Engineering Computation of Structures: The Finite Element Method by Maria Augusta Neto Ana Amaro Luis Roseiro José Cirne & Rogério Leal

Author:Maria Augusta Neto, Ana Amaro, Luis Roseiro, José Cirne & Rogério Leal
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.74)

with

(4.75)

where T is the transformation matrix for the truss element, given by

(4.76)

and R is the transformation matrix from the local coordinate system to the global coordinate systems, whose components are

(4.77)

To evaluate the direction cosines, the three-dimensional orientation of the beam element need to be defined, as for the case of 2-D beams. The two nodes of the finite element are used to define the local axis. However, the orientation of axes and can still rotate around the axis of the beam. To prevent this problem, one additional point in the local coordinate must be defined. ADINA program uses this auxiliary point to specify the cross-section dimensions of the beam, as point out in Fig. 4.24. This point can be selected according the desired orientation of the beam, but should never be selected at the local axis. More details about the computation of these direction cosines can be view in the literature [5].

Using the transformation matrix, T, the matrices for space finite elements in the global coordinate system can be obtained as

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