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Submodeling Technique in Stress Analysis
M a r c h 2 0 1 1
Submodeling Technique in Stress Analysis | March 2011
© 2010, HCL Technologies. Reproduction Prohibited. This document is protected under Copyright by the Author, all rights reserved.
TABLE OF CONTENTS
Abstract ............................................................................................. 3
Abbreviations .................................................................................... 4
Market trend/ Challenges .................................................................. 5
Solution ............................................................................................. 6
Best Practices ................................................................................. 12
Common Issues .............................................................................. 13
Conclusion....................................................................................... 14
Reference ........................................................................................ 15
Author Info ....................................................................................... 15
Submodeling Technique in Stress Analysis | March 2011
© 2011, HCL Technologies. Reproduction Prohibited. This document is protected under Copyright by the Author, all rights reserved.
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Abstract
This technical paper explains the information about the submodel
techniques used in the stress analysis by Finite Element Analysis. It
highlights the necessity of submodels in stress analysis to reduce
the run time which in turn influences the budget and deadline of the
entire product design and development cycle. Submodel techniques
are introduced in the stress analysis because of the limitation of the
full model to capture the correct stress concentrations at critical
locations. If the critical location is known prior to analysis, it is
always recommended to include the refined mesh at critical
locations embedded in the full global model itself. This may require
sophisticated high end computing systems to optimize the run time.
This whitepaper explains the basic process involved along with
different types of submodels used in the stress analysis of the
component or entire systems. This paper also explains the reason
behind the selection of different types of sub models based on the
critical locations, attenuation length for the cut boundary locations of
the submodel and some of the checks to ensure that the submodel
results are accurate.
The submodel techniques are basically used in the stress analysis
of components supporting LCF(Low Cycle Fatigue) computation,
Crack induction, Crack propagation, non linear buckling of the
structure under huge static loads. Submodels can be used in both
two dimensional and three dimensional analyses. The principle and
methodology remain same in both cases. Three dimensional sub
models are explained in this paper as they need very close attention
with respect to analyses, accuracy and model setup.
Other application could be in Heat transfer and computational fluid
dynamics.
Submodeling Technique in Stress Analysis | March 2011
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Abbreviations
Sl. No. Acronyms Full form
1 2D 2 dimensional
2 3D 3-dimensional
3 LCF Low Cycle Fatigue
Submodeling Technique in Stress Analysis | March 2011
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5
Market trend/ Challenges
In a typical stress analysis of a component the model size is
dependent up on the program requirement, available budget and
computing facilities. The time to build the model is linearly related to
the model size. The complexity of the model and degrees of
freedom present in the model is nonlinearly related to the time taken
to complete the analysis. The material nonlinearity and
consideration of friction at the interfaces further complicates the
analysis. The assumptions in the model may further reduce the
scope of the analysis. In such cases submodels are very handy to
speed up the solution time and obtaining the accurate results at the
critical locations. Submodels allow the reduction of model size in the
global full model hence reducing the analysis time.
Submodels are constructed and run at locations of the global full
model where mesh is not fine enough to capture the accurate
stresses. Extreme care should be taken to ensure that the source of
geometry taken for the submodel is same as that used in the global
model. As far as possible the features at the critical locations such
as fillets, chamfers and blends should be present in the global
model.
The basic principle of submodeling is based on the St. Venant‟s
principle, “if an actual distribution of forces is replaced by a statically
equivalent system, the distribution of stress and strain is altered only
near the regions of boundary condition application”. Hence the cut
boundary locations for the submodels are chosen at a safer
distance from the area of interest where displacements are
converged. This distance from the critical location is termed as
attenuation length. This makes reasonably accurate stresses can be
obtained at the critical locations.
Submodeling Technique in Stress Analysis | March 2011
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Solution
1. Basic Process map for performing submodel analysis
Figure 1 shows the basic process map for performing the submodel
analysis. The steps remain same for both 2D and 3D submodel
analysis. Assessment of the submodel results for accuracy and
correctness is explained in next sections.
Figure 1: Basic process map for performing sub model analysis
2. Necessity to perform sub model stress analysis
Most of the time Global models are restricted to have coarse mesh
with fairly finer mesh at the critical locations. The peak stress at
critical location might be due to the mesh factor, local distortion of
the geometry such as fillets due to coarseness of the elements and
insufficient elements across thickness. Following are some of the
Basic Process map
Necessity to perform sub
model analysis
Types of submodel analysis
Checklist
Submodeling Technique in Stress Analysis | March 2011
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checks with the global full model results which will help user to
decide upon the necessity to perform submodel analysis.
2.1 Mesh discretization error
As a general rule, If the maximum error estimated at the critical
location is more than 5% , refinement of the mesh is required or the
submodel need to be run at this location with finer mesh.
In case of stress analysis supporting LCF life analysis for crack
induction case, the mesh convergence criteria for global full model
may be very stringent. The difference between nodal stress and
elemental surface stress at critical location should be approximately
1% of the maximum stress at the critical location. The stress
gradient (element –to – element / node – to – node) at critical
location across all directions should be smooth. And the stress
gradient in major stress component direction should be
approximately 1% of the maximum component stress at the critical
location. User can see ref.[1] and ref.[2], for more information on the
mesh discretization error and submodeling analysis information.
2.2 3D Features
In case of analyzing the 2D models with the approximation of 3D
features such as scallops, bolt holes, key slots etc., the stresses
may not be correct at these features. In this case actual 3D
submodels need to be analyzed with cut boundaries from the global
full models.
In case of 3D global models there may be complex 3D features
such as multiple fillets, chamfers and blends etc. The finer mesh at
all features may render the model size huge enough to slow down
the analysis time. In this case based on the loading condition and
resulting critical location, quick sub models can be prepared and
analyzed to get the accurate results at the critical locations.
3. Types of sub models in stress analysis
Based on the critical location in the global full model with respect to
the cut boundary locations and other interfacing components there
can be three types of the submodels which can be analyzed using
cut boundaries from the global full model. The decision to select the
type of submodel mainly depends upon the attenuation length of
critical location from the submodel cut boundaries and interfaces of
neighboring components. The displacement boundary conditions
are obtained from interpolation of the shape function from the global
full model results.
Attenuation Length is defined as the distance at which the localized
effect of critical location on stresses and displacements settle down
in the global full model. In case of cylindrical components the
Submodeling Technique in Stress Analysis | March 2011
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attenuation length from the critical location is computed as shown in
Figure 2. In other components the attenuation length can be
computed based on the convergence of the displacements away
from the critical location such that the displacement gradient
between adjacent nodes is negligible.
Figure 2: Attenuation length computation for cylindrical components
Figure 3 shows the cross section of the critical location of two
cylindrical flanges connected through bolted joints. Based on the
attenuation length of the critical location, we can decide upon the
type of submodels need to be analyzed.
Figure 3: Critical location from the global full model
3.1 Type A Submodel
If the critical location is sufficiently away from the interfaces, the
submodel is very simple. No contact interfaces are considered in
this sub model as shown in Figure 4.
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Figure 4: Type A submodel
3.2 Type B Submodel
In case critical location stresses are driven by the magnitude of the
interface loads, user need to consider the interface load effect in the
submodel. Interfaces may be satisfying the attenuation length
requirements and change in the distribution of the interface loads
may be having insignificant influence on the critical location stresses.
In this case user need to build the Type B submodel as shown in
Figure 5 with contact interface cut boundaries
In Type B submodel, user need to run the two pass analysis as the
interface load magnitude is affected by the stiffness of the submodel
due to mesh refinement. The displacement boundary condition
obtained from the initial interpolation from the global full model
results at interfaces need to be scaled for the pass two run such that
the resultant reaction force in the submodel matches with the
resultant gap load in the global full model. The difference between
the global full model interface load and resultant reaction forces at
interface cut boundary should be less than 10% of the interface load.
Figure 5: Type B submodel
3.3 Type C Submodel
If the critical location stresses are influenced sufficiently by the
magnitude and distribution of the interface loads, Type C submodels
need to be considered as shown in Figure 6.
In this case we need to consider the neighboring components as
well in the analysis. The effect of friction can also be considered in
this type of submodels.
Submodeling Technique in Stress Analysis | March 2011
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Figure 6: Type C submodel
Among three types of the submodels, Type A and Type B runs
faster compared to the Type C sub models. The decision between
the Type B and Type C submodel is difficult. In this case it is
recommended to run both submodels in parallel and compare the
results between two submodels. In all cases the stress at critical
location should satisfy the error estimation and stress gradient
requirements explained in section 2.1.
4. Checklist for the submodel analysis
Following are some of the checks need to be conducted in order to
perform the successful submodel analysis.
Verify the global full model stresses at critical location for the
mesh discretization error and stress gradients as explained in
section 2.1.
If highly sophisticated computing facility is available, include the
embedded submodel in the global full model itself. In this case
the quick submodel is run to check the mesh fineness alone.
Verify the source of geometry for both global full model and
submodel. All features at the critical location should be present
in both global full model and submodel.
Ensure that the sufficient elements present across the thickness
to accommodate bending effects.
Appropriate type of the submodel need to be decided to
accommodate the effect of neighboring components.
Nodes at the cut boundary locations need to be oriented similar
to the global full model including the interface locations.
The material input file used for the submodel should be same as
that used in the global submodel.
Submodeling Technique in Stress Analysis | March 2011
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All other loads such as point loads, temperatures and pressures
should be applied at all locations similar to the global model
Cut boundaries should be defined with sufficient attenuation
length from the critical location.
Ensure that difference in reaction forces at cut boundary
locations are within 5% of the reaction forces from global full
model results.
After the submodel analysis, the results need to be checked
again for the mesh fineness and stress gradients as explained
in section 2.1.
Submodeling Technique in Stress Analysis | March 2011
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12
Best Practices
Figure 7 shows the complete process map for the selection of
submodel types for any circumstances in the complete stress
analysis process.
Figure 7: process map explaining the submodel type selection
Submodeling Technique in Stress Analysis | March 2011
© 2011, HCL Technologies. Reproduction Prohibited. This document is protected under Copyright by the Author, all rights reserved.
13
Common Issues
Pitfalls of submodel analysis approach
Following are some of the pitfalls of the submodeling approach used
in stress analysis. In such cases user should take appropriate
precautions to perform the submodel analysis correctly.
Extrapolation errors in the body forces due to the geometrical
changes and mesh size between global full model and
submodel. This may require user to run the additional analysis
to get the accurate body forces in the submodel. (In case of
temperatures, user may need to run the stand alone thermal
analysis of the submodel to get the accurate temperatures at
the submodel region.)
Sometimes applying displacements as cut boundaries in all cut
boundary locations may render the over constraining of the sub
model giving spurious stresses at the cut boundary locations.
(Applying forces as cut boundary will solve this issue. This may
need to match the mesh of submodel at cut boundary locations
as that in global full model.)
The distributed load is applied using the pilot node in global full
model; the appropriate portion of the load should be applied in
the submodel at the load application area.
If the global model is run with inertia relief (due to the
unbalanced loads), user should include the inertia relief load
effect from the global full model results into the submodel
analysis.
Pitfalls
Submodeling Technique in Stress Analysis | March 2011
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14
Conclusion
This paper gives an overview of how sub modeling techniques help
to simulate the global model with fairly accurate stresses at critical
locations. It explains the attenuation length requirements and also
some of the stress gradient checks to substantiate the accuracy of
the stresses at critical locations. It explains the types of sub models
and the circumstances when to use particular type of submodel for
the stress analysis. The pitfalls of submodel approache are helpful
for the user to perform the submodel analysis accurately without any
compromise on the quality of outcome.
Submodeling Technique in Stress Analysis | March 2011
© 2011, HCL Technologies. Reproduction Prohibited. This document is protected under Copyright by the Author, all rights reserved.
15
Reference
[1] http://www.ansys.com/events/proceedings/2002/PAPERS/9.pdf
[2] http://www.ansys.com/events/proceedings/2002/PAPERS/53.pdf
Author Info
Ramadas Nayak, B.E.
Ramadas Nayak received his BE in Mechanical
Engineering from Mysore University, India in
1997. He has more than 11 years of experience
in the domain of Aviation Gas turbine
technology. He has worked in both Rotors and
load bearing structural components of
commercial Aero Engines. He has worked
extensively on both cold and hot parts of the
Aero Engines. He performed all analyses with
ANSYS software in his career. He is currently
working with HCL Technologies supporting the
product development and product support
discipline of customer with Finite Element
Analyses of commercial Aero Engine Structural
components.
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