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Assigned 3/20/14

FLORIDA INSTITUTE OF TECHNOLOGYMECHANICAL AND AEROSPACE ENGINEERING DEPARTMENT

MAE 3150: Aerospace Computational TechniquesSpring 2014

Homework 5Due April 3, 2014

1. Construct the weak form of the following linear equation. Identify the primary and secondary variables.

2

27 1 0 0 2

0 2 2 0

d ux

dx

u u

2. Construct the weak form of the following linear equation. Are the boundary conditions essential or natural?

2

2

2

0

0

0 0

x x L

d u

x f x x Ldx

du du

dx dx

3. Construct the weak form of the following nonlinear equation. Identify the BCs as either essential or natural.

0

0 0 1

0 1 2x

d duu f x

dx dx

duu udx

4. Construct the weak forms of the following nonlinear equations representing the Euler-Bernoulli-von Karman

nonlinear theory of beams:

2

22 2

2 2

2

2

0

10

2

1

2

0 at 0,

0, ox x L

d du dsEA f x L

dx dx dx

d d s d ds du dsEI a q

dx dx dx dxdx dx

u s x L

ds d sEI M

dx dx

Hint: Look at example 2.4.3 (pg. 502) in the text to see how to find the weak forms for a system of equations.

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Assigned 3/20/14

5. Using a 2-parameter (N= 2) approximation and algebraic polynomials for the basis functions, compute the Ritz

coefficients for the approximate solution to

1 0, 0 1

0 0, 1 1

d dux x

dx dx

u u

Ans: 55 201 2131 131,c c

6. Problem 2.8 in the text. (Page 533)

7. Problem 2.16 in the text. (Page 534)

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