Subject: FINITE ELEMENT ANALYSIS Given the quadragonal element for plane stress.(5,4)(1,3)(0,1)(6,0)(a) Introduce a "parent domain" bounded by the lines & = ±l and 7= +1. Usethe shape functions fromlectures or textfrom parent domain to global domain and show that the mapping is unique.to find a mapping x = x(§, n) and y = y(£,7(b) Move node 4 to position (3,2) and show that in this case the mapping is notunique.(c) a surface element dA can be written as:dA = detJ df dnDetermine which (r,y) correspond to (6,7) = (-0.8, 0.8) and (§, n)(0.8, -0.8). Then determine det J at these points. What does det J ex-press?

Answered: Image /qna-images/answer/cf41f721-e50f-4043-83c0-e352373046a1.jpg

Given the quadragonal element for plane stress. (5,4) (1,3) (0,1) 2 (6,0) (a) Introduce a "parent domain" bounded by the lines &=±1 and 7= +1. Use the shape functions fromlectures or text from parent domain to global domain and show that the mapping is unique. to find a mapping z = r(§,n) and y =y(§,7 %3D (b) Move node 4 to position (3,2) and show that in this case the mapping is not unique. (c) a surface element dA can be written as: dA = detJ df dn Determine which (x,y) correspond to (5,7) = (-0.8, 0.8) and (6, n) = (0.8, -0.8). Then determine det J at these points. What does det J ex- press?

Given the quadragonal element for plane stress. (5,4) (1,3) (0,1) 2 (6,0) (a) Introduce a "parent domain" bounded by the lines &=±1 and 7= +1. Use the shape functions fromlectures or text from parent domain to global domain and show that the mapping is unique. to find a mapping z = r(§,n) and y =y(§,7 %3D (b) Move node 4 to position (3,2) and show that in this case the mapping is not unique. (c) a surface element dA can be written as: dA = detJ df dn Determine which (x,y) correspond to (5,7) = (-0.8, 0.8) and (6, n) = (0.8, -0.8). Then determine det J at these points. What does det J ex- press?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

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Subject: FINITE ELEMENT ANALYSIS

Given the quadragonal element for plane stress.
(5,4)
(1,3)
(0,1)
(6,0)
(a) Introduce a "parent domain" bounded by the lines & = ±l and 7= +1. Use
the shape functions fromlectures or text
from parent domain to global domain and show that the mapping is unique.
to find a mapping x = x(§, n) and y = y(£,7
(b) Move node 4 to position (3,2) and show that in this case the mapping is not
unique.
(c) a surface element dA can be written as:
dA = detJ df dn
Determine which (r,y) correspond to (6,7) = (-0.8, 0.8) and (§, n)
(0.8, -0.8). Then determine det J at these points. What does det J ex-
press?

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