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This assignment solution was submitted to Amar Sharma for Finite Element Method course at Aligarh Muslim University. It includes: Derive, Corrdinate, Transformation, Matrix, One-dimensional, Element, Denote, Nodal, Displacements
Typology: Exercises
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Finite Element Methods Assignment No. 5 Problem No. 6.
Problem No. 6.
Derive the coordinate transformation matrix for the one-dimensional element shown in Figure 6.3, where qi and Qi denote, respectively, the local (x, y) and the global (X, Y) nodal displacements of the element.
Solution:
From figure 6.3, we see that,
1 1 cos^2 sin 2 1 sin^2 cos 3 3 cos^4 sin 4 3 sin^4 cos
q Q Q q Q Q q Q Q q Q Q
1 1 2 2 3 3 4 4
cos sin 0 0 sin cos 0 0 0 0 cos sin 0 0 sin cos
q Q q Q q Q q Q
Hence, transfer matrix is,
