Problem 4: In the Figure shown, the Q8 element has equally-spaced nodes. The nodes 1, 4, 6 of the Q8 element are collapsed into one node; and nodes 7 and 2 are moved towards the collapsed node at a distance equal to one fourth the length of the element sides 1-8 and 1-3 to form an F6 element, as shown below. The F6 element is used to model fracture mechanics problem with the crack tip placed at the collapsed node. 1) Derive x and y in terms of and n for the Q8 element where and n are coordinates of the master element. 2) Modify and derive x and y in terms of and n for the F6 element. η 3) Determine the variation of Exx and Eyy along r. Check for singularity at the collapsed node.

Problem 4: In the Figure shown, the Q8 element has equally-spaced nodes. The nodes 1, 4, 6 of the Q8 element are collapsed into one node; and nodes 7 and 2 are moved towards the collapsed node at a distance equal to one fourth the length of the element sides 1-8 and 1-3 to form an F6 element, as shown below. The F6 element is used to model fracture mechanics problem with the crack tip placed at the collapsed node. 1) Derive x and y in terms of and n for the Q8 element where and n are coordinates of the master element. 2) Modify and derive x and y in terms of and n for the F6 element. η 3) Determine the variation of Exx and Eyy along r. Check for singularity at the collapsed node.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter8: Applications Of Plane Stress (pressure Vessels, Beams, And Combined Loadings)

Section: Chapter Questions

Problem 8.2.8P: A spherical steel pressure vessel (diameter 500 mm, thickness 10 mm) is coated with brittle lacquer...

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