MIT2_092F09_hw1 - 2.092/2.093 FINITE ELEMENT ANALYSIS OF...

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2.092/2.093 F INITE E LEMENT A NALYSIS OF S OLIDS AND F LUIDS I F ALL 2009 Homework 1 Instructor: Prof. K. J. Bathe Assigned: Session 3 TA: Seounghyun Ham Due: Session 5 Problem 1 (30 points): Consider the truss problem already discussed in class, in linear elastic analysis, but with all displacement boundary conditions removed and no applied load. A m 2 = cross-sectional area of each bar, E N m 2 , and a [ m ] . U 4 U 2 Y X 4 2 U 8 U 5 U 7 4 U 6 3 5 U 8 2 3 U 3 U 1 a 1 1 a a 1
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= a) Develop by the physical reasoning used in class that is “by inspection” the K matrix for U 1 ⎤⎡ R 1 K ⎢⎥⎢⎥ U ⎥⎢ R 8 ⎦⎣ 8 b) Now assume U 1 = U 2 = U 4 = U 7 = U 8 = 0 and the external loads, R
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MIT2_092F09_hw1 - 2.092/2.093 FINITE ELEMENT ANALYSIS OF...

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