Twist Analisys of “Not Standard Sections”

August 15, 2009 by Luigi Giaccari 
Filed under: FEM 
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Torsional Analisys
Purpose of this program is studying a not standard section subject to torsional stress. Not standard means the section is not included in engineering Handbooks. It can be studied with FEM analysis with commercial softwares, but sometimes this can become very rough.
Fortunatly Prandtl theory of membrane analogy comes to help, here a simple fem solution with linear triangular element is provided.Given a meshed geometry, it computes the shear stress distribution and stifness using Prandtl membrane analogy. As all fem programs, to give accurate
results, it needs a denser mesh were stress are supposed to have greater gradient and value.

This is a linear analysis effective for small displacements problems with homogeneous isotropic materials.
The tangential elastic modulus will be computed as G=E/(2*(1+poisson));
Note that there is no need of torque value, because of the linearity hipothesis, stresses,rotations and torque are univocally determined once only one of them is known.

Stiffnes modulus is calculeted in Nm/rad, this means is the rotation(rad) provoked by a 1Nm torque to a 1m length bar of the given section.

Inputs:

  • p : Nx2 array of nodes coordinates, [x1,y1; x2,y2; etc]
    IMPORTANT: computation have been made using millimeters!
  • t : Mx3 array of triangles as indices, [n11,n12,n13; n21,n22,n23; etc]
  • E : Elastic modulus of material
  • poisson : poisson ratio of material

Outputs: A grafical rapresentations of:

  • Shear stress
  • Membrane Analogy
  • Stres/torque relationship
  • Tau Flow

The call is:

TorsionFem(p,t,E,poisson)

so it is just necessary to have mesh and materials data.

For bugs, questions, suggestions just contact me at:

giaccariluigi@msn.com

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