2010

July 2010

# Terms used in analysis - Set 2 - #12-18

Posted by Joe Galliera Jul 26, 2010
I thought it might be a good idea to provide some basic definitions of terms that  are used in analysis that are good to know to be able to communicate  intelligently about Simulation.  These are not meant to be  definitive technical definitions but more fundamental knowledge of these  terms (i.e. they are mostly coming off the top of my head as I'm typing).  If  you believe that I am off on any of these, please let me  know.

Last time two of  the terms that I gave were von Mises and shear stresses; there's many more  components of stress than that.  Here's 12 to 18:

12. normal  stress - if you were to take a look at an infinitesimally small cube  oriented in the global coordinate system, the normal stress is the stress  that develops normal to the face.  Normal stress is denoted by the Greek letter sigma, σ, and subscript is the face that it is normal to, eg. σx.  From last time, shear stress is defined as  the stress that is tangential to the face, usually denoted by a Greek tau, τ, and subscript is the face and then the direction of  shear, for example τxz is on the x-face in the  z-direction.  Thus for a given cube face, there is a single normal stress and  two shear stresses.  Both normal and shear stresses are vectors, having  direction and magnitude, and since the proposed cube we are looking at is  infinitesimally small, the stresses on opposing faces are equal in magnitude but  in the opposite direction.  Thus for a given cube, there are a grand total of 3  normal stresses and 6 shear stresses.  The below image can be helpful in  describing the stress vectors:

13. shear  modulus - primarily denoted as G, is the ratio of shear stress to shear  strain.  For a linear isotropic material, it is useful to know that any 2 moduli  can determine any other elastic moduli (a full matrix can be found at the bottom  of http://en.wikipedia.org/wiki/Elastic_modulus).   G = (E/2)/(1+ν), where E is Young's modulus and ν is Poisson's ratio.  In SW SIM, if you define E and ν for a linear isotropic material, I recommend keeping shear  modulus blank and the software will compute it by itself (if you put in a value  it will use that one instead so again best to keep it  blank).

14.  principal stresses - at any point in a stressed body (in this case  let's take the same point as given above), there exists three planes where there  are no shear stresses and the normal stress vectors to these planes are in  "principal" directions, and are denoted σ1, σ2, and σ3, (or  in SW SIM we name them P1, P2 and P3).  The normal and shear stresses from the  stress cube above go through a matrix transformation (resulting in a matrix  where all off-axis terms are zero) to obtain the principal directions, which are  orthogonal to one another meaning that they are completely independent  directions.  It is always true that P1 ≥ P2 ≥ P3.  In an pure tensile load, all  three principal stresses are positive; in a pure compressive load, all 3 are  negative; and when the signs of the principal stresses are mixed (P1 is positive  and P3 is negative), then this usually means the body is in bending.  I  typically recommend to set your Simulation options to always show P1 and P3  stress components in addition to von Mises stress.

15. bending  stress - Thinking of shell elements, they tend to bend easily because  they are thin.  During bending, compressive and tensile stresses develop; the  maximum value of these stresses are on opposite sides of the outermost thickness  of the shell, and the stress varies linearly through its thickness.  The bending  stress is the slope of the line between compressive and tensile stresses through  the thickness of the shell.

16.  membrane stress - is the stress in the plane of the shell that develops  if the compressive and tensile stresses have different magnitudes.  If the  tensile stress is greater, then the membrane is pulled along the direction  of the shell plane; if the compressive stress is greater, then the material in  the membrane is compressed.
So in conclusion  for a shell, show P1 & P3 for both top and bottom of the shells and both the  membrane and bending stresses.

17. torsional stress - is a stress due  to a twisting of an object due to an applied torque.  It is a type of shear  stress with an specific equation Tr/J to calculate it by hand based on the  applied torque T, the radius r from the axis of torque, and the object  (typically a cylindrical shaft) with a polar moment of inertia J.  The max  torsional stress is on the outer max radius, or surface, of the  shaft.

18.  Hertzian contact stress - the compressive stress due to contact of two  curved parts under load.  The important thing to note for Hertzian stresses is  that the max stress occurs close to the area of contact in the subsurface, or  just below its surface, thus the mesh needs to be finest below the surface so  creating a mesh control just inside the sphere near the contact is important.   Another important thing to know is that it is very difficult to get an accurate  Hertzian contact stress result.

Do not distribute or reproduce without  the written consent of Dassault Systèmes SolidWorks Corp.

# Terms used in analysis - Set 1 - #1-11

Posted by Joe Galliera Jul 26, 2010
OK, so I took a bit of a hiatus from the blog. I'll try to  make this up somehow.

During this time away, I  thought it might be a good idea to provide some basic definitions of terms that  are used in analysis that are good to know to be able to communicate  intelligently about Simulation.  These are not meant to be  definitive technical definitions but more fundamental knowledge of these  terms (i.e. they are mostly coming off the top of my head as I'm typing).

I have a list of  about 150 good to know analysis terms that I want to (hopefully) get through all of them eventually, so here  we go to start 1-11:

1. FEA (or  finite element analysis) - sometimes referred to as FEM (M meaning  method).  The method used by the structural analysis modules of SW SIM by  breaking the CAD models into smaller pieces, called elements, on which the  physical properties, loads and restraints are applied and finally solved  collectively.

2.  Pre-processing - what is done in setting up the analysis model prior to  solving.  This may include: creating the geometry; simplifying it for analysis  purposes; applying material properties; applying loads, restraints, connectors  and contacts; and meshing the model.  This is basically formulating a question;  if this is not done appropriately, people may refer to this as GARBAGE IN, which  leads to GARBAGE OUT (in the post-processing phase).

3.  Solving - takes the input by the user from the pre-processing phase,  puts it into a form preferred by the solver, and calculates a solution for the  question.  The solution is typically very precise, but whether it is accurate is  left for interpretation in the post-processing phase.

4.  Post-processing - or viewing and evaluating the results from the  solver.  There are many methods available to view the results, such as contour  plots, section/cut plots, probing, tables or listing of values, and charts.   Evaluating results can be challenging and can be helped by experience and  judgement, but I think that answering the question "Does this move or react to  the loads as expected in reality?"  Thus determining whether the output is good  or not (GARBAGE OUT), we can say whether we need to go back to the  pre-processing step or not.  If accurate results are required then more than one  solution for finer mesh sizes will be required.  Accurate results may not be  needed if one is comparing different design configurations where consistency is  more important.

5. Modulus  of Elasticity - also known as Young's Modulus.  It is a material  property relating the stress in the material to how much it is strained, and is  typically obtained by pulling a sample of the material in a testing machine.  It  is a linear ratio of stress over strain, so it has the same units of stress  (psi, ksi, Pa, MPa) since strain is without units, and is valid up to the point  of yielding in the material.  Materials which are linear-elastic follow Hooke's  Law.

6. Hooke's  Law - Hooke's law of elasticity is an approximation that states that  the extension of a spring is in direct proportion with the load added to it as  long as this load does not exceed the elastic limit. Materials for which Hooke's  law is a useful approximation are known as linear-elastic or "Hookean"  materials. Hooke's law in simple terms says that strain is directly proportional  to stress. (Definition taken directly from Wikipedia.)

7. von  Mises stress - or equivalent (tensile) stress.  The von Mises stress  is meant as a way to try to fully describe the multiaxial stress state as a  positive scalar value, which also makes it nice to show as a contour plot.  It  has its downfalls in that: it doesn't tell the whole story in how a part is  being stressed, thus one should not rely on this quantity alone to get the full  picture, so show additional stress components such as principal, normal and  shear stresses; and secondly it's based on what's called 'distortion energy'  simply meaning that it's good for deformations that distort the geometry, like  pushing a small area on the outside of a sphere, and ignores uniform deformation  (or hydrostatic stress), like a uniform pressure on the entire outside of the  sphere.  Note that von Mises yield criterion surface circumscribes (fully  envelops) the Tresca max shear stress criterion surface, thus von Mises is less  conservative.
History buffs might  like to know that while it primarily carries von Mises' name, it was formulated  by Maxwell many years before and others, so the entire mouthful name for the  stress criterion is Maxwell-Huber-Hencky-von Mises theory (which I'm  guessing was just shortened to 'von Mises.')

8. Shear stress - is the stress  applied tangential to a face of a material, as opposed to normal to the  face.

9.  Poisson's ratio - symbolized by the Greek letter nu, ν, is the ratio of how much a material contracts in the  direction perpendicular to the direction pulled, or transverse direction.  It  describes similarly how it much it expands transversely when compressed.  The  Poisson's ratio of an isotropic, linear-elastic material must be -1<ν<0.5, but most materials are greater than 0.   Orthotropic materials can have Poisson's ratios outside of these limits.  Rubber  materials have a Poisson's ratio very close to 0.5, such as 0.4999, and cork has  a Poisson's ratio of nearly zero which is why it's used for sealing bottles so  that it can be inserted and removed while still holding the internal pressure.   Negative Poisson's ratio materials are called auxetic, and here is a cool animation  of an example.

10. CFD (or  computational fluid dynamics) - CFD is a general term applied to the  approach to solving the fluid dynamics equations numerically with a computer, as  opposed to experimental or analytical methods.  The method that SW Flow  Simulation uses is the finite volume (FV) method.  Our SW Flow Simulation  software is classified as a CFD program, although Flow Simulation (and FloWorks  before it) helped pioneer a subset of CFD called EFD.

11. EFD (or  Engineering Fluid Dynamics) - is an upfront approach to CFD that offers  a straight-forward easy-to-use interface that speaks the language of the design  engineer working with fluids.  Key technologies include: direct use of  SolidWorks CAD data; automatic detection of fluid volume; Wizard interface;  automatic meshing; automatic laminar-transitional-turbulent modeling; automated  control of analysis runs; robust convergence behavior; simulation of design  variants; and results reporting and presentation in MS  Office.