submodeling technique in stress analysis

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



3

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.



4

Abbreviations

Sl. No. Acronyms Full form

1 2D 2 dimensional

2 3D 3-dimensional

3 LCF Low Cycle Fatigue



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.



6

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



7

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



8

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.



9

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.



10

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.



11

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.



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



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



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.



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.

http://www.ansys.com/events/proceedings/2002/PAPERS/9.pdf




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submodeling technique in stress analysis

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