ME6124 Sum2020 HW1 - Homework1 PDF

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ME 6124 Finite Element Method – Theory and Practice Homework #1 – Due: May 21, 2020 Q1. Consider the bar shown in the figure given below. An axial load of P = 670,000 N is applied as shown. The bar is made of aluminum and titanium alloy Ti-6Al-4V as shown in the figure. Use finite-element formulation and a) Determine the nodal displacements b) Determine the reaction forces

Q2. Consider the wall of three homogeneous slabs in contact as shown. Establish the steady-state heat transfer equilibrium equations of the analysis problem. The heat conduction law is q = k T, where q is the total heat flow, T is the temperature drop in the direction of heat flow, and k is the conductance or surface coefficient. Use the finiteelement formulation and write the equations in matrix form for each element and for the system of equations. Conductance 16k Conductance 11k

Conductance 18k

Surface conductance 7k

Environmental temperature T5

Prescribed Temperature T1

T2

T3

T4

If k = 350 W/m°C, T1 = 100 °C, and T5 = 20 °C, compute the unknown temperatures and heat fluxes.

Q3. Consider the structure shown below that consists of 4 bars. The stiffnesses of the bars are: k1 = 22, k2 = 15, k3 = 9, k4 = 20 The load is P = 14. Element lengths: L1 = 100, L2 = 100, L3 = 200, L4 = 80 Elastic modulus, E = 200e9

a. b. c. d. e.

Develop the equations for all 4 elements. Substitute values into the equations. Assemble the system of equations, KU = F. Determine the unknown displacements. Determine the unknown reaction forces. Compute the strains and stresses in the elements....