MIT2_092F09_sol1

MIT2_092F09_sol1 - 2.092/2.093 FINITE ELEMENT OF SOLIDS AND...

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2.092/2.093± F INITE E LEMENT OF S OLIDS AND F LUIDS F ALL 2009± Homework 1- solution Instructor: Prof. K. J. Bathe Assigned: TA: Seounghyun Ham Due: Problem 1 (30 points): The truss geometry is shown below. Bar mumbers are circled. Joint numbers are placed adjacent to their respective joints. U 4 U 2 For a linear static analysis, we have: K 8×8 U 8×1 =R 8×1 a) The K matrix is calculated column by column. The i th column of the stiffness matrix represents the external force vector required to give the structure unit th displacement about the i degree of freedom and zero displacement about all other degree of freedom. Take a look at one example how to construct it. Calculate column 5:± Imposing the following displacement pattern:± U 5 =1, U 1 =U 2 =U 3 =U 4 =U 6 =U 7 =U 8 =0 a a a 1 2 3 4 5 U 8 U 5 U 3 U 1 U 7 U 6 1 3 2 4 Session 3 Session 5
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After assembling all columns, the following K is determined: 1 1 1 1 + 1 -1 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 -1 0 1 0 0 + 2 2 2 2 2 2 2 2 1 1 1 1 0 0 + 1 0 -1 EA± 2 2 2 2 2 2 2 2 K = 1
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.092 taught by Professor Klaus-jürgenbathe during the Fall '09 term at MIT.

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MIT2_092F09_sol1 - 2.092/2.093 FINITE ELEMENT OF SOLIDS AND...

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