Identify the primary and secondary variables

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

723_Construct the linear equation.png

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

166_Construct the linear equation1.png

3. Construct the weak form of the following nonlinear equation. Identify the BC's as either "essential" or "natural."

944_Construct the linear equation2.png

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

1737_Construct the linear equation3.png

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.

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

1548_Construct the linear equation4.png

Reference no: EM13699566

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