A region on the surface of a body including a Point P is subjected to a...

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A region on the surface of a body including a Point P is subjected to a pressure of 200 psi. At Point P the surface normal is given by 27+10+11k Calculations show that the stress state at Point P is given by 20000 3000 -6400 Op = 3000 - 3000 2000 psi -6400 2000 -854.546, Could this calculated stress state be correct?... Does this stress state satisfy the given pressure boundary condition? To receive credit, support you answer with calculations. Note: Use the methods given in class (e.g. do not use an Eigenvalue-Eigenvector approach). - Surface normal 2^ + 3JT15 200 psi pressure Problem 3 Calculate the nine 3D strain values and the six 3D rigid-body rotation values given the displacements below Ux=Cxx z Uy = Cyx y U = Cz-y Problem 4 (a) Does the matrix given below represent a valid strain tensor? Show mathematically why or why not. (0.2 y2 0 0\ 0 -0.2x 0 0 0 (b) Regardless of your answer to part (a), illustrate the displacement field UX and Uy by showing a deformed and undeformed square mesh as done in lecture. (c) Comment on the angles between the deformed gridlines. Are the angles consistent with the Shear Strain value given in the matrix of part (a)? Problem 5: Beginning with the 3D Navier Equation, (A+)vdivu+uvu+p=0, show that the correct simplified form for Plane Stress Problem 5: Beginning with the 3D Navier Equation, (A+) Vdivu+pvu+p = 0, show that the correct simplified form for Plane Stress conditions is given by where E 2(1-v) ax \ax E a auy + ay ( 2 (1-v) ay (aux + Buy ) + Uy +Py = 0 ay V = (+) [10 pts] ax A region on the surface of a body including a Point P is subjected to a pressure of 200 psi. At Point P the surface normal is given by 27+10+11k Calculations show that the stress state at Point P is given by 20000 3000 -6400 Op = 3000 - 3000 2000 psi -6400 2000 -854.546, Could this calculated stress state be correct?... Does this stress state satisfy the given pressure boundary condition? To receive credit, support you answer with calculations. Note: Use the methods given in class (e.g. do not use an Eigenvalue-Eigenvector approach). - Surface normal 2^ + 3JT15 200 psi pressure Problem 3 Calculate the nine 3D strain values and the six 3D rigid-body rotation values given the displacements below Ux=Cxx z Uy = Cyx y U = Cz-y Problem 4 (a) Does the matrix given below represent a valid strain tensor? Show mathematically why or why not. (0.2 y2 0 0\ 0 -0.2x 0 0 0 (b) Regardless of your answer to part (a), illustrate the displacement field UX and Uy by showing a deformed and undeformed square mesh as done in lecture. (c) Comment on the angles between the deformed gridlines. Are the angles consistent with the Shear Strain value given in the matrix of part (a)? Problem 5: Beginning with the 3D Navier Equation, (A+)vdivu+uvu+p=0, show that the correct simplified form for Plane Stress Problem 5: Beginning with the 3D Navier Equation, (A+) Vdivu+pvu+p = 0, show that the correct simplified form for Plane Stress conditions is given by where E 2(1-v) ax \ax E a auy + ay ( 2 (1-v) ay (aux + Buy ) + Uy +Py = 0 ay V = (+) [10 pts] ax