# FEA Consulting Part 4: Simulation and Analysis

© Glew Engineering Consulting, inc. 2016

Welcome again to our series on finite element analysis (FEA).  In the last blogs, I covered steps on setting up a computer-aided design (CAD) model and how to set up the mesh and boundary conditions, the most crucial steps in FEA simulation.  In this blog, I’ll look at the actual simulation and analysis, which can be the most time-consuming stage in the process.

As a reminder, for an example I’ve been using a recent project we worked on involving punching shear in reinforced concrete.  We were examining the effectiveness of reinforcing a column-supported concrete slab against the possibility of that column punching through the concrete.

# Types of Analysis

Once the CAD model has been created, the materials properties defined, the mesh generated, and the loads and boundary conditions set (leaving a model looking like Figure 1), the model is set for analysis.  There are a few different types of analysis software that FEA programs can utilize, based on the specific scenario being modeled.

• Linear: Linear analysis is useful for simpler systems with small deflections, linear elastic properties, and unchanging loads and boundary conditions. This type of analysis runs faster than nonlinear types, since it simplifies many of the parameters in the governing equations used to calculate results. However, those same simplifications can lead to invalid results if the model deforms too much under load.  Experienced engineers may recall the difference between “engineering strain” (e = ΔL/L) and “true strain” (ε = ln(1 + e)); the two are equivalent for small values of ΔL, but quickly diverge as the deformation increases.
• Nonlinear: Nonlinear analysis types encompass more complicated problems involving motion, nonlinear elastic or plastic materials, time-dependent changes to loads and constraints, or large deflections and changes in load direction due to those displacements. Nonlinear analysis can be more complicated to set up and take longer to run, but it is necessary for certain scenarios. The physics of certain problems are inherently nonlinear, such as radiation and fluid dynamics.
• Thermal: Thermal analysis calculates temperature and heat fluxes due to thermal loads, either for steady-state systems or time-variant systems. The latter can be used for materials that change phases between solid and liquid.
• Electrostatic: Electrostatic analysis can calculate current, electric field, and voltage distribution based on induced electrical parameters.

# Time-Consuming Analysis

At the most basic level, all of the above types of analysis essentially work the same way.  Each of the thousands or hundreds of thousands of elements in a model is represented by a series of partial differential equations representing their stress and strain.  While partial differential equations are difficult to solve manually, a computer can solve them rapidly by using the value at one boundary, checking the error, and iterating through again until the error is minimized.  It solves the equations for one element, then moves on the next element using the solutions from the last one.  The computer iterates through the entire model in this fashion, so the time begins to add up quickly when analyzing a complex model.  The most complex models can require hours or days to iterate through every element until the accumulated error has been sufficiently reduced.

# Reinforced Concrete Problem

For example, in our reinforced concrete problem we initially attempted a linear analysis, to ensure that the system was responding to the loads and constrains correctly.  However, we quickly realized that linear models would not suffice, considering the complex behavior of concrete under loads (it can withstand a lot of compressive force but fails very quickly under tension), the added complexity of adding two layers of rebar reinforcement, and finally the possibility of large deflections over such a big model.  We achieved our final results using Autodesk Simulation’s “Mechanical Event Simulator (MES) with nonlinear materials” simulation mode.  MES was designed to simulate dynamic events that occur over a period of time or with significant movement or deformation, like our meters-long section of concrete flexing under its own weight.

# Mesh Refinement Studies

We also ran a mesh refinement study alongside our analysis, which Autodesk™ automates as part of the analysis process. We reduced the element sizes on the model to 70%, 45% and 20% of the original sizes, making the mesh progressively finer and finer.  One might think of this like increasing the resolution on an image so that smaller details become clearer.  In FEA, mesh refinement increases the accuracy of the results and can get rid of outlier data like unreasonably high stress values.  For our model, however, we showed no difference in the stress values between the any of the refinements.  The only thing that changed was the elapsed times for meshing and analysis, which jumped from 6 minutes at 100% element size to 1 hour at 20% element size.  This just shows that we generated an excellent mesh to start with, as it produced accurate results but worked very efficiently at the same time.

Table 1: Mesh Refinement Study (reproduced with permission of G. Karampatsos)

[i]
Figure 2: Shear stress with decreasing element size (reproduced with permission of G. Karampatsos) [i]

Figure 3: Total runtime with increasing element size

Glew Engineering has done FEA consulting on a variety of projects, from semiconductor chambers and optical systems to vehicle lifts, heat exchanges and smart phone headsets.  Most of these we can’t post for proprietary reasons.  Take a look at our finite element analysis consulting services, and let us know how we might help you.

## References

[i] Karampatsos, G. (2015). Shear behaviour of a reinforced concrete slab when shear bolts are applied.

# FEA Consulting Part 3: Meshing and Boundary Conditions

Figure 1: Closeup, exploded view of our concrete slab mesh

We’ll continue on now with our blog series on finite element analysis (FEA).  After discussing how to best set up a computer-aided design (CAD) model for FEA simulation, in this blog I’ll cover the next step: meshing the model and applying boundary conditions.  “Meshing” is the process by which the CAD model is separated into discrete finite elements; it can be done in the same program that runs the FEA numerical simulation later, or it might be performed in a standalone program, depending on your software.  Boundary conditions are the loads (forces, movements, impacts, etc) and constraints that interact to actually cause deformation and stress in each element, and in turn the model as a whole.

# Mesh Generation

The mesh essentially gives finite element analysis its name; breaking a large complex shape into many smaller simple shapes allows the FEA program to easily evaluate the stresses for those simple shapes.  In a 3D element like our concrete slab in Figure 1, these elements might be simple cubes, or they might be more irregular pyramids and tetrahedrons.  Once the meshing program has evaluated the behavior of each discrete shape, it can integrate the data from these elements to create a model for the complex shape as a whole.

## Automatic versus Hand Generation

FEA can be performed by hand, as it was during its initial development in the 50s and 60s (Comini, p. 1)

[i].  Most FEA software still allows the user to develop meshes by hand, but for anything beyond the simplest shapes it becomes quite time consuming.  It must also be redone for each design iteration.

In general, it is preferable to allow a meshing algorithm to generate the mesh.  Based on a few parameters that the user can adjust, including ideal element size and aspect ratio, the program will move through the model and attempt to create a cohesive mesh.  However, despite many improvements over the years, automatic mesh generation is still not foolproof.  Even a simple flat plate can be have trouble meshing, if there are discontinuities in the boundary conditions.

## Guided Automatic Generation

Meshing programs usually offer tools to locally refine a mesh at specific spots on the model.  Autodesk Simulation, for instance, allows the user to create nodes on the model and then force the mesh to generate elements of a smaller size in a certain radius around that node.

The best solution for mesh generation is a compromise between drawing the mesh by hand and giving the meshing program total control.  An experienced FEA consultant can design or reconfigure a CAD model such that it encourages the mesh to form a certain way.  With an understanding of mesh generation algorithms, how meshes should be formed for certain constructions (for instance, at sharp corners or through thin plates), as well as how the algorithm interacts with the CAD file, an expert FEA engineer can make the meshing program run in predictable and useful ways.  Figure 1, at the opening of the blog, shows a portion of our final mesh after we’d guided its generation with some careful CAD work.  This is one reason that Glew Engineering keeps multiply CAD licenses, to correct CAD designs for FEA purposes.

# Boundary Conditions

FEA is the solution of partial differential equations for many small elements, with certain boundary conditions applied to the perimeter and perhaps internal nodes.  The boundary conditions are thus the loads.  FEA modeling is always concerned with how an object will respond to some external stimulus, simply called the loads.  Force on a part results in deformation, or motion.  If the part is static, then there must be reaction forces opposing the loads.  The concrete slab in this problem is being pulled down by gravity and the loads placed on the floor, but opposed be the support columns and constraints around the perimeter of the floor.  Without specifying both the applied loads and external constraints, the floor would not be static.

There are a few types of loads that a CAD model can be subjected to in a FEA program.  A force pushes or pulls on a specific section of the model, while a pressure exerts a distributed force across a surface.  An impact is simply a force that is exerted instantaneously but then drops to zero.  Objects can also be set with an initial velocity, to study collisions.  Enabling gravity pulls all of the elements downward equally.  Lastly, for thermal or electrostatic analyses, surfaces can be set to a specific temperature or exposed to an electrical current.

Gravity is essential in this simulation, since the main contributor to punching shear is the weight of the concrete slab itself.  In civil engineering, the weight of the structure is called the “dead load”.  There was also a “live load”, representing the people, furniture and equipment on top of the slab.  We modeled these loads with a pressure, or equally-distributed force, across the top surface of the slab.  The live load pressure is represented in Figure 2 as the orange force arrows pressing down on every element along the top surface.

## Constraints

Constraints prevent some part of the concrete slab from moving vertically, which causes the weight to deform the slab.  Every model needs a set of physical constraints keep it from flying off into infinity while still letting it bend, expand or contract as it would in real life.  These constrains can prevent translation (movement) in the x, y and z directions or rotation about the x, y and z axes.  Many times the constraints on a given surface will involve restraining some translational axes and some rotational axes.  If the model has been cut across a symmetry plane, for instance, then the elements on that surface need to be constrained such that they can’t move across it or rotate into it (otherwise our side and the mirrored side would rotate into each other, which we can’t allow).

The small red circles shown in Figure 2 mark the constraints on every node (the intersections between element) along one symmetry plane on our slab.  To obtain the correct symmetry behavior, we set:

• No translation in the x-direction
• No rotation about the y-axis
• No rotation about the z-axis

# Applying loads and constraints in FEA

The initial steps in setting up an FEA model determine the simulation.  The CAD model may need to be constructed in a certain way to allow the mesh to generate.  Then, that mesh needs to meet certain criteria if it’s going to be useful and give accurate results.  The loads need to be set correctly. Appropriate constraints ensure that the system is not under- or over-constrained.  Accurate and useful results in FEA simulation requires one to be careful and thorough in the initial setup.

Glew Engineering has done FEA consulting on a variety of projects, from semiconductor chambers and optical systems to vehicle lifts, heat exchanges and smart phone headsets.  Most of these we can’t post for proprietary reasons.  Take a look at our finite element analysis consulting services, and let us know how we might help you.

# References

[i] Comini, G., & Giudice, S. (1994). Finite element analysis in heat transfer: Basic formulation and linear problems. Washington, D.C.: Taylor & Francis.

# FEA Consulting Part 2: CAD Model Preparation

Figure 1: Reinforced concrete mesh

Welcome back to our blog series on FEA.  In the last blog entry, we introduced some of the fundamental concepts in finite element analysis (FEA).  This entry in the blog series focuses on the initial steps in preparing a computer-aided design (CAD) model ready for use in an FEA program.  Since FEA programs are very sensitive to the data they have to work with, it’s important that the CAD models being analyzed are compatible with the analysis methods the FEA program uses.

In order to illustrate my points throughout the blog series, I will introduce a recent FEA consulting project that we completed.

# Modeling Punching Shear in a Concrete Slab

We were recently approached by an academic, who was examining the behavior of a reinforced concrete slab with a concrete column through the center.  This configuration can be problematic in that it can lead to a phenomenon known as punching shear or “punch through.” An insufficiently reinforced concrete slab can fail in shear around a supporting column.  You might recall that pressure is force divided by the area.  A person in tennis shoes and a person in stiletto heels (Figure 2) exert the same force (their weight) on the ground they stand on.  However, the pressure exerted by the stiletto heel is much greater than the flat shoe, since the contact area is so much smaller, and the heels are likely to punch into the ground.

Figure 2: Stilleto heels; fine on concrete, impossible on dirt
christian-louboutin-stilettos-sling-back-platform-pumps-black by Maegan Tintari / CC BY 2.0

This academic was investigating the effectiveness of a Ancon Building Products’ Shearfix system which uses vertical rebar studs set in the concrete during pouring, as shown below in Figure 3.  He had constructed analytical models, and wanted verification that a numerical calculation would give similar results.  We agreed to assist, and will be using our work on this concrete problem as an example for these blogs.

Figure 3: Ancon Shearfix punching shear reinforcement in a concrete slab

As reviewed in the introductory blog of this series, one often needs to clean up or simplify CAD models before we can analyze them in FEA software.  Sometimes this means simplifying a model so that the FEA software can create the mesh and analyze the model faster and more accurately.  In other instances, due to interferences or missing surfaces, the model might not mesh correctly at all, which must be repaired.

## Interferences

In CAD parlance, an interference in a model is an occurrence where two solids or surfaces overlap.  This can happen in a computer, but not in real life.  It is up to the engineer or designer to correct the problems.  If any parts intersect in the same space, the FEA program will not be able to mesh correctly at that point, let alone mathematically analyze the behavior of such a physically impossible situation.

We created a simple example to illustrate the example in Autodesk Inventor™, as shown in the Figure 4 below.  The hole for the bolt is too narrow, and overlaps.  Most CAD programs have an interference check feature, which in this case lights up where the sides of the bolt are inside the block. It is not unusual that overlap or interference is the design intent, as in an interference fit. Nonetheless, one would still need to modify the CAD drawing to generate a mesh in an FEA program.  If one was interested in the stresses due to the interference fit, that must be handled separately.  A meshing program would not be able to mesh this piece correctly with overlapping parts.

Figure 4: Interference in a CAD model

## Complex features

Many parts and assemblies have complex features that don’t actually affect their structural integrity.  In our reinforced concrete problem, for instance, the rebar studs have a raised pattern around their sides to provide a better bond with the concrete, visible in the Figure 5 below.  However, since we simply set the concrete and rebar as bonded in the FEA program, these raised patterns will only significantly increase the complexity of the mesh; better to leave the rebar as smooth cylinders.

Figure 5: Typical steel reinforcement bars (rebar)
Rebar by Shauqee Pauzi /  Freeimages.com

## Symmetry

One of the most important concepts that can improve FEA performance is the use of symmetry.  The concrete problem we were presented involved a square concrete slab 6 meters to a side; with elements small enough to model the behavior across the 30mm-wide rebar studs, a 6m x 6m square would require millions of elements.  However, by taking advantage of the equal loading across the slab and three sets of 2-fold symmetry (horizontally, vertically, and one about the 45° diagonal), we could slice the slab down to one eighth (½3) of the size, as shown in Figure 6.  By setting the correct boundary conditions (discussed in the next blog), the results in our slice would mirror back out to the rest of the slab.  This simple change cut our meshing and analysis time by approximately 88%.

Figure 6: Symmetry planes used in our concrete slab FEA

# CAD Preparation is the Key to FEA Success

Any mechanical engineer or draftsperson working on an elaborate and complex CAD model will no doubt be proud of their work.  Unfortunately, if they insert that complicated model straight into an FEA program, it’s likely that the program will take hours to analyze the model, if it can mesh it at all.  For the best results, a CAD model must be reduced in size and complexity just the right amount, so the numbers are still accurate but the model runs efficiently as well.   After all, no one wants to subcontract out to Rip Van Winkle to collect their simulation results once they finish compiling 100 years later.

Glew Engineering has done FEA consulting on a variety of projects, from semiconductor chambers, piping, optical systems, vehicle lifts, heat exchanges, smart phone headsets and others.  Most of these we can’t post for proprietary reasons.  Take a look at our finite element analysis consulting services, and let us know how we might help you.

# FEA Consulting Part 1: Introduction

Figure 1: FEA mesh and shear stress results for a reinforced concrete slab

# Finite Element Analysis Consulting (FEA)

In this series of blogs on FEA, we will first cover some basic elements common to many FEA projects, and then in subsequent blogs in this series, illustrate those methods through examples.

One of the services that Glew Engineering Consulting provides is finite element analysis consulting (FEA).  FEA consulting has been a great boon to the engineering profession, allowing mechanical engineers and civil engineers to accurately model the stress and strain behavior of complicated parts and assemblies prior to building physical prototypes.  FEA programs are capable of predicting the effects of loads and impacts, variations in temperature, changes in pressure, and more, on an object modeled in a computer-aided design (CAD) program.  However, finite element analysis requires a good deal of forethought and careful review to ensure that the meaningful results.  Even if the engineer is an FEA expert, complicated models can be very time-consuming.  An engineer might leave their FEA stress analysis running overnight, only to check the results in the morning and find that a corner of the model has a stress concentration (or “stress riser”) 10 times higher than should be possible.  This is often due to an inadequate mesh at that specific point.  In this case, he/she must adjust the model or mesh and then perform another overnight run.  Furthermore, as much as FEA software has improved, it still requires a certain level of expertise. The programs sometimes crash or can’t converge after a 99% successful operation, consuming valuable time, and leaving few clues as to how to debug the problem.

With the considerable costs of performing FEA, many organizations lack the resources (skill, time, or money) to take full advantage of the method’s capabilities.  As such, many of these groups turn to engineering firms that offer FEA consulting, such as Glew Engineering Consulting, when they need accurate and trustworthy analysis performed on their products.

Those designing products usually rely on others to perform the FEA. The FEA may be performed by an in-house FEA group, or an external consulting group. Sometimes, even with an internal FEA function, it is not uncommon to out-source some of the FEA effort due to exceeding manpower capacity during a design crunch, exceeding licensed seat requirements, or lacking special skills for certain analysis.  Alternatively, a company sometimes needs an independent third part to perform the analysis.

# A Brief Intro to FEA Methods

## Why many small finite elements

The stress and strain on a portion of material is the solution to a partial differential equation with certain boundary conditions.  These equations can only be solved for certain simple shapes.  Thus, real parts, which generally have complex shapes, are broken into many small elements or sections that can be solved.  Computers can efficiently solve the partial differential equations numerically for each small section, and then move onto the next section until the entire part is solve in small pieces.  In that it is a numerical solution, the computer iteratively solves the equations, applying the boundary conditions, again and again, until the error is minimized to an acceptable level.

As defined by the McGraw-Hill Dictionary of Scientific and Technical Terms, finite element analysis is as follows:

“An approximation method for studying continuous physical systems, used in structural mechanics, electrical field theory, and fluid mechanics; the system is broken into discrete elements interconnected at discrete node points” (5th ed., pp. 756-757)

## Three steps of FEA

At a high level, there are essentially three steps in performing an FEA on a part or assembly:

• Mesh the model, and apply boundary conditions or loads and constraints.
• Analyze the model.
• Prepare the results in user friendly form.

## Meshing the Model and Boundary Conditions

This system of elements and nodes is call the “mesh”, and the engineer has the option of constructing it manually or letting the computer generate it automatically.  It is generally preferable to let the software mesh it automatically, but this requires that the CAD model be intelligently edited beforehand. Sometimes, one must define the mesh by hand, but this has many disadvantages.  Besides the mesh, the software also needs to know the material properties for every part is an assembly: the density, stress criteria, elastic behavior, thermal properties, or any other pertinent property.  Most FEA programs have a library of standard materials from which the user can select.  You can see the mesh as the network of fine lines in Figure 1.

### Correcting CAD Files for FEA

Most FEA software fails to mesh if there are interferences in the model.  Fortunately, most CAD programs have the ability to easily identify interferences. Also, complex features in the CAD file may needlessly complicate the meshing, but have no impact on the calculated stress, so they must be simplified before FEA analysis.  For at least these reasons, it is useful for FEA consultants to have the same CAD program with which the designer first created the model. Often, the FEA consultant must edit the CAD files to make them FEA friendly.  For this reason among others, Glew Engineering keeps PTC Creo™, Dessault Solidworks™ and Autodesk Inventor™.

### FEA Mesh refinement

Meshes must be fine enough to give accurate results, but not so fine as to choke the computer by requiring excessive memory and computational power.  This is known as mesh refinement.  Basically one can refine the mesh, make it smaller as appropriate, until the results do not change.  There are automated routines for doing this, but they come with limited success.  Experience and understanding fundamental FEA concepts is the best guide to creating a mesh that is of the proper size.  Then, when one refines it, there is hopefully little to no meaningful change in the results.

## Boundary Conditions: Applying Loads and Constraints

Once the component or assembly mesh is fully defined, it needs loads and constraints.  The load can be any external operator that affects the component, whether it is gravity, pressure, impact, force, temperature, electric charge, or initial velocity.  The component then must be held in place with the right constraints.  With no constraints, the object will simply fly to infinity and beyond once a load is applied; with too many constraints, the program might find itself trying to divide by zero or evaluate an infinitely stiff surface.

## Setting the Analysis Type

FEA programs offer a number of different methods of analyzing a model, depending on the type of loading conditions and the expected response.  We typically use Autodesk Simulation, which breaks the analysis types into four main selections, each with many sub-options.  The main types are as follows:

• Linear: Linear analysis is useful for simpler systems with small deflections, linear elastic properties, and unchanging loads and boundary conditions.
• Nonlinear: Nonlinear analysis types encompass more complicated problems involving motion, nonlinear elastic or plastic materials, time-dependent changes to loads and constraints, or large deflections and changes in load direction due to those displacements.
• Thermal: Thermal analysis calculates temperature and heat fluxes due to thermal loads, either for steady-state systems or time-variant systems.
• Electrostatic: Electrostatic analysis can calculate current, electric field, and voltage distribution based on induced electrical parameters.

## Preparing the Results and Drawing Conclusions

The results of FEA are generally given in a report.  The FEA software will automatically generate the highlights of a report, but the analyst must augment that report with answers to specific questions posed by their client.  The raw data is of little or no use to the client, and must be distilled into a usable form.

Along with their analysis suites, most commonly-used finite element analysis programs offer a wealth of reporting options.  The FEA programs store the analysis results at each node, so the engineer can examine the stress, strain, displacement, and reaction forces and moments throughout the model.  You can see the color overlay in Figure 1, indicating the shear stress on the model.  Beyond simply viewing numerical results, most programs allow the engineer to create graphical representations as well, overlaying colored contour plots onto the model surface or outputting to graphs and charts.  In addition to their convenience in generating reports, these graphical tools also help the engineer analyze their own work.  The FEA consultant must view their results from with at least two goals in mind:

• Answer the original questions that led them to perform FEA.
• Ensure that the results they’re observing are accurate and representative of the actual physical system.

With the right tools and expertise, an FEA consultant or engineer can reap tremendous rewards with the proper use of FEA software.  This series of blogs will take a look at getting the most out of an FEA program, and some of the common pitfalls that FEA users encounter.

Glew Engineering has utilized FEA on a variety of projects, from semiconductor chambers and optical systems to vehicle lifts, heat exchanges and smart phone headsets.  Most of these we can’t post for proprietary reasons.  Take a look at our finite element analysis consulting services, and let us know how we might help you.

### References

Parker, S. (1994). McGraw-Hill dictionary of scientific and technical terms (5th ed., pp. 756-757). New York: McGraw-Hill.