caeai guide to fea of part to part connections

8/19/2019 CAEAI Guide to FEA of Part to Part Connections

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Engineer’s Guide to Finite ElementAnalysis of Part-to -Part Connections


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Engineer’s Guide to Finite Element Analysis of Part-to-Part Connections

Copyright © 2014Published by Computer Aided Engineering Associates Inc.

All rights reserved. Except as permitted under U.S. Copyright Act of 1976, no part of this publication may be reproduced, distributed, or transmitted in any form or by anymeans, or stored in a database or retrieval system, without the prior written permissionof the publisher.

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Engineer ’s Guide to Finite Element Analysis of Part-to-Part Connectio


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Chapter 1

Modeling Bolted Connections 4

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Chapter 2

Modeling Bolted Joints & Understanding Load Transfer 9

Chapter 3

Large Scale Modeling Techniques 12

Chapter 4Using Constraint Equations in a Structural Analysiswith Large Deformations 15

Chapter 5

About CAE Associates 18

Engineer ’s Guide to Finite Element Analysis of Part-to-Part Connecti

Table of Contents


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Bolted connections are common to many industries where standards (ASME, AISC, San-dia National Labs, ASTM, etc.) exist for bolt design procedures.

These regulations and recommended practices provide tools to size bolts and deter-mine bolt torque loads based on the design environment. Yet, when it comes to includ-ing your bolted joint in your nite element model there is often confusion on how toproceed. How much detail is needed and how do I account for the bolt pre-load? Can Idetermine if I will lose my pre-load? Do I need to model the bolt? the nut? the threads?

Bolted connection analysis is no different than any other nite element calculation, inthat the engineer needs to understand the analysis end goal prior to any calculations. Three basic requirements of a bolted connection are that the bolt must have adequatestrength, the joint must remain intact and the connection must have adequate fatigueand fracture life. These requirements may or may not need to be addressed using thenite element method. The following list provides three levels of modeling recommen-dations based on the listed “assumed” analysis goals. They are listed in order of increas-ing level of nite element analysis complexity and accuracy, with each method requiringmore work than the previous simulation:

1) “I just need the bolt loads and I will design my bolts by hand using industry

standards, spreadsheets, etc. Cyclic loading is not an issue.”

(a) One does not need to always include the bolt in the nite element model, but canuse shared nodes or couples to join two bodies. Forces and moments can then beextracted from the nite element model at these nodes and applied to the bolt design“hand” calculation.


Chapter 1: Modeling Bolted Connections


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(b) If there is a gap between the parts, use a rigid beam or multi-point constraint ele-ment to tie the two bodies together. Spoke elements or constraint equations can alsobe used to distribute the load locally so that singular stresses do not occur at the fas-

tener (bolt head and/or nut) connection. Many nite element codes have automatedfeatures such as spot welds (Figure 1) that can be used to simulate this type of connec-tion automatically.

2) “I need to understand the load history in the bolts to assure that the minimumand/or maximum bolt forces are not exceeded.”

(a) The components to be bolted together must have contact elements dened alongtheir mating surfaces. The bolt needs to be modeled explicitly, but can be simpliedusing one or two beam element(s) to model the nominal bolt shaft. Bolt pre-load forcesare typically generated in the rst step of the analysis using one of the following meth-ods:


Figure 1: Spot Weld Modeling of aSeries of Bolts using Beam Elements –Plate Deformation

Chapter 1


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i. Constraint equations (The bolt is split into two elements and a relative overlap is induced to create tensile forces in the beams) Figure 2). ii. Imposed initial strain iii. Contact interference if the bolt head/nut are modeled iv. Thermally induced initial strain via contraction of the bolt shaft. Iterations are required to get the correct bolt initial pre-load modeled since the required bolt strain is a function of both the bolt and connecting plate

assembly stiffness.

(b) A sequential load history is needed to track the bolt force behavior over the entireload history. The nal bolt force will be a function of the load history. Be careful not to

use constant constraint equations if large rotations of the bolt are expected.

(c) Most standard bolts are designed for the bolt to fail prior to thread slippage, so thereis no need to model the threads in most bolt design-analyses.

Chapter 1

Figure 2: Bolt Preload Modeled Explicit lusing Automated Constraint Equations –Maximum Principal Stress


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3. “My bolt is non-standard and I would like to design the bolt such that thetransfer of loading to the threads is more uniform than a standard bolt wherethe rst couple threads carry all the load.”

(a) In addition to including the items listed above, explicit modeling of a threaded con-nection is required in this case, but can be greatly simplied by assuming an axisym-metric thread prole.

(b) Contact elements with or without friction should be modeled between the threadand nut and between the plates and bolt assembly if lift-off and onset of slippageneed to be evaluated.

(c) A material model including plasticity is likely required in the thread regions since lo-cal yielding is common at the thread root.

(d) Fillet radii need to be included as well along with a rened mesh at the contactinterface and thread roots where stresses peak (Figure 3).

(e) A fracture mechanics evaluation might also be warranted to examine potentialcrack growth at the locations of peak tensile stresses.

Chapter 1

Figure 3: Hoop Stress in Detailed ThreadedConnection Axisymmetric Analysis


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There are many other scenarios that could be included in the nite element model ofa bolted connection. Submodeling can often be used to develop more detailed boltmodeling with a local independent nite element model that accesses interpolateddisplacements boundary conditions from the global analysis. More details about mod-

eling of bolted connections can be found in the 2012 NAFEMS publication “FEM Ideali-sation of Joints”, compiled by Peter Hopkins, ISBN 978-1-874376-72-9.

Remember to develop a clear objective prior to building your model and note thatthe simplest approach is often the best!

Chapter 2 will discuss the importance of load transfer through mechanically fastened joints - like some of the connections described in Chapter 1.

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Chapter 1


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Understanding how structural parts interact and transfer load through mechanicallyfastened joints has long been a critical aspect of design. Even with the developmentof integrally machined parts, additive manufacturing, friction stir welding, and adhesive joining to name a few, many assemblies large or small still require some form of goodold fashioned nuts and bolts.

To support the investigation of joint load transfer and the resultant material stresses inparts, many companies turn to nite element (FE) modeling and analysis to investigatethe details. Engineers responsible for the structure have many pressing questions: Willmy parts stay assembled together in their load environment? Will the fasteners or theparent material break rst? Is the joint durable and can the parts sustain repeated load? These questions have to be answered!

Fortunately, we can accurately assess load transfer and material response through FEmodeling of the representative parts. Of course, there are many approaches to thisbased on the focus of your analysis. There are different levels of pertinent analyses rang-ing from coarse mesh shell & beam modeling to sophisticated detailed 3D solid model-ing.

While there are merits to simple forms of FE modeling, here is an approach that is very

useful in a variety of applications : model the 3D assembly and fasteners with detailedsolid nite elements. Most structures analyzed these days are modeled in a 3D CADsystem to ensure the three “f”s : form, t, and function of our parts. We can take advan-tage of the existing CAD assembly of those parts combined with parametrically denedhole size, fastener pattern, and addition of the 3D solid FE fastener in the model.


Chapter 2: Modeling Bolted Joints &Understanding Load Transfer


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Fortunately, with modern software capabilities we have automated 3D modeling tools(note Figure 1) to help us create these types of sophisticated assemblies and set up mat-ing surfaces with contact describing the interaction between parts.

Some investigative failure problems show the importance of this approach. As oneexample, a part was prematurely cracking in a primary load transfer joint. However, theinitiation of the crack was not at a hole edge or stress concentration location, as onemay expect. The crack origin was originating under the head of the fastener and out-side of the hole. After some detailed FEA of the scenario, there was a collective “aahh”from the customer while reviewing the FE results presentation that nally correlatedthe crack initiation site using the FE predictive tools. The 3D analysis captured the loadtransfer through frictional shear between the parts rather than pure bolt bearing. As

shown in Figure 2, considering the same fastener clamp-up load, low values of frictionresulted in peak stresses occurring at the edge of the hole. As the friction was in-creased, more load was transferred through shear between the plates and peak stressesoccurred away from the hole. Fastener clamp-up, parent material stiffness, surface cur-vature, and bearing transfer were all captured by this 3D joint analysis method.

Figure 1 - 3D Solid FE Model of a Bolted Joint.

Chapter 2


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Chapter 2

Figure 2 - Di fferent Load Transfer Mechanisms in a Bolted Joint.

Simpler tools based on analytical solutions often cannot capture some of these nuancesof load transfer. A 3D modeling approach at critical joint areas is recommended inorder to best understand the mechanisms of load transfer. Also, to assess uncertainties,sometimes you must bound the answers to the problem. For example, run solutionswith small or large bolt preload and small or large friction coefficients in the analysis.

Using some automated postprocessing techniques with the 3D solid model can yielduseful information regarding load transfer in your joint. In addition to investigatingcritical material stress results, the various contact pairs can be automatically queried todetermine load per fastener through each layer in the material. This approach is helpfulto plan out your most efficient joint load transfer.

But, with the additional accuracy comes the cost of performing the analysis. As withother general nonlinear analyses and larger problems, these runs will often take signi-cant computing time. But, don’t let this deter you.

In Chapter 3, learn how to tackle these larger scale problems with greater accuracy andefficiency!


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Engineer ’s Guide to Finite Element Analysis of Part-to-Part Connection

These common and consistent names across all databases in the assembly should beused to identify material properties, boundary conditions, loads and contact pairs. De-pending upon the software, it might be easier to assign materials, for example, withineach database. In other FEA software, it might be easier to use the named attributeswithin each database to assign the materials once combined into the full assembly.

Whichever approach is used, these properties saved into each individual database musttransfer into the main assembly and will be used to dene their respective conditions.

Assembly Contact: All the individual databases will eventually be assembled andconnected together in the full model. The use of bonded contact will be of great im-portance in assembly modeling as it allows for all the components to be meshed inde-pendently by each engineer, without having to know what the mesh on all the othercomponents will look like. Some FEA software, like ANSYS Mechanical, has the built incapability to automatically recognize mating surfaces and create a bonded contact pair.If this capability is not available when combining the full assembly, this is when the con-sistent naming of surfaces facilitates manually setting up the contact between compo-nents. For example, two anges each meshed and saved into two different databasesby two different FEA consulting engineers. The two anges are to be bonded togetherin the full assembly. The surface on one ange could be named “bond_A1_to_B1” andin the other database the mating surface is named “bond_B1_to_A1”. Listing all the con-

tacts that need to be bonded together in a master le will make it easy to automate thecontact creation with a short script.

Chapter 3


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The above gure is an illustration of two independent databases that are meshed,setup with boundary conditions, loads, material properties, named selections and con-tacts. Once the bonded contact pair is dened between the identied surfaces in theassembled model, it’s ready to solve.

Model Documentation: Lastly, all the details of each database should be documentedby the engineer throughout the setup process. This document will allow for all the FEAconsulting engineers to keep track of what’s in each model and how they’ll all cometogether once assembled. Clear and consistent communication between all engineersis critically important for the nal model to be assembled accurately.

This modular simulation system technique for creating a large assembly model alsomakes it possible and very easy to swap in and out new components without affectingthe rest of the assembly. This modular simulation approach scales very well when usedin a design of experiments (DOE analyses) to perform quick design changes on thecomponent level and determine the full system’s response to the new design.

In Chapter 4, the pitfalls of relying on constraint equations when modeling bolted con-nections are explained.

Chapter 3


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You may have heard the disclaimer in CAE Associates’ ANSYS update seminars, trainingclasses and e-Learning webinars: be careful about using constraint equations in a largedeformation analysis. Well, what’s that all about? Constraint equations are a very con-venient way to connect and/or dene relative motion between bodies. They allow usto create cyclic and repetitive symmetry boundaries. They provide a way to control thedisplacement of a collection of nodes all tied to a single master node. Best of all they doall these useful things while reducing the size of the mathematical problem by remov-ing degrees of freedom from the model. Why then are they a cause for concern in largedeformation analyses?

First let’s talk about what happens when we include large deformation effects in ournite element analysis models. Large deformation, a type of geometric nonlinearity,includes the following items:

Updating certain load vectors (pressure, for instance) to account for the defor-mation of a structure. These are so-called follower forces. Updating the stiffness of elements experiencing signicant deformation (largestrain effects) or rigid body rotation.

Considering the deformed shape in the calculation of stress. The change in thelength of the moment arm in a beam under a bending load is a typical example of this.

Including stress-stiffening effects that result from loading like the membrane orin-plane stiffness of a thin structure subjected to an out of plane load.

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Chapter 4: Using Constraint Equations in aStructural Analysis with Large Deformations


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If the bolt experiences large rotation, the bolt preload direction needs to be updatedwith respect to the current bolt axis. However, when a constraint equation preload isused, the pretension direction remains in the undeformed Z-axis direction as illustrated

in Figure 2 below. For a large rotation angle, α, the error in preload direction couldcause signicant error in the results.

The good news is that if your bolt preload is applied in regions of the model that arenot undergoing large rotations, they will still be valid. For this reason, it is important tocheck your initial results carefully. If you do see large rotations of the bolts in preloaded

regions there are other ways to apply bolt preload correctly. One approach is to usea multi point constraint (MPC) with preload capabilities in place of the actual bolt ge-ometry, if your FEA software supports it. This is a more advanced form of a constraintequation that will update with large deformation.

Chapter 4

Figure 2


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Since 1981, CAE Associates been helping companies large and small maximize valuefrom engineering simulation through expert FEA consulting and CFD consulting ser-vices.

As an ANSYS channel partner since 1985, we provide full service technical support toover 100 companies in our region, including some of the world’s largest and sophisti-cated users of simulation like General Electric and United Technologies.

We offer a range of consulting options to t unique and specialized needs of our clients.It could be as simple as getting to the bottom of a product failure, or as complex asdeveloping the infrastructure and process for simulation within the entire organizationusing a combination of software, training, mentoring and automation.

Our team of senior technical specialists bring graduate-level educations and an averageof 15 years of real-world experience in a variety of industries including: aerospace, elec-tronics, consumer product, turbomachinery, civil engineering, manufacturing, biomedi-cal, energy, and nuclear power.

For questions and to nd out more about how CAE Associates can help you solve

your engineering analysis challenges, please contact us at [email protected].

Chapter 5: About CAE Associates Inc.

caeai guide to fea of part to part connections

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