How to select an Element Type in performing FE analysis?

An element is fundamental building block of a finite element model and its proper selection plays a pivotal role in analyzing the problem on hand. In this article, I would explain the types of elements and their properties that will help you to make a better selection for your FE analysis.

Properties of Elements

An element represent a subdomain of engineering problem. The vertices of elements are called nodes. Sometimes, extra nodes are also located inside elements. These nodes serves following purpose:

• Element Geometry

The geometry of elements can be defined by proper placement of its nodes. They can have 1D, 2D or 3D dimensions. The number of nodes increases with increase in the element dimensionality thus require more computational resource.

In structural applications, the 1D structure elements are better suited for FE modeling of long prismatic sections like rod, pipe, beam etc. where length dimension is significantly larger than the cross-section dimensions. For plan stress or strain problems of shell and plates etc., where length and width dimensions are much larger than thickness, 2D structural elements can better for FE idealization. The 3D structural elements are generally use to analysis the structures where all three dimensions of are comparable or there is need to investigate in detail complex 3D state of stress or strain.

Figure 1. Geometry of 1D, 2D and 3D structural elements

It is interesting to note that there are some special elements which have no dimensionality like lumped spring, point mass, contact elements etc. Such elements are used in an abstract way during FE modelling, so be ready face this reality.

• Element Response

The response of elements is governed the attributes of its nodes. The nodal attributes are the unknown primary or state variables in the FE model that are computed at nodes, that’s why, these are called nodal displacements or nodal degrees of freedom (dofs), and are represented with {u}. There is one-to-one correspondence between the nodal dofs {u} and associated nodal forces {f}, and this defines the constitutive relationship at the element level i.e. {f} = [K]{u}, and the element response is dictated by this constitutive model working behind it.

In nutshell, the element response is expressed in terms of its dofs which are calculated during analysis. For structural elements, the dofs are displacement and rotations at each node, for thermal elements, the dof is temperature.

Selecting of a Right Type

When you want to build a FE model, you should use your engineering knowledge and judgement to identify the key variables that govern its behaviors. Say, you want to do a coupled thermal-stress analysis of a product. The geometry of product is such that all its dimensions are comparable. For this case, a 3D element would better idealize its geometry. Next, requirement would be to make sure that the selected 3D elements have relevant dofs that can capture the required coupled thermal-stress interaction i.e. temperature dof in addition to displacement degree of freedom to capture the coupled thermal-stress interaction.

Never trust your memory, always consult manuals of a commercial software packages to find appropriate element types for your FE model. The manuals not only list in detail the attributes of elements, its applications and limitations, and its formulation but also provides guidelines and example problems.

About the Author: Dr. Khazar Hayat is a professional engineer with almost 15+ year of experience in research, design, analysis and development of products made of fiber reinforced plastics composites (FRPCs). Currently, he is working as an Associate Professor at Mechanical Engineering Department, The University of Lahore, Pakistan, can be reaching by emailing at khazarhayat@gmail.com.