Differential Equations Solutions 170

Differential Equations Solutions 170 - | x | ≤ α and | y...

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180 Chapter 29. Solutions: Case Study: Elastoplastic Torsion: Twist and Stress -1 -0.5 0 0.5 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 x y Figure 29.1. Mesh used for a circular cross-section. -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 x 0.5 1 1.5 2 2.5 Figure 29.2. Solution for the elastic model using a circular cross-section. as long as the denominators are nonzero. Since
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Unformatted text preview: | x | ≤ α and | y | ≤ β , we conclude that the solution we seek has λ satisfying 0 ≤ λ ≤ min( α 2 , β 2 ). So we can solve our problem by solving the nonlinear equation f ( λ ) = ³ x α ´ 2 + µ y β ¶ 2 − 1 = 0...
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