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Finite Element Analysis (FEA): Pre-processing

The following four-article series was published in a newsletter of the American Society of Mechanical Engineers (ASME). It serves as an introduction to the analysis discipline known as the finite element method (FEM). The author is Steve Roensch, an engineering consultant and expert witness specializing in finite element analysis.

Second in a four-part series.
Previous: Finite Element Analysis (FEA): Introduction

The Pre-processing Phase

As discussed in the introduction, finite element analysis is comprised of pre-processing, solution, and post-processing phases. The goals of pre-processing are to develop an appropriate finite element mesh, assign suitable material properties, and apply boundary conditions in the form of restraints and loads.

Meshing: Nodes and Elements

The finite element mesh subdivides the geometry into elements, upon which are found nodes. The nodes, which are really just point locations in space, are generally located at the element corners and perhaps near each midside.

  • 2D / Thin Shell: For a 2D analysis or a 3D thin shell analysis, the elements are essentially 2D but may be "warped" slightly to conform to a 3D surface. An example is the thin shell linear quadrilateral. "Thin shell" implies classical shell theory, "linear" defines the interpolation of mathematical quantities, and "quadrilateral" describes the geometry.
  • 3D Solid: For a 3D solid analysis, the elements have physical thickness in all three dimensions. Common examples include solid linear brick and solid parabolic tetrahedral elements.
  • Special Elements: There are many special elements, such as axisymmetric elements for situations where geometry, material, and boundary conditions are symmetric about an axis.

Degrees of Freedom (DOF)

The model's degrees of freedom (dof) are assigned at the nodes.

  • Solid Elements: Generally have three translational dof per node (X, Y, Z translation). Rotations are accomplished through the relative translation of groups of nodes.
  • Thin Shell Elements: Have six dof per node: three translations and three rotations. This allows for the evaluation of bending stresses due to rotation, bypassing the need to model physical thickness.

The assignment of nodal dof also depends on the class of analysis. For example, a thermal analysis only requires one temperature dof at each node.

Developing the Mesh on CAD Geometry

Developing the mesh is usually the most time-consuming task in FEA. The modern approach is to develop the mesh directly on the CAD geometry, which typically comes in three forms:

  1. Wireframe: Points and curves representing edges.
  2. Surfaced: Surfaces defining boundaries.
  3. Solid: Defining where the material is.

Solid geometry is preferred, but often a surfacing package can create a complex blend that a solids package will not handle. An underlying rule of FEA is to "model what is there," yet simplifying assumptions must be applied to avoid massive models.

Meshing Algorithms: Mapped vs. Free

The geometry is meshed with either a mapping algorithm or an automatic free-meshing algorithm.

  • Mapped Meshing: Maps a rectangular grid onto a geometric region. It allows the use of accurate and computationally cheap solid linear brick elements but can be difficult to apply to complex geometries.
  • Free Meshing: Automatically subdivides regions into elements. Advantages include speed and easy transitioning (denser mesh in high-gradient regions). Disadvantages include potentially huge models and the use of expensive solid parabolic tetrahedral elements.

It is crucial to check elemental distortion prior to solution. A badly distorted element can cause a matrix singularity, killing the solution, or deliver very poor answers.

Material Properties and Boundary Conditions

Material properties vary with the solution type. A linear statics analysis requires an elastic modulus, Poisson's ratio, and density. Thermal analyses require thermal conductivity and specific heat.

Boundary Conditions:

  • Restraints: Declaring a nodal translation is fixed or a temperature is set.
  • Loads: Forces, pressures, and heat flux.

It is preferable to apply boundary conditions to the FEA software geometry rather than specific nodes, allowing the software to transfer them to the underlying mesh. This facilitates easier re-meshing and optimization.

Continue to Part 3:
Finite Element Analysis (FEA): Solution

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