Direct Variational and Weighted Residual Methods: Classical Trial Function Methods - Mechanics of Structures: Variational and Computational Methods - page 454

FIGURE 7.2
Ritz method for a fixed-hinged beam.

The trial function for case C led to the exact solution. The results are summarized in
Fig. 7.2.

EXAMPLE 7.6 A Field Theory Problem: Torsion
Apply the Ritz Method to find the warping function, torsional constant, and stresses for an
elliptical cross-section (Fig. 7.3) of a uniform bar subjected to a pure torque.
From the principle of vir tu al work (Chapter 2, Example 2.8), generalized to include the
applied distributed torque m x ,

− δ W =

V (τ xy δγ xy + τ xz δγ xz )

dV + m x δφ dx = 0 (1)

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