How to perform Finite Element Analysis (FEA)?

Whether you are an expert or novice, irrespective of the type of problem belonging to any engineering discipline you want to solve, regardless of using your own FEM tool or an open-source software or a commercial package, you have to follow the these standardized steps to complete your FE analysis.

In this article, I would explain the essential steps involved in completing your FEM based analysis.

Essential steps to conduct Finite element analysis (FEA)

1. The first step involved the decomposition of the problem domain into small finite subdomains, called elements. The power of FEM lies in its ability to discretize a complex continuous domain into finite elements and nodes. This process is also called meshing. The purpose of meshing process is to prepare a set of unknown variables to be determined over the entire domain where solution is to be obtained.
2. Select an appropriate mathematical model i.e. governing differential equation, related to your analysis type and convert it into element model by using FEM. Assign these elements to the discretized domain. Say, you are solving structural problem, then, you have to develop your own structural element or choose from already available catalogue of elements, and assign it to the discretized domain along with relevant material properties.
3. During this step, the stiffness matrix of each element is assemble into a global stiffness matrix representing the entire discretize domain.
4. Apply loads and boundary conditions.
5. Solve for unknown displacement vector (i.e. primary or state variables).
6. Calculate dependent or secondary variables, if required.

Figure 1. A general procedure for Finite Element Method (FEM) based analysis.

The procedure of performing FEA using above steps seems very cumbersome, but, in actuality it is not. Many commercial software packages have been develop to simplify the FEA. For commercial tools, the above steps, also shown in Figure 1, can be categories as following stages:

Preprocess

This stage covers step# 1 to 4 listed above. The geometry of problem is either modelled in FEA software, or may be imported. Then, it is meshed. There are meshing tools available in the software packages which mesh automatically but also manual mesh control. After meshing, the element type is selected for already developed catalogue of elements depending on the nature of analysis to be perform. These elements are assigned to the meshed domain along with relevant material properties. Next, appropriate load and boundary conditions are defined.

Solution

At solution stage, an appropriate solver is selected to find out the unknown displacement variables. A solver is an algorithm that efficiently solves a big set of simultaneous algebraic equations to compute unknown state variables.

Post-process 

It involved the derivation of dependent or secondary variables from primary or independent variables, and plotting and visualization of results as per requirement.

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.