Problem 4-1: Working with Airy's Stress Function. A brass-strip and a steel strip are perfectly bonded...

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Problem 4-1: Working with Airy's Stress Function. A brass-strip and a steel strip are perfectly bonded at the interface. The composite strip is straight at 20 C. max p = 6M H2 L x H 6M max p = H2 Figure 1: Loading of a plate subjected to constant end-moments. Proposing the following form or Airy's stress function F(x, y) = ax + a2xy + 3y + 4xy + 5xy+a6x + a7y + a8xy + a9xy 1. Show that F(x, y) satisfies the bi-harmonic equation, AAF = 0. 2. Express the stress state based on this function, F(x, y). 3. Use the boundary conditions to identify the coefficients ak, k = 1, 2, ..., 9. 4. Express the final stress state based on this function, F(x, y), and compare the solution to a beam of length L subjected to equal magnitude but opposite orientation end moments, M. 5. Is the beam solution for this problem an exact solution of the 2D problem? (Yes or No). Justify your answer in one sentence. Problem 4-1: Working with Airy's Stress Function. A brass-strip and a steel strip are perfectly bonded at the interface. The composite strip is straight at 20 C. max p = 6M H2 L x H 6M max p = H2 Figure 1: Loading of a plate subjected to constant end-moments. Proposing the following form or Airy's stress function F(x, y) = ax + a2xy + 3y + 4xy + 5xy+a6x + a7y + a8xy + a9xy 1. Show that F(x, y) satisfies the bi-harmonic equation, AAF = 0. 2. Express the stress state based on this function, F(x, y). 3. Use the boundary conditions to identify the coefficients ak, k = 1, 2, ..., 9. 4. Express the final stress state based on this function, F(x, y), and compare the solution to a beam of length L subjected to equal magnitude but opposite orientation end moments, M. 5. Is the beam solution for this problem an exact solution of the 2D problem? (Yes or No). Justify your answer in one sentence.