A square domain is modeled using either one bilinear rectangular element or two lin. triangular elements as shown below. a) Determine the system element matrix for the Laplace equation for each discr- b) Determine the displacement at the center of the domain (0.5,0.5) in terms of displacement. Hint: You need to assemble the stiffness matrix for the system on the right to form a from the two 3*3 element matrices. 1.0 4 1.0 4 3.

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Chapter4: Numerical Analysis Of Heat Conduction
Section: Chapter Questions
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A square domain is modeled using either one bilinear rectangular element or two linear
triangular elements as shown below.
a) Determine the system element matrix for the Laplace equation for each discretization.
b) Determine the displacement at the center of the domain (0.5,0.5) in terms of the nodal
displacement.
Hint: You need to assemble the stiffness matrix for the system on the right to form a 4*4 matrix
from the two 3*3 element matrices.
y
1.0
4
1.0
4
3
(3
1
2
X.
1.0
1.0
Transcribed Image Text:A square domain is modeled using either one bilinear rectangular element or two linear triangular elements as shown below. a) Determine the system element matrix for the Laplace equation for each discretization. b) Determine the displacement at the center of the domain (0.5,0.5) in terms of the nodal displacement. Hint: You need to assemble the stiffness matrix for the system on the right to form a 4*4 matrix from the two 3*3 element matrices. y 1.0 4 1.0 4 3 (3 1 2 X. 1.0 1.0
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