Consider the three-dimensional isotropic linear elastic plate subjected to applied tractions po 0 and a...
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Consider the three-dimensional isotropic linear elastic plate subjected to applied tractions po ≥ 0 and a temperature gradient AT as shown in Figure 1. The plate is restricted from movement in the x- and z-directions so that we may take u = 0, w = 0, and v = = v(y). We neglect body forces and we assume v(y = 0) = 0. Note: Parts 1, 2, and 3 (with the exception of 3.b) are independent and will be graded as such. 1. (20 points) Assuming isothermal conditions for now, i.e. AT = 0, determine the elastic field in the solid. In other words, solve the field equations for o, e, and vu everywhere inside the plate. 2. (20 points) Taking po = 0 and AT 0, solve the field equations for a, e, and v. 1 3. (35 points) Assume now that po #0 and AT # 0. (a) (20 points) Determine o, e, and v everywhere inside the plate. (b) (8 points) Verify that the results from parts 1, 2, and 3(a) satisfy the principle of superposition. (c) (7 points) Predict the pressure po that will cause yield using the von Mises yield criterion for E = 107 psi, v= 1/3, AT = 100° F, - α = = 10-5/°F, Oy = 50 ksi. y↑ X Po Ih Po Figure 1: Schematic of the plate described in Problem 1. Consider the three-dimensional isotropic linear elastic plate subjected to applied tractions po ≥ 0 and a temperature gradient AT as shown in Figure 1. The plate is restricted from movement in the x- and z-directions so that we may take u = 0, w = 0, and v = = v(y). We neglect body forces and we assume v(y = 0) = 0. Note: Parts 1, 2, and 3 (with the exception of 3.b) are independent and will be graded as such. 1. (20 points) Assuming isothermal conditions for now, i.e. AT = 0, determine the elastic field in the solid. In other words, solve the field equations for o, e, and vu everywhere inside the plate. 2. (20 points) Taking po = 0 and AT 0, solve the field equations for a, e, and v. 1 3. (35 points) Assume now that po #0 and AT # 0. (a) (20 points) Determine o, e, and v everywhere inside the plate. (b) (8 points) Verify that the results from parts 1, 2, and 3(a) satisfy the principle of superposition. (c) (7 points) Predict the pressure po that will cause yield using the von Mises yield criterion for E = 107 psi, v= 1/3, AT = 100° F, - α = = 10-5/°F, Oy = 50 ksi. y↑ X Po Ih Po Figure 1: Schematic of the plate described in Problem 1.
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To solve the given problem we will address each part step by step Well start by defining the governing equations and boundary conditions for each case ... View the full answer
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Introductory Financial Accounting for Business
ISBN: 978-1260299441
1st edition
Authors: Thomas Edmonds, Christopher Edmonds
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