Basic FEA Procedures - Classes

foulgirlsUrban and Civil

Nov 15, 2013 (4 years and 1 month ago)

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2D Analyses

Mesh Refinement

Structural Mechanics

Displacement
-
based Formulations

But first …


MARC output for beam elements …










They make physical sense to me!

For conventional (non
-
numerically integrated) elastic beams (types
31, 52, 98), there are no layers
-

so only the generalized strains and
stresses are reported for these elements. Refer to
Marc Volume B:
Element Library for a definition of the generalized
strain and stress
output for each element type. Equivalent quantities are not
computed for these element types since they do not make
physical

numerical analysis
sense. The thermal strain tensor (post code 371)
or its associated components (post codes 71
-
76) are available.


(marc_2010_doc_volume_c.pdf, pg. 419, footnote to Table 3
-
4 “Element Post Codes”)

Physical/Mathematical/Numerical


Be ever
-
vigilant when using FEA software



What is Physically simple (e.g.
s

= My/I) may not
appear

in a mathematical formulation


Obviously important, but an optional post
-
processing step



What appears in a mathematical formulation may be
obscure

in a numerical implementation


Continuous quantities evaluated at discrete points

MARC Beam Elements


MARC has nine different beam elements:


13


14


25
-

52


76


77


78


79


98



Element Type is selected through Description and Options



Pay attention to the Patran forms and look at the .dat file …


ELEMENTS , 52,

BEAM SECT

BEAM


0, 4.0000E
-
4, 1.3333E
-
8, 1.3333E
-
8, 2.2533E
-
8, 4.0000E
-
4, 4.0000E
-
4,

LAST

Post Codes


See marc_2010_doc_volume_c.pdf


Table 3
-
4 “Element Post Codes”)








Patran offers this option in the Load Step specification

264 Axial Force (for beam elements)

265 Moment
Mxx

(for beam elements)

266 Moment
Myy

(for beam elements)

267 Shear Force
Vxz

(for beam elements)

268 Shear Force
Vyz

(for beam elements)

269 Torque (for beam elements)

Load Step Creation (Modification)

Beam Elements, Refined Mesh


Create Mesh with Global Edge Length set to 0.5 (equivalence!)

Deformed Shape
x

100


Tension, compression, and bending effects mixed

Axial Forces (Post Code 264)


Magnitudes are very similar to the Truss version


You must calculate axial stress (F/A) on your own if you want it!

Bending Moments


Small magnitudes overall, but could be significant locally

Getting to Know Elements


“Experiment” with simple situations …

To Refine, or Not To Refine …


It depends on the
purpose

of the analysis, the
types
of elements

involved, and what your FEA code does


For bar (truss) and beam elements:


Am I after displacements, or strain/stress?


Does my FEA code include analytical strain/stress?


What results does my FEA code produce?


Can I just do my own post
-
processing?



Always

refine other element types

2D Idealizations


There are no 1D problems, but we have 1D elements


There are no 2D problems, but we have 2D elements



These situations idealize to 2D:


Plane strain


Plane stress


Axisymmetry


Plates and Shells



2D Elements


The most commonly used element types


Always use a 2D element if it is appropriate


Never use a 2D element if it is not


Appropriate use can depend on loading and material
properties as well as geometry



You know it is a 2D element if:


The third dimension is not part of the finite element mesh


Thickness and other element properties are specified

Plane Stress*


Geometry is f
lat

but not
slender

(occupies x,y plane)


Loading within the plane of the large dimensions


Stretch, compression, shear, etc. all OK


No transverse loading


All
z
-
containing stress components zero


Assume stresses constant through thickness


A consequence of “thinness” and lack of bending


* We are skipping plane strain, it’s just not that common