One-Dimensional Finite Elements by Andreas Öchsner & Markus Merkel
Author:Andreas Öchsner & Markus Merkel
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham
Fig. 8.17Timoshenko bending element with quadratic shape functions for the deflection and the rotation: a deformation parameters; b load parameters
Solution
Evaluation of the general Lagrange polynomial according to Eq. (8.149) under consideration of 3 nodes yields the following shape functions for the deflection and the rotation:
(8.177)
(8.178)
(8.179)
With these shape functions the submatrices in Eq. (8.152) result as follows through analytical integration:
(8.180)
(8.181)
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