tangential derivatives can PROBLEMS INVOLVING LARGE STRAINS AND ROTATIONS 43 be determined by suitably differentiating the shape functions for v on dB.

Its divergence with respect to reference coordinates gives the negative of the body force per unit reference volume, but written in the current basis. Similarly, its dot product with the reference normal gives the traction vector per unit reference surface area, but also in the current basis. This is because the "natural" bases for S involve a reference basis on the left and a current basis on the right! This fact becomes clear when some of these equations and variables are written in general tensor notation.

Closed-form expressions exist for the corner tensor Cjj for two-dimensional problems [see, for example, Mukherjee (1982)]. 6 Plane Stress Now, cr13 = cr23 = 0-33 = 0. 90),

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