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Manoj Chopade
Roll No : 21ME Design (II Semester)
Shear locking Phenomenon
27thMay 2014
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How Does Finite Element Analysis
Work? The mathematical representation of
the physical system in FEM is byusing nodes and elements.
The process of creating nodes andelements is said as discretization or
meshing. The number of degrees of freedom
in each node depends on theelement type.
As the FEM model has finite DOF as
against infinite DOF in actualstructure, FEM solutions areapproximate and FEM model isstiffer
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Shear locking Phenomenon
Error called locking and how it is being overcome
by the commercial FEA codes.
In spite of providing approximate solutions to
problems which cannot be solved analytically, there
are some situations for which convergence is poor inFEM.
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LOCKING :
Locking means the effect of a reduced rate ofconvergence in dependence of a critical parameter.eg.slenderness of the plate in case of transverseshear locking.
Because of locking , wrong displacements , falsestresses, spurious natural frequencies areencountered.
Shear locking occurs on use of fully integratedlinear elements that are subjected to pure bending.The formulation of these elements promotes shearstrains that do not really exist
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Shear locking:
Timoshenko beam theory works for all l/d ratiowhereas Bernoullie beam theory works for only large
values of l/d ratio.
In thick beams , shear deformation becomes
predominant and Bernoullis theory wont giveaccurate result.
Shear locking occurs in elements which account for
shear deformation ,when these elements are used in
modeling bending predominant beams .
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Shear locking occurs in elements which account for shear
deformation ,when these elements are used in modeling bending
predominant beams .
A Cantilever beamsubjected to loading at the
free end is analysed with
the following properties :
Youngs Modulus = 200GPa
Poissons Ratio = 0.3
Ansys Element SOLID 45
and SOLID 185 is
considered.
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Meshing:
L/d ratio = 25 L/d ratio = 5
The beam is meshed such that there are 4 elements in height , 10 elements along
the length and 1 element along the width.
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The analytical solution for the tip deflection in case of a
cantilever problem is calculated from
P= Forceacting on the tip of the beam, L= Length of the beam (span) , E= Modulus of elasticity, I =Area moment of inertia
The Answer obtained analytically for a cantilever beam of
L/D ratio 25 is 0.312 cm The free end deflection obtained from SOLID45 is 0.308
cm whereas from SOLID185 element the tip deflection is
found to be 0.1514 cm .
The difference between the results is due to shear locking
and it is not an approximation error.
])(10.071.01[3
3
2
23
L
D
L
D
EI
PLs
http://en.wikipedia.org/wiki/Forcehttp://en.wikipedia.org/wiki/Span_(architecture)http://en.wikipedia.org/wiki/Modulus_of_elasticityhttp://en.wikipedia.org/wiki/Area_moment_of_inertiahttp://en.wikipedia.org/wiki/Area_moment_of_inertiahttp://en.wikipedia.org/wiki/Modulus_of_elasticityhttp://en.wikipedia.org/wiki/Span_(architecture)http://en.wikipedia.org/wiki/Forcehttp://en.wikipedia.org/wiki/Force5/25/2018 Shear Locking
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Shear Locking
For a Beam in Pure Bending the shear strain is Zero
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Tip deflection values in cm
s.no L/D
ratio
ANALYTICAL
SOLUTION
SOLID 45 % Error SOLID185
(reduced
integration)
1. 25 0.3128 0.308 50.8% 0.3328
2. 20 0.16028 0.1578 39.6% 0.1705
3. 15 0.0677 0.0667 26.68% 0.0720
4. 10 0.02014 0.0196 26.28% 0.0214
5. 5 0.002569 0.002523 6.8% 0.002757
Compression Sheet
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Interpretation of the results :
It is clear from the table, as the beam thicknessincreases (as shear becomes predominant) the error
is minimized.
The error in the tip deflection values of bendingpredominant beams is due to Shear locking.
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THANK YOU
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References :
Finite Element Analysis by C.S.Krishnamoorthy , IIT ,Madras.
Strength of Materials- Elementary theory and problemsby Stephen Timoshenko
Eric Quili Sun, Shear locking and hourglassing in MSC
Nastran, Abaqus and Ansyswww.cmmacs.ernet.in/cmmacs/pdf/
www.imechanica.org
www.mscsoftware.com/events/vpd2006/na/presentations/
.../27.pdfwww.eng-tips.org
www.springerlink.com
www.openpdf.com
www.sciencedirect.com
http://www.cmmacs.ernet.in/cmmacs/pdf/http://www.imechanica.org/http://www.mscsoftware.com/events/vpd2006/na/presentations/.../27.pdfhttp://www.mscsoftware.com/events/vpd2006/na/presentations/.../27.pdfhttp://www.eng-tips.org/http://www.springerlink.com/http://www.openpdf.com/http://www.sciencedirect.com/http://www.sciencedirect.com/http://www.openpdf.com/http://www.springerlink.com/http://www.eng-tips.org/http://www.eng-tips.org/http://www.eng-tips.org/http://www.mscsoftware.com/events/vpd2006/na/presentations/.../27.pdfhttp://www.mscsoftware.com/events/vpd2006/na/presentations/.../27.pdfhttp://www.imechanica.org/http://www.cmmacs.ernet.in/cmmacs/pdf/Top Related