Determination of stresses from their stress trajectories in plane elastic systems: the five constant theorem

✍ Scribed by A. W. Sáenz

• Publisher: Springer Vienna
• Year: 2009
• Tongue: English
• Weight: 219 KB
• Volume: 208
• Category: Article
• ISSN: 0001-5970
• DOI: 10.1007/s00707-008-0118-3

✦ Synopsis

Let K be a cylindrical region of finite height, having a generator parallel to the z-axis and a bounded, simply connected cross section S whose boundary is a sufficiently smooth Jordan curve. Moreover, let the material in K be elastic and isotropic, and in a state of plane stress or plane strain of elastic equilibrium, under the action of a conservative, z-independent body-force field and appropriate boundary tractions. We prove that at each z the principal stress-trajectory net corresponding to the stresses τ x x , τ xy , τ yy is a 2-5 real-parameter family, as conjectured by Neményi.