The nodal coordinates and the nodal displacements for some plane stress elastic element is listed in the following problem. The element is 0.1 m thick. The coordinates and displacements are given in meters. (a) Calculate K(1,1) of the element stiffness matrix (b) Calculate the element stress 01 16 0 (N/m²) 6] [16 4 D = 106 4 1 N =(a, + bịx + 1y) 2A 1 N2 = (az + bzx + czy) 2A 1 N3 = (az + b3x + C3y) 2A bị = y2 - y3 %3D C1 = X3 - X2 C2 = x1 - X3 C3 = X2 - X1 a1 = x2y3 – x3Y2 %3D b2 = y3 - Yı %3D a2 = X3y1 – X1Y3 %3D az = X1y2 - X2y1 b3 = y1 - Y2 X2 = 1 Y2 = 1 v2 = 0.001 X1 = 2 X3 = 1 Y1 = 2 U1 = 0.003 Y3 = 0 Uz = 0.0015 V1 = 0 v2 = -0.003 Vz = 0.0 %3D

The nodal coordinates and the nodal displacements for some plane stress elastic element is listed in the following problem. The element is 0.1 m thick. The coordinates and displacements are given in meters. (a) Calculate K(1,1) of the element stiffness matrix (b) Calculate the element stress 01 16 0 (N/m²) 6] [16 4 D = 106 4 1 N =(a, + bịx + 1y) 2A 1 N2 = (az + bzx + czy) 2A 1 N3 = (az + b3x + C3y) 2A bị = y2 - y3 %3D C1 = X3 - X2 C2 = x1 - X3 C3 = X2 - X1 a1 = x2y3 – x3Y2 %3D b2 = y3 - Yı %3D a2 = X3y1 – X1Y3 %3D az = X1y2 - X2y1 b3 = y1 - Y2 X2 = 1 Y2 = 1 v2 = 0.001 X1 = 2 X3 = 1 Y1 = 2 U1 = 0.003 Y3 = 0 Uz = 0.0015 V1 = 0 v2 = -0.003 Vz = 0.0 %3D

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Concept explainers

Strain energy

The term strain indicates the variation in an object's length, area, and volume when the object is subjected to an external force. The external force may be of normal, shear, moment, torque, etc. The strain in an object depends on the types of external force and cross-section of the object. Mathematically, the evaluation of strain can be obtained with the help of elastic constants.

Question

The nodal coordinates and the nodal displacements for some plane stress elastic
element is listed in the following problem. The element is 0.1 m thick. The coordinates and
displacements are given in meters.
(a) Calculate K(1,1) of the element stiffness matrix
(b) Calculate the element stress
[16
D = 106| 4
4
01
16 0 (N/m²)
61
1
N1 = (a1 + bịx+ Cy)
2A
1
N2 =
2A
-(a2 + b2x + c2y)
1
Na =
(az + bzx + C3y)
2A
b1 = y2 - y3
a1 = X2y3 - X3y2
a2 = X3y1 - X1y3
C1 = X3 – X2
C2 = X1 – X3
C3 = X2 - X1
b2 = y3 - Yı
az = X1y2 - X2y1
b3 = y1 - Y2
X1 = 2
X2 = 1
X3 = 1
y2 = 1
v2 = 0.001
Y1 = 2
Y3 = 0
U1 = 0.003
Uz = 0.0015
V1 = 0
v2 = -0.003
v3 = 0.0

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