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###### Mechanical Engineering

1. The figure below shows the geometry of a 0.25-in. thick specimen used in the tensile test of a plate with a circular hole. The specimen is designed to have uniform stress cr. of 10 ksi along Section A-A and Section C-C due to the applied load, F. You are running the analysis to determine the stress distribution around the hole.

For this specimen, sketch the finite element model you would use to analyze the stress field due to the applied load, F. Be sure you include and clearly label:
a) Symmetry, if appropriate b) Boundary conditions (No rigid body motions are permitted!) c) Loading d) The element type that should be used (for example, 1D bar, plane stress quad, 8-node brick, etc.) e) Any special meshing accommodations (regions you would refine, etc.).

2. The figure on the right shows a proposed six-node, 2D quadrilateral element. This element is isoparametric and, as pictured, uses a second order interpolation on one axis and a linear interpolation on the other. Answer the following questions regarding this element:
a) What are the appropriate shape functions for each node? Recall, shape functions must equal 1 at the node with which it is associated, and zero at all other nodes.
4.  (-1,1)
6, (4,0) (4, 4)
A '1
b) What is the form of the displacement approximation for this element? (u = ao + alf + ...)
c) Is it possible for the sides of the physical clement to be curved? Explain

3) Use the Redlich-Kwong equation of state to answer the following questions:
RT a P=  V — b \iT'13(v + b) a. Derive the reduced parameter equation of state, i.e., solve for a and b and plug back in b. Plot the reduced parameter equation of state on a P-v plot for reduced temperatures of TR = 1, 1.5, 1.75, 2 c. Plot the van der Waals equation of state (EOS) and the Redlich-Kwong EOS for TR = 1 and 1.5 and compare them to the water data attached in the excel sheet.

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