Simulation Transition: Meshing and Elements

It’s probably safe to assume that the majority of us had a Lego collection as a kid. They came in a variety of different shapes and sizes, from rectangular blocks to thin long ones. Each was designed with a particular purpose and application. We spent many a rainy day figuring out how to erect our favorite spacecraft or robot with these blocks.

This is exactly what meshing does for our computer-aided design models on which we seek to conduct analysis. Just as every Lego brick had a purpose, some more so than others, in the world of simulation our “Legos” are a variety of different elements. This month, we look at the array of elements and provide some insight into their application in the world of simulation analysis.

Why Mesh?

But why do we have to mesh before running a simulation? To answer this, think back to the area under the curve in math class. An accurate way to assess the area under a continuous curve is to imagine that there are tiny squares filling an area we are adding up. If we increase the quantity of these squares by making them smaller, we will eventually converge to a common value after several iterations.

This process, in theory, is precisely how we approach meshing of unique 3D CAD models. Due to the nature of CAD models, it’s only natural to consider that each model may require different geometric elements. The most commonly used elements in finite element analysis can be categorized as one-, two- and three-dimensional.

Dictated by Dimensions

One-dimensional elements are commonly referred to as beams. Imagine a long, slender structure such as a bridge, steel building or a vertically erected truss structure. Most of these structures are prismatic in profile, meaning that the cross-section is uniform along the length of the columns.

During the design phase of such structures in CAD, we commonly use 3D sketching for the initial layout, and add weldments to simplify construction of the design. These types of CAD models can be suited for using one-dimensional beam elements.

One benefit of using beams is that they require less computational resources due to reduced degrees of freedom. One-dimensional elements are used in three-dimensional analysis problems. The one-dimensional categorization refers to the geometric layout, which is comprised of two nodes at each end. Both nodes are the point of reference for where translation and rotation degrees of freedom exist.

Shells are the two-dimensional elements. They are primarily used in applications such as thin parts like fuel tanks, membranes and sheet metal panels. You may be noticing a trend that the structure’s geometry generally dictates which elements are used. Note that some software vendors will use draft-quality shell elements and high-quality elements. This difference relates to adding more nodes at the midpoints, increasing accuracy and computing resources.

Last, we have our three-dimensional elements. These elements are used in solid models with extrusions, lofts and organic surfacing shapes. They are by far the most commonly used element in most analyses.

Elemental Differences

Each element in this category has its advantages and disadvantages. A quick internet search will yield various technical white papers that discuss these differences.

Brick, Hexahedra and Tetrahedron are the most common used configurations across the simulation software vendors. All elements follow the same principle of having nodes at each geometrical end point, and some in their midpoints. From a geometric standpoint, mathematical efficiencies and approximations tend to be the key leading differences among them.

Next month we will dive into further detail about specifics in identifying the quality of a mesh by evaluating aspect ratios, Jacobian points and techniques for using adaptive meshing. We will set out to answer the question: What defines a great mesh?