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Areas of ExpertiseFinite Element Analysis


Innovex uses the latest in Finite Element Analysis (FEA) software to solve complex design problems. Our FEA experts stay on the leading edge with constant training and approved simulation validation, enabling us to consistently produce fast and accurate results. Here we provide some insight into the FEA process.

For an example of this process in action, please see this ASME pressure vessel sample problem.

Conceptual Introduction

Model Creation and Simplification

Creating good FEA models from scratch or simplifying existing ones consists of removing features or parts that will not affect the simulation results. This may result in suppressing a large portion of the model or adding material to irrelevant holes. Areas that may cause software instabilities are also fixed during this process, such as removing short edges and faces, or adding small fillets to sharp corners.

There are three main reasons for FEA model simplification: speed, accuracy, and stability. The amount of time it takes to run a simulation can be drastically reduced based on how much of the original CAD model can be simplified. Removing unnecessary parts is a large component to this, but also removing or optimizing features that create an excess of mesh elements can reduce the overall time as well. Adding fillets and elements to corners will eliminate inaccuracies in corners, but this should only be applied sparingly as the mesh is increased. FEA stability can be increased by removing small features that are insignificant such as short faces and edges.


In order to run a simulation the FEA software must discretize the model into small shapes (elements) that are connected at the elements nodes. Generally, a higher amount of nodes and elements results in higher accuracy mesh. However; the more elements and nodes that the model contains, the more calculations the software must determine, thus escalating the simulation computation time (from an hour to potentially days). Meshing is a fine balance between accuracy and time, therefore; it is crucial to determine the required amount of mesh refinement in the areas of concern.

Boundary Conditions

Model restraints are applied to the model to accurately depict its environment. Restraints include fixed geometry, hinges, roller/slider, on faces, reference geometry, bolts, springs, symmetry, etc. Incorrectly applied restraints can drastically alter the results of the simulations. For example, over constraining the model can create non-existent stress concentrations and overly stiff parts or the opposite perhaps by providing an abundance of flex which may now ignore areas of high stress.


Choosing the correct simulation solver will not only produce the results quicker, but can be the difference between an accurate and inaccurate simulation. In Solidworks Simulation, for example, the most common solver is FFE as it is used for simulations with more than 100,000 nodes, however; do not use with models containing instabilities, immediate changes in deflection, or models with excessive contact sets. Direct sparse is to be used for small studies that have a maximum of 30,000 nodes or studies containing materials with varying Young’s Modulus values. When direct sparse is required and the model mesh has a vast amount of nodes – use large problem direct sparse.

Interpreting Results

Simulation results can be extracted in various amounts of ways. This includes, factor of safety plot, stress plot, displacement plot, strain plot, reaction force, remote interface force, free body force, contact/friction force, connector force, result comparisons, and mesh details. Further detailed results can be obtained through result simulation probes, sensors, and orientation plots such as vertical displacement.

Checking for Accuracy

Achieving an accurate mesh is an important step that is often overlooked by amateur users. Multiple criteria must be satisfied before it is approved for accuracy, this includes reviewing the model for skewed element aspect ratios, error plots, stress gradients, and mesh independence plots. The ideal aspect ratio of an element is 1, meaning all sides of the element are of equal length. Due to holes, edges, and other geometries the ideal ratio cannot always be achieved. It is ideal to have at least 95% of the elements less than a 3:1 ratio and zero elements above 10:1 as skewed elements can result in large interpolation error. Energy norm error plot depicts the error percentage in regards to the difference between nodal and element strain and stress. If the plot determines that a group of elements have large error then it means the stresses at the nodes vary vastly from the Gauss points and therefore; requires additional refinement to reduce the error caused from extrapolating. Smooth stress gradients is a quick visual check to the model to determine if the mesh is reaching independence and should be used as an overall check. A mesh independence plot compares element or node stress values in areas of concern to the total amount of elements or nodes in the entire model. If the stress value insignificantly changes after numerous amounts of elements have been added to the mesh then mesh independence has most likely been achieved.

Linear vs Non-Linear

Benefits of Each

Linear finite element analysis is used for material that stays below its yield point. This type of simulation is relatively easy to setup and quick to obtain results. Linear analysis is also easier to validate with hand calculations.

Non-linear is used for materials or geometry that changes throughout the simulation. Material change occurs when the model exceeds its yield strength. Geometry change happens when the model shape changes drastically during the simulation due to its loading.

Limitations of Each

Linear FEA must have a linear material (stress proportional to strain), insignificant geometry changes, and cannot have loads or restraints that alter.

Non-linear is limited by extreme distortion scenarios and also by having an excessive amount of nonlinear contacts.

Examples of Geometric Non-Linearity

A part that deforms more than half its own thickness needs to have its stiffness re-evaluated due to the change that large change in its geometry. High pressure acting on a plate with large spans would fall under this category.

Examples of material Non-Linearity

All material that exceeds its yield point and approaches its tensile strength is considered to be non-linear. Between these points the material will undergo permanent deformation and its stress values are no longer proportional to its strain. This includes metal being permanently stretched or an excessive load permanently compressing a piece of rubber.


FEA vs Hand Calculations

Hand calculations are to be used whenever possible. It is the preferred method for simple and quick calculations and is necessary even for the more complex scenarios where it is preferable to use FEA. The reason for this is validation. Calculating a simple free-body-diagram and comparing to the simulation will ensure the simulation is on the right track.

However, hand calculations will not easily deliver detailed information and accuracy when using FEA on complex simulations. This is where FEA shines and becomes critical in competitive markets. Being able to analyze a part and obtaining detailed information on weak and strong points will enable material and strength optimizations and confidence in the overall design.

Uses of FEA in Codes (API and ASME)

Often codes allow for less conservative designs if developed with an FEA to identify weak or problem areas with far greater accuracy than can be accomplished using hand calculations. Some codes in fact require the use of FEA to meet their regulations.

Versus Physical Testing

Physical testing can be expensive. There are the obvious costs involved in materials and labour to produce testing samples or prototypes, procure testing equipment, logistically arrange and execute the testing and possibly repeat to verify design improvements. Often FEA offers a means to provide just as much insight, if not typically more, at a lower cost. Many more tests and test iterations can be done. Performance measurements can be taken that would physically be impossible or too cost-prohibitive to measure. Environmental conditions can be easily altered. There are many features available to the FEA analyst that proves it a valuable tool that has become a common part of the design process. Physical testing should still be done at some point in a design’s implementation; however, virtual testing and simulation helps to get to that final design stage more quickly and more cost effectively.