Download e-book for iPad: A course in continuum mechanics Vol. I Basic equations and by L. I. Sedov, J. R. M. Radok

By L. I. Sedov, J. R. M. Radok

ISBN-10: 900179680X

ISBN-13: 9789001796808

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Extra info for A course in continuum mechanics Vol. I Basic equations and analytical techniques

Example text

8] F. B. Belgacem, P. Hild, and P. Laborde: Mathl. Comput. Modelling, Vol. 28 (1998), p. 263. [9] P. Hild: Comp. Meth. Appl. Mech. , Vol. 184 (2000), p. 99. [10] T. W. McDevitt and T. A. Laursen: Int. J. Num. Meth. Engng, Vol. 48 (2000), p. 1525. [11] M. A. Puso and T. A. Laursen: Comp. Meth. Appl. Mech. , Vol. 193 (2004), p. 601. [12] K. A. Fisher and P. Wriggers: Comput. , Vol. 36 (2005), p. 226. [13] B. I. Wohlmuth: SIAM Journal on Numerical Analysis, Vol. 38 (2000), p. 989. [14] B. Flemisch, M.

Normal direction: unilateral contact law In the normal direction, the contact problem is governed by the non penetration condition. This kinematic condition imposes that the gap between the contacting surfaces must remain always positive (then we say there is a separation situation) or zero (corresponding to a contact situation). Instead of using the gap variable to formulate the normal contact we will use the normal penetration kn , the same variable but with its sign changed. To quantify the normal penetration, we calculate the relative vector between two particles and project it on the contact frame normal kn = (X − y) · n (5) magnitude that must remain always negative in separation, or equal to zero in contact.

5 that is discretized using a regular mesh of 96 quadrilateral boundary elements and 98 nodes, see Figure 13. 5, is approximated using 20 quadrilateral boundary elements and 25 nodes. 25 between them. Displacement boundary conditions are imposed on the top face of the block. 005(1 − t) is applied for t ≥ 1. Normal and tangential tractions under the block for different time steps are also represented in Figure 13. In the solution for t = 1, when no lateral displacement exists, the outside corners of the block experience nearly singular stresses that are damped by the coarse mesh used.

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A course in continuum mechanics Vol. I Basic equations and analytical techniques by L. I. Sedov, J. R. M. Radok


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