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In class, we used the 3D form of the von Mises and Tresca yield functions: f(σij, oyo) = f(oij, oyo) = ) = (0₁ - 0₂)² + (01 − 03)² + (0₂-03)² - 0₂0 ≤ 0, max (|01 – 02], |02 - 03|, |03 - 01) - σyo ≤ 0 Derive the appropriate form of these yield functions for plane stress problems and plot the resulting curves in the 0₁-02 plane. Note that the curves trace out the intersections between the 3D yield surfaces and the 01 - 02 plane in principal stress space.

In class, we used the 3D form of the von Mises and Tresca yield functions: f(σij, oyo) = f(oij, oyo) = ) = (0₁ - 0₂)² + (01 − 03)² + (0₂-03)² - 0₂0 ≤ 0, max (|01 – 02], |02 - 03|, |03 - 01) - σyo ≤ 0 Derive the appropriate form of these yield functions for plane stress problems and plot the resulting curves in the 0₁-02 plane. Note that the curves trace out the intersections between the 3D yield surfaces and the 01 - 02 plane in principal stress space.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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In class, we used the 3D form of the von Mises and Tresca yield functions: ƒ(σij, Øyo) 1⁄2 (01 − 02)² + (01 − 03)² + (0₂ − 03)² − 0,0 ≤ 0, ƒ(σij, σyo) = max (01 - 02|, |02 - 031, 03-01) - 0y0 ≤0 Derive the appropriate form of these yield functions for plane stress problems and plot the resulting curves in the 0₁-02 plane. Note that the curves trace out the intersections between the 3D yield surfaces and the σ1 – σ2 plane in principal stress space.
Transcribed Image Text:In class, we used the 3D form of the von Mises and Tresca yield functions: ƒ(σij, Øyo) 1⁄2 (01 − 02)² + (01 − 03)² + (0₂ − 03)² − 0,0 ≤ 0, ƒ(σij, σyo) = max (01 - 02|, |02 - 031, 03-01) - 0y0 ≤0 Derive the appropriate form of these yield functions for plane stress problems and plot the resulting curves in the 0₁-02 plane. Note that the curves trace out the intersections between the 3D yield surfaces and the σ1 – σ2 plane in principal stress space.
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