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.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Thermal Properties of Materials

In mechanical engineering, the thermal property is represented as the physical quantity that is relevant to the application of heat. The thermal properties are evaluated by variations in any specific material due to low heat or high heat. The quantities that influence the thermal property of the materials are mass, density, temperature, and many others.

Question

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.
model fracture mechanics problem with the crack tip placed at the collapsed node.
The F6 element is used to
1) Derive x and y in terms of g 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 g and n for the F6 element.
3) Determine the variation of ɛxx and ɛyy along r. Check for singularity at the collapsed node.
y
y
7
(2,2)
(0,2)
8
6
7
O 5
1,4,6
r
2
1
3
3
(0,0)
(2,0)
F6
Q8

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