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Finite Element Analysis Assignment 6
- Obtain an approximate solution of the following boundary value problem using two linear
triangular element as shown in the following figure. 2 2 2 2 4 0 2 0 1
T T (^) x , y x y with the boundary conditions: along 1-2: T = 2 along the other boundaries: T n 2.
- Obtain an approximate solution of the following boundary value problem using two linear
triangular elements as shown in the following figure. 2 2 2 2 1 0 0 1 0 0 5
x , y. x y with the boundary conditions
∂ψ/∂y = 0 on C 1 ψ = 0 on C 2 and C 3
∂ψ/∂x = 0 on C 4
- Obtain an approximate solution of the following boundary value problem using two linear
triangular elements as shown in the following figure. 2 2 2 2 2 2 4 0 0 1 0 1
^
u u (^) x y x , y x y For non-constant coefficients, use values at element centroids as constant average values for
the entire element with boundary conditions
(^21) (^24) (^32) (^33)
on on 2 2 on 2 2 on
u x C u y C u x y y C u y x x C
- Obtain an approximate solution of the following boundary value problem using two linear
triangular elements as shown in the following figure. 2 2 2 2 4 10 0
T T T
x y with the boundary conditions: along 1-2: T = 2 along the other two boundaries: T n 2 T.
- For the element shown in the following figure, the solution at the nodes is given as follows:
T 0 10 20 0 0 50 0 0 T
Compute the solution and its x and y derivatives at the point 1 , 1 . The nodal coordinate
vectors are as follows:
T n T n
X
Y
- Evaluate matrices (^) p ^ T A
k P NN dA and vector 2
^
S
r N dS for the element in
Problem 7. Assume P = 2 and = 2 resulting from a natural boundary condition on side 5 6 7. Use 33 integration. Show complete calculations for at least one Gauss point.
- The state of stress at a point is given as follows:
2 2 2 2 2 2 2 2 ( , ) 0
xx yy zz xy yz xz
y c x y x c y x x y f x y
Determine f ( , x y ) so that the stress distribution may be in equilibrium in the absence of body forces.
- Develop a deformation field u x y ( , ) , v x y ( , ) that describe the deformation of the finite
element shown in the following figure. From this determine x , y , xy. Interpret your
answer.
- Compute stresses and strains at a point located at (2,2) for the problem shown in the
following figure, using only one quadrilateral element. Assume plane strain conditions. E = 20.6842GPa, = 0.25, thickness = 0.0254 m.
(0, 0) (5, 0)
(0, 10) (5, 10)
(4, 0) (9, 0)
(5, 10) (10, 10)
