A large thin plate is subjected to certain boundary conditions on its thin edges (with its large faces free of applied stress), leading to the stress function ? = Ax³y² - Bx? A. Use the Biharmonic equation to express A in terms of B. B. Calculate all stress components. C. Calculate all strain components (in terms of B, ? (Poisson’s ratio), E (Young’s Modulus) and/or G (Shear Modulus). D. Check that the compatibility equation is satisfied. E. Check that the equilibrium equations are satisfied.
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Assume the numerical values as: E = 72 GPa, Poisson's ratio = 0.35; Dimensions of the plate L × b × t = 200 × 20 × 5 mm³. P = 7200 N. A thin plate of width b, thickness t, and length L is placed between two frictionless rigid walls a distance b apart and is acted on by an axial force P. The material properties are Young's modulus E and Poisson's ratio v. a) Find the stress and strain components in the xyz coordinate system. (b) Find the displacement field.
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Determine the nodal displacements and the element stresses, including principal stresses and angles, for the thin plate shown below with uniform shear load acting on the right edge: Use Young's modulus E = 3.0x10^7 psi, Poisson's ratio v = 0.30, and thickness t = 1 in. (Hint: use the submatrix approach to reduce your workload i.e. apply homogeneous essential boundary conditions to avoid computing corresponding components when you calculate the element stiffness matrix) 10 in. s = 5000 lb/in. 20 in.
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