Back to Search
Start Over
Approximate expression of the Prandtl membrane analogy in linear elastic pure torsion of open thin-walled cross sections and regular polygons
- Source :
- International Journal of Solids and Structures. :109-118
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- This paper presents a new general methodology to obtain an approximate analytical expression of the Saint-Venant's torsion. The shear stress in each of the principal Cartesian directions is obtained by the derivation of the stress function, whose analytical expression is obtained from the Prandtl analogy. The proposed methodology uses two variables quadratic piecewise functions to define the Prandtl membrane. This document shows that the approximate procedure is especially suitable for steel shapes, giving values very close to those obtained with more precise methods. The main advantage of the presented methodology is its simplicity, which makes it useful for both pedagogic and practical applications. Several examples are developed.
- Subjects :
- Applied Mathematics
Mechanical Engineering
Prandtl number
Mathematical analysis
Linear elasticity
Regular polygon
Torsion (mechanics)
02 engineering and technology
021001 nanoscience & nanotechnology
Condensed Matter Physics
Membrane analogy
law.invention
symbols.namesake
020303 mechanical engineering & transports
Quadratic equation
0203 mechanical engineering
Mechanics of Materials
law
Modeling and Simulation
symbols
Piecewise
General Materials Science
Cartesian coordinate system
0210 nano-technology
Mathematics
Subjects
Details
- ISSN :
- 00207683
- Database :
- OpenAIRE
- Journal :
- International Journal of Solids and Structures
- Accession number :
- edsair.doi...........9854746a3244a3544fca72b1327f3872