4 - Memorial University of Newfoundland DAI

Furthermore, from equation (3.56), the following relationship la obtained:
Suhsliluling equation (3.57) into the above exp~sion lead6 to:
Ilcna, it is correct to write:
and
[TI = Iam,1-'[a.,l. (3.62)
witom [a,,] ia lhe flexibility matrix of the mader DOP and the inversion
will give thc lransformation rn :rix. (The inversion of [a,,] is less expensive,
since it is of a iav order.) It may be recalled that [TI is the matrix which
relates the displacements of the slave nodes to thaae of the master nodes.
Existing PEM pmgrams such as SAP IV, GTSTRUDL, etc., auld be
used lo compulc (om,] and [a,.[. The following atep are suggested:
(a) . . . first, identify the master DOF;
(b) find tho mrreponding deflection along dl the master DOF and arrange
lhem as the 1st column of matrix lo,]; and
(c) choose the corresponding deflection along all the slaveDOF and arrange
them as the 1st column of the matrix [a,].