A composite rod BM, of rectangular cross section, is made up of segments BC, CD,

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A composite rod BM, of rectangular cross section, is made up of segments BC, CD, and DM. Across the segment BC, the depth varies linearly from 2a at B to 3a at C. The depth of segment CD is 3a throughout its length, 2L. Across the segment DM, the depth varies linearly from 3a at D to a at M. The Young's modulus for the segments BC, CD, and DM, are 2E, E, and 3E, respectively. Axial point loads P, 3P, and 2P are applied to C, H and M respectively, as shown in Fig 12.2. Write down the stiffness matrix [K] and the force vector {F} for a four finite element model of the rod, whose elements are labeled (1)-(4), in Fig 12.2. Enforce the fixed displacement boundary conditions on [K] and {F}. A copy of a Matlab script('rod_fea.m') is provided for you in the Homework Sets folder on Blackboard. Modify this Matlab script for a finite element displacement analysis for this rod. Run the script to determine the displacements of points C, D, and H on the rod. Report your results here in terms of P, E, a, b, and L. Also, provide a hardcopy of your modified Matlab script. Include your name in a comment line in this copy of your Matlab script. Use the results for displacement found in b) to determine the element that is subjected to maximum axial stress.

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