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• Gustavo Mollica

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ENME E3332x – A First Course in Finite Elements Instructor : Professor J. Fish CEEM, Fall 2015

Homework 1 Problem 2.1 (30%): For the spring system given in the next figure

a. b. c. d.

Number the elements and nodes Compute the global stiffness and force vector Partition the system and solve for the nodal displacements Compute the reaction forces

Problem 2.2 (30%): Show that the equivalent stiffness of a spring aligned in the x direction for the bar of thickness t with a centered square hole shown below is:

k

5Etab l a  b

where E is the Young’s modulus and t is the width of the bar (Hint: subdivide the bar with a square hole into 3 elements).

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ENME E3332x – A First Course in Finite Elements Instructor : Professor J. Fish CEEM, Fall 2015

Problem 2.4 (40%): Given the three-bar structure subjected to the prescribed load at point C equal to 103 N as shown in the following Figure. The Young’s modulus is E  1011 Pa , the cross-sectional area of the bar BC is A1  2 102 m2 and that of bar BD and BF is A2  1102 m2 . Note that point D is free to move in the x-direction. Coordinates of joints are given in meters. a. Construct the global stiffness matrix and load matrix. b. Partition the matrices and solve for the unknown displacements at point B and displacement in the x-direction at point D. c. Find the stresses in the three bars. d. Find the reactions at nodes C, D and F.

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