FEA Engineering White Papers

Here you will find an assortment of FEA white papers and presentations produced by the Predictive Engineering staff on topics such as Fracture Mechanics & FEA, Small Connection Elements, Linear & Nonlinear Buckling Analysis, RBE and Modeling Composites.

White Papers

Why natural frequency analysis is good for you and your design

This article, reproduced from a three-part series in Desktop Engineering magazine, is a great introduction to the power of Finite Element Analysis to solve problems relating to vibration that often drives early product failure due to fatigue damage or just outright failure.

Introduction: Analysis work is rarely done because we have spare time or are just curious about the mechanical behavior of a part or system. It’s typically performed because we are worried that the design might fail in a costly or dangerous manner. Depending on the potential failure mode our anxiety might not be too high, but given today’s demanding OEMs and litigious public, the task could involve high drama with your name written all over it.

Keeping it Simple: In finite element analysis (FEA), these natural frequencies are called eigenvalues and their shapes are noted as eigenvectors or eigenmodes. This nomenclature is rooted in German and the word eigen denotes “characteristic” or “peculiar to” and came into common usewithmid-19th century mathematicians. With dynamic analyses, you’ll also see the terms normal modes and normal modes analysis. The use of the word normal prior to mode is just another way to say natural, characteristic, or eigen. When describing mode shapes, our preference is to just say normal modes since they represent the inherent natural response of the structure.

Dynamic Load Consideration: When a structure is loaded in a transient or time-varying fashion (e.g., when an electric motor creates a constant, sinusoidally varying load), if the eigenvalue of the structure is lower or higher than the excitation frequency, the structure will just behave as if the load was applied statically. Let us say that we have this structure with an eigenvalue at 10Hz and it is whacked by a transient (e.g., half sinewave with frequency of 10Hz), we would expect the structure to vibrate subsequent to the hit and then gradually return to its static zero-stress condition.



Linear Dynamics part 2

Vibration analysis can show detailed structural behavior under dynamic loading

In Part 2 of the Desktop Engineering magazine article, we explore vibration analysis and how it can show detailed structural behavior under dynamic loading. This article shows how we leverage Part I to indicate how the structure might respond to a vibrating load without having to do any type of more complex analysis. In short, this article shows how to interpret your normal modes results like a “pro”.

The Dominators: Modes with Mass: An interesting fact about normal modes analysis is that we can associate a percentage of the structure’s mass to each mode. With enough modes, you get 100 percent of the mass of the structure, though for complex structures this can mean hundreds of modes. The common thought is that if you capture 90 percent of the mass of the structure that will be good enough. For now, we’ll start classically and then show what this concept means in a real-world engineering situation.

Making Your Ride Smooth As Silk: Ever wonder what makes a quiet ride in a motor vehicle? It has to do with avoiding modes that might be driven to resonance; that is to say, keeping the structure dynamically static in its mechanical behavior. In an analysis of a modern motor home, imagine the FEA model is highly idealized using beam elements for the small structural tubes, plate elements for the main longitudinal beams, and lots of mass elements to represent the engine, air conditioners, water and diesel tanks, and passengers. After a normal modes analysis, we have 45 modes ranging from2.3Hz to 15Hz.

Advanced Analysis Checklist: Don’t panic when you have eigenvalues right on top of your operating frequencies. Only natural frequencies with significant mass participation factors are important. Eigenmodes have directions as do their mass participation fractions. Investigate these directions and see if they correspond to your forcing-function direction. If they don’t (let’s say they’re orthogonal), then the structure will remain dynamically stable.



Linear Dynamics part 3

Extracting real quantitative data to anticipate everything from earthquakes to rocket launches

In Part 3 of the Desktop Engineering magazine article, we look into extracting real quantitative data to anticipate everything from earthquakes to rocket launches.

Introduction: If you’ve kept up with this series of articles, you now know more about the dynamic behavior of structures than 95 percent of your peer group within the design and engineering world. And after reading about how vibration analysis reveals key information about structural behavior (see DE, April and May 2008), the terms “natural frequencies, normal mode shapes, mass participation factors, and strain energy” have become integral to your vocabulary. Up to this point the discussion has centered on qualitative terms about the mechanical response of structures due to dynamic loading. In this last part, we'll show how to extract real quantitative data (i.e., displacements and stresses) from a simple normal-modes analysis.

Doing It On The Cheap: The dynamic response of a structure is derived from its individual normal modes. If you hit your structure, its dynamic response is formed by the summation of its individual modes. Mathematically, we know that each one of our normal modes

has a frequency, a mode shape, and a bit of mass associated with that shape (a mass participation factor).All of this data is derived from the basic equation of motion: ma+kx = 0 From this equation, the standard linear dynamics solution can be derived as: v = K / m

where vis the frequency or eigenvalue of the system. Since no forces are involved in this equation we can't have any real displacements or stresses. If we want real data, we need real forces as in: (ma+kx = F).

Modal Frequency Sweep (MFS): Frequency-based loads are more common than you might think. Our previous example was of a vibratory conveyor. Since that was rather straightforward, let's look at something a bit more complex.

Power Spectral Density (PSD) Analysis: Satellites are expensive and failure is even more expensive. During launch (Figure 3a) they get pounded by a broad and chaotic spectrum of vibrations (accelerations) from the rocket motor, stage separation, acoustical noise, etc. No single acceleration frequency dominates and there are multiple layers of noisy events that occur randomly.



Bolt preload adds quite a bit of complexity to any model since the analysis procedure is nonlinear (geometrically nonlinear) and that two sequential nonlinear runs are required to arrive at the final “bolt preload solution”. The utility of this approach lies in its ability to quantitatively calculate the bolt axial and shear forces for any type of bolted connection. Additionally, if bolt fatigue is important, then a bolt preload approach is invaluable.

What is bolt preload?
Bolt preload is used to clamp together two plates or two structures and create a frictional lock between the members and reduce the effects of cycling loading on the bolt. With respect to the laWer (i.e., bolt fatigue), bolt preload can make all the difference between a safe, long-­‐lasting structure or catastrophic failure.

Where to use bolt preload?
Bolt preload is not a free lunch. To effectively use bolt preload on FEA connections requires many additional steps and it converts a linear run into a nonlinear run that requires two sequential nonlinear analysis where (i) the bolt preload is applied and then (ii) the external structure load is applied.

What is covered in this white paper?
This white paper will cover a the basics of setting up you model for bolt preload, theoretical foundation, examples of its use and a bolt fatigue primer.

Engineering Comment:
Bolt preload adds quite a bit of complexity to any model since the analysis procedure is nonlinear (geometrically nonlinear) and that two sequential nonlinear runs are required to arrive at the final “bolt preload solution”. The utility of this approach lies in its ability to quantitatively calculate the bolt axial and shear forces for any type of bolted connection. Additionally, if bolt fatigue is important, then a bolt preload approach is invaluable.

 



Fracture Mechanics and Finite Element Analysis Image

This white paper was done to provide an easy to understand approach to the use of finite element analysis (FEA) toward fracture mechanics. It starts off with a review of fracture mechanics and boils it down to a simple principle of energy in (loading) equals energy out (fracture).

Introduction: Fracture mechanics and finite element analysis are 20th-century technologies that have a profound impact on the way engineers design mechanical devices. structures and material systems. Although there is a wealth of literature in the e two fields. the basic concepts of these technologies are simple. Fracture mechanics describes the transfer of mechanical energy toward the creation of crack surfaces, i.e., the first law of thermodynamics. Finite element analysis is a numerical technique that solves continuum problems with an accuracy acceptable to engineer. Together these technologies provide powerful tools to predict critical loads or crack sizes that may cause fracture in proposed designs or existing structures. With the advent of modern personal computers and finite element codes it may now be much simpler to solve engineering fracture mechanics problems a priori rather than after a catastrophic fracture event. The foundation of fracture mechanics was laid in the 1920s by A.A. Griffith while he was working for the Royal Aircraft Establishment at Farnborough, U.K. According to J.E. Gordon, Griffith asked: "Why are there large variations between the strength of different solids. Why don't all solids have the same strength. Why aren't they much stronger?"

Conclusion: In conclusion. the engineer should realize that analytical results are only as good as the experimentally measured fracture toughness data and that the fracture toughness of a material is not single-valued but may vary significantly due to environmental or fatigue effects. Furthermore, the presented approach is quite basic and one should consider that the field of fracture mechanics is rich with analyses that did not work. This discussion has not considered the effects of fatigue, corrosion, or thermal mechanisms on the fracture process-these can play a dominant role depending on the service environment. Nonetheless, engineering has often been a discipline of making science work and, when properly applied, the use of fracture mechanics principles and finite element analysis can be a useful tool to ensure that the engineer creates the safest, toughest, and lightest structure.



Fracture Mechanics of Glass Image

Glass is a fantastic material for subsea use. It’s incredibly strong in compression, transparent, and also relatively light. This white paper explores the fracture mechanics of glass using FEA to simulate both static and dynamic stresses in a glass hydrosphere.

Introduction: Research on the use of glass for submersible applications mostly ended in the 1970’s as world interest in the deep parts of the ocean shifted elsewhere. While glass had some early successes, research halted with the rise in acceptance of acrylics for shallow submersible ports and the realization by Naval research that glass is not a good material to resist nearby explosive detonations. Since that time considerable advances in fracture mechanics, reliability analysis, coatings, and manufacturing techniques have occurred.

What We Did: Dr. George Laird, Predictive Engineering - DOER contracted with Dr. Laird to model and study glass mechanics and brittle material failure modes and mitigation using Finite Element Analysis (FEA) and other tools. In the initial meeting he theorized the likely failure mode of the Hyper-Hemi design may be from Mode II fracture growth (see center case below) around stones or other impurities in the glass. He will help us further investigate the Stress intensity factor for Mode II (KIIC ) in glass, calculate acceptable values for flaw density, and develop scale model tests to quantify safe working stresses and cycle life. Studying theories presented to use by Corning for use in glass port seating. He has already started FEA modeling work. An amendment to this entry is that Mode II fracture has been deemed less likely than initially theorized. The current understanding is that a buckling failure is the most likely result; there is a 4X FOS in the current concept.



This white paper will walk you through the use of NX Nastran and LS-DYNA to do classical Eulerian Buckling, geometric nonlinear buckling and complete, full-physics nonlinear buckling (LS-DYNA). We will also show you how to validate your linear buckling analysis with a non-liner static analysis. Additional examples are presented on flange crippling and then finally the application of these techniques to the buckling analysis of a beer can and then an eight-passenger, deep-diving luxury submarine.

Everybodys’ First Buckling Analysis Model: The cross-section properties and equations given above provide all the necessary ingredients to calculate the buckling load of the column.  The factor “K” shown above is used to classify the beam’s end conditions (Manual of Steel Construction, 8th edition, American Institute of Steel Construction).  The buckling load depends upon whether the beam’s end points are fixed, pinned or partially constrained.

Geometric Nonlinear Analysis of Simple Column: A geometric nonlinear solution, as the name implies, only looks at the effects of large deformation on the FEA model and ignores all material nonlinearities.  The general approach is that the regular and differential stiffness matrices are generated and the solution is solved in an incremental approach.  That is, as load is applied and the structure deforms, the stiffness matrix is reformed to account for the deformation within individual elements.  This is a robust approach and captures all of the relevant physics of the buckling approach except for that of material instability.  However, we’ll show how to address material nonlinearity within a geometry buckling analysis and determine whether the analysis must include this extra nonlinearity or not.

Flange crippling is something that is often encountered in the design of highly loaded aerospace structures where paper-thin flange sections are the standard.  Crippling is a localized buckling mechanism that is driven by high compressive loads.  Figure 22 provides some background on the crippling mechanism.  As Figure 22 shows on the far left, the main portion of the extruded section might be stable but its collapse or global buckling is initiated by a localized buckle at its weakest point.  These types of structures are outside the realm of hand calculations; however experimentally derived charts exist  that allow the designer to make safe design choices about section thicknesses.  One designer suggestion is that, if it is not detrimental to the overall design, one can just specify that all flange sections have a b/t < 5 and then be free of any crippling consideration.

Download support files (508 KB ZIP)

Download webinar video (114 MB WMV)



This set of notes taken from one of our technical web seminars, condenses down in a logical fashion the very complex behavior of multi-point constraints which form the numerical foundation of RBE2 and RBE3 elements. Examples are presented to illustrate good and bad modeling practices.

Download model files (24.4 MB ZIP)

Download webinar video (165 MB WMV)



Modeling Composites with Femap

This 100+ page Handbook is intended to be the starting point for engineers that are interested in simulating the mechanical response of composite materials using Femap and then analyzing their models using NX Nastran or LS-DYNA. Basic laminate modeling theory is introduced and then tied back to how it is implemented within Femap. We also provide some easy to use rules such that one can create their own composite mechanical properties based on the rule-of-mixtures and cover the limitations of this method.

Important Chapters in this Handbook are: Composite Micromechanics, Laminate Modeling in Femap, Creating a 2D Laminate Model in Femap, Creating a 3D Laminate Model in Femap, Modeling a Sandwich Composite, Laminate Failure Theories in Femap, Modeling the Failure Behavior of Composite Laminates, Four-Point Bending of a Sandwich Composite Using Femap and NX Nastran and a very useful Addendum.

Foundation: This Handbook provides the foundation for users looking to model laminate and sandwich composites using Femap. Besides the basic setup for building the model, a full comparison is given between hand-calculations and NX Nastran and LS-DYNA results. Although not intended for composite experts, this paper will be a useful resource for many engineers facing the challenge of checking their results and building models.



Small Connection Elements (RBE2, RBE3 and CBUSH) Image

This white paper assumes that the reader has the basics of FEA down pat and an inkling of how R-elements work. The objective is to describe in detail how to use R-connections and CBUSH elements correctly and with confidence.  If you make it through this note, you’ll most likely know more about these little connections than 99% of your peers.

Introduction: We’ll cover the basics of MPC terminology which is the foundation of the RBE2 and RBE3 connections.  A keen understanding will be provided on how to think in terms of independent and dependent nodes.  It’ll be obvious after this discussion that it is not logical to apply SPC’s to dependent nodes or to connect other dependent nodes between different R-elements.  Best practices will be covered and some recommendations given (e.g., be careful when using MPC’s in a nonlinear analysis and especially so when large displacements are involved).

The thermal CTE capability of the RBE2 connection will also be covered for completeness.

Lastly, the CBUSH element will be introduced and applications given on how to use this replacement for the CELAS element.  The downfalls on using this element will be discussed and also why this element is a useful as a companion to the RBE2 and RBE3 elements.

The Basics About Multi-Point Constraints (RBE2 and RBE3 Elements): The tomes that have been written about R-type elements number in the dozens.  In their usage they have friends and foes.  For one highly experienced Nastran engineer that I know, the use of RBE3 elements is generally prohibited among their crew simply due to their ability to suck the life (i.e., load) out of a standard analysis run and such death-inducing ability is often reason enough to just say “no” to their usage.

To get a handle on how R-elements work, it is best to think of them as multi-point constraints (MPC).  Which then leads to the question as to what exactly is a MPC?  Taking a look at the NX Nastran Element Library Reference, one is presented with some dense logic but at its core, it defines a MPC as a linear equation among chosen displacements that is equal to zero. 

Interested in viewing the online technical seminar and support files for this topic?
Click here to find the files on our partner website, Applied CAx.

 

 



Vibration analysis is a huge topic and is easily the second most common type of FEA analysis after the basic static stress analysis. Within the field of vibration analysis, the most common type of analysis is that based on the linear behavior of the structure or system during its operation. That is, its stress/strain response is linear and when a load is removed, the structure returns to its original position in a stress/strain free condition.

What’s Covered: Foundation of Frequency Analysis, Standard Normal Modes Analysis, Modal Frequency Analysis, PSD Analysis, Direct Transient Analysis, Model Checkout (mass and constraints) and Additional Reading

An Excerpt From the White Paper: Standard Normal Modes Analysis: To see how this is applied in practice, we will run through an analysis project from start to finish (Normal Modes, Modal Frequency, PSD and Direct Transient). The model has been tweaked to protect the innocent.

We are starting with a PCB with two heavy electrical components. The PCB is a plate structure and the electrical components are modeled with solid elements. The PCB is screwed into a heavy component at the ends. The client must demonstrate that their PCB component can survive GM’s vibration, PSD and Direct Transient (pothole) specifications (but that has been modified to confuse any automotive spies).



See Analysis Data's True Colors Image

This article printed in Desktop Engineering's March 2011 edition is helpful when it's time to convince your engineering lead to trust your finite element stress data results. The paper explains why you don't always get what you want—and how to get what you need when analyzing data's true colors.

Introduction: Whenever you see a stress contour plot, just assume that it is wrong,” says Mark Sherman, head of the Femap Development Team for Siemens PLM Software Solutions. Although Sherman’s comment sounds a bit dramatic, it’s par for the course in computer modeling, where a common saying is “garbage in, gospel out (GIGO).”

White Paper Outline: How Stresses are Calculated in FEA, De-Bugging Jagged Stress Contours, Judging Good and Bad FE Shapes, Saint-Venant’s Principle of Decreasing Load Effects, Interpreting Stress Results and Visualizing Beyond FEA

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