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prob_14_02_01 - (c The element is axisymmetric and[k is...

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Problem 14.2-1 Given: In Fig. 6.8-1, dashed lines represent displaced positions of a four-node bilinear element. If the element is axisymmetric rather than plane, x represents the radial direction and y is parallel to the axis of revolution (not shown). Which of the eight displacement modes are associated with zero strain energy in the element and which are not? Answer for each of the following situations. (a) The element is plane and [k] is integrated by one Gauss point. (b) The element is plane and [k] is integrated by four Gauss points.
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Unformatted text preview: (c) The element is axisymmetric and [k] is integrated by one Gauss point. (d) The element is axisymmetric and [k] is integrated by four Gauss points. Solution: zero strain energy modes nonzero strain energy modes (a) Plane element, 1 Gauss point 1, 2, 3, 7, 8 4, 5, 6 (b) Plane element, 4 Gauss points 1, 2, 3 4, 5, 6, 7, 8 (c) Axisymmetric element, 1 Gauss point 1, 3, 7, 8 2, 4, 5, 6 (d) Axisymmetric element, 4 Gauss points 1 2, 3, 4, 5, 6, 7, 8...
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