Steps in FEA: An Overview

In the FEA vs. FEM article, we distinguished the two by introducing FEM as the numerical foundation of FEA. It is the underlying method that makes FEA works. Let us now look at the following steps involved in running a general FEA and their conceptual difference should become even clearer when compared with the Steps in FEM.

     The common steps for carrying out a general purpose FEA is summarised below:

1. Model Idealisation
2. Spatial Domain Identification
3. Element Selection
4. Mesh Discretisation
5. Material and Geometric Definition
6. Boundary Conditions
7. Pre-analysis Checks
8. Job Submission
9. Results Verification

1. Idealise Geometric Model

     The first step involves defeaturing small details of the model. Defeaturing is necessary but must always be done carefully as it is often the major source of error of an analysis. Assumptions made in this step will affect the results strongly and must be coherent throughout the analysis. For example, fillets are often omitted as they are difficult to mesh. However, defeaturing fillets in the region of interest for stress can be a hazardous decision due to stress singularity, which is common in structures with sharp re-entrant corners.

Thin Shell vs. Thick Shell

Thick shells are capable of modelling transverse shear deformation whilst thin shells do not. Thick shells are governed by the Mindlin–Reissner (thick shell) theory. As the shell thickness decreases, the problem tends to favour Kirchhoff (thin shell) theory which neglect the inclusion of transverse shear deformation. This is pretty much similar to the thin (Euler-Bernoulli) vs. thick (Timoshenko) beams comparison.

     Typical thickness for thin shell is <5% whilst thick shell theory applies within the 5-10% range. Anything significantly >10% should not be modelled using plate theories.

A comparison of the differences between thin and thick shell theories.

Theory	Thin shell Kirchoff-Love	Thick shell Mindlin-Reissner
Thickness vs. percentage of in-plane dimensions	Thickness < 5%	5% < thickness < 10%
Key assumptions	• Plane remains plane • Normal remains normal • Thickness is not affected by deformation	• Plane remains plane
Degree of freedom per node	• Translations Ux, Uy, Uz • Rotations Rx, Ry, Rz	• Translations Ux, Uy, Uz • Rotations Rx, Ry, Rz
Transverse shear deformation	No	Yes

See also
Types of elements in the element library

Membrane, Plate and Shell Elements

A comparison of the differences between membrane, plate and shell elements.

Element	Membrane	Plate	Shell
Engineering components	Pressure vessels, oil tanks, ship hull, wing skin
Analogous to	Truss	Beam with no axial stiffness	Beam
Number of nodes	Usually three: One each at the top, middle and bottom
Displacement degree of freedom	• Translations Ux, Uy	• Translations Uz • Rotations Rx, Ry	• Translations Ux, Uy, Uz • Rotations Rx, Ry, Rz
Stress output	• In-plane stresses	• Bending stresses • Additional transverse shear stresses for thick plates	• In-plane stress • Bending stress • Additional transverse shear stresses for thick shells

Also read
Types of elements in the element library

Thin Beam vs. Thick Beam

Standard beam theory (Euler-Bernoulli bending theory) assumes no deformation by shear. This can be safely applied to thin beams that are long and slender. For short and deep beams however, displacement due to shear becomes hugely important which is included in the formulation of thick beam element. Below is an exaggerated example of shear deformation:

Displacement due to shear that standard beam theory does not take into account

     This effect is the key that distinguish between the Euler-Bernoulli and Timoshenko (thick beam theory) bending theories. See below for a direct comparison between thin and thick beams.

Table illustrating the differences between thin (Euler-Bernoulli) beams and thick (Timoshenk) beams. Diagram in "look" section is adapted from Wikipedia.

Also read
Types of elements in the element library

What are Isoparametric Elements?

The truth is, you are probably using isoparametric elements without noticing it. In classes, we might have been asked to derive stiffness equations for elements of simple shapes such as rectangles or cuboids. This is to favour hand-calculations using simple equations.

In the real world however, most objects take irregular shapes. A Jacobian mapping process is therefore required to accommodate for this shape irregularity. Non-isoparametric elements can only be implemented to regular shapes and use shape functions solely for the purpose of displacement interpolation. Isoparametric elements on the other hand can be used to model irregular shapes. They use shape functions not only for displacement interpolation, but also to represent the irregular element geometry. This means shape functions are now responsible for both the displacement interpolation and element shape. This also means that modelling a curved surface within one single element is now made possible.

A mesh of isoparametric elements

In practice therefore, most elements offered by FEA programs are isoparametric elements. They are so widely used that they are not often stated in the user manuals.

Straight Beam vs. Curved Beam

Table illustrating the differences between straight and curved beams

See also

Types of elements in the element library