3. Consider the following tapered rod of uniform modulus of elasticity E, uniform density p, length...

 

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3. Consider the following tapered rod of uniform modulus of elasticity E, uniform density p, length L, and non-uniform circular cross-section A = A (2 - x1/). The rod is loaded by gravity acting in the x-direction and supported by a spring of stiffness k at its end. Using the principle of stationary potential energy, derive the governing equation and boundary conditions for this structure. Describe the physical significance of each boundary condition. Assume 11 is the only non-zero strain. 4. Integrate the field equations derived in problem 3 to solve for the displacement field u exactly. 5. Use the following trial function to approximate the displacement field for the rod in problem 3 via the Rayleigh-Ritz method. Using a computer program, plot the exact solution and the approximate solution with E = p = L = k = 1 and A = 0.1. U = Cx + x + 3x + x X1 k g 3. Consider the following tapered rod of uniform modulus of elasticity E, uniform density p, length L, and non-uniform circular cross-section A = A (2 - x1/). The rod is loaded by gravity acting in the x-direction and supported by a spring of stiffness k at its end. Using the principle of stationary potential energy, derive the governing equation and boundary conditions for this structure. Describe the physical significance of each boundary condition. Assume 11 is the only non-zero strain. 4. Integrate the field equations derived in problem 3 to solve for the displacement field u exactly. 5. Use the following trial function to approximate the displacement field for the rod in problem 3 via the Rayleigh-Ritz method. Using a computer program, plot the exact solution and the approximate solution with E = p = L = k = 1 and A = 0.1. U = Cx + x + 3x + x X1 k g

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Answer 3 Strain energy U EA2 xL2dwdx dx Potential energy of ex... View the full answer