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Unformatted text preview: To show that the nodal forces are workequivalent to the element weight for a Q4 element of unit thickness: total work of the nodal forces=(v 1 +v 2 +v 3 +v 4 )W/4 total work of the body force: By performing the indicated integration, the two work expressions can be shown to be equal. dxdy v y x N dxdy A W y x v i i i A W = = 4 1 ) , ( ) , ( ( ) i i i A W v dxdy y x N ) , ( 4 1 = = 7 Connecting beam and plane elements Since all of the previous plane elements have translational dof only, no moment can be applied to their nodes. Therefore the connection (a) of a beam and a plane elements cannot transmit a moment and the beam element can freely rotate. (Singular K !) A solution is in (b) where beam is extended. Rotational dof at A, B and C are associated with the beam elements only. A plane element with drilling dof would also work but is not recommended....
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This note was uploaded on 06/06/2011 for the course EAS 4240 taught by Professor Peterifju during the Spring '08 term at University of Florida.
 Spring '08
 PETERIFJU

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