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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. 
A 
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.