The fundamental idea behind Finite Elemental Method involves approximating complex shapes by using a combination of simpler regular shapes, such as rectangles or triangles. These smaller shapes, known as finite elements, are assembled to model the original part accurately.  

Finite elements occupy distinct sub-spaces within the complex shape, allowing for easier visualization and modeling of objects like engines, airplanes, machine components, or skeletons. Unlike finite difference models, finite elements do not overlap in space.  

Application of Finite Element Analysis 

Traditionally, mechanical systems were analyzed by formulating differential equations based on relevant variables. However, solving these resulting mathematical models, especially nonlinear partial differential equations, was often impractical.  

This is where Finite Elemental Method becomes useful. Finite Element Analysis (FEA) refers to applying FEM to specific areas of analysis. FEA is a numerical method that provides approximate solutions to complex mechanical engineering problems.  

It diverges from using infinitesimally small or differential elements employed for centuries to derive differential equations. Originally a branch of solid mechanics, FEA has expanded its reach with the advent of advanced CAD and CAE tools.  

It is now extensively used in solving design problems across various engineering fields, including aerospace, defense, automotive, electromechanical systems, consumer goods, heavy engineering, industrial machinery, power, and energy.  

The following are the steps involved in FEA:  

Divide the integration interval 

The numerical result is an approximation of the exact solution.  

Select appropriate simple functions to represent the true function within each sub-interval 

The accuracy of the numerical result depends on the number of sub-intervals and the chosen approximation function.  

FEA software systems typically require the following information:  

• Spatial coordinates of nodal points
• Elements connecting the nodal points
• Mass properties and boundary restraints
• Details of loading or forcing functions
• Analysis options  

 
FEA finds application in various areas, including stress and structural analysis, and can integrate data from tools such as kinematics analysis and computational fluid dynamics.  

Some specific applications of FEA software include mechanical engineering design, computer-aided drafting (CAD) and engineering simulation services, structural analysis, modal analysis, solid mechanics, mold flow analysis, fatigue and fracture mechanics, thermal and electrical analysis, and sheet metal forming analysis. 

This article was contributed by our expert Mohit Singh

Frequently Asked Questions Answered by Mohit Singh

Q1. What is the fundamental idea behind the Finite Elemental Method (FEM)? 

The fundamental idea behind FEM is approximating complex shapes by using a combination of simpler regular shapes, such as rectangles or triangles, known as finite elements. 

Q2. How are finite elements used in FEM? 

Finite elements are assembled to model the original part accurately. They occupy distinct sub-spaces within the complex shape, allowing for easier visualization and modeling of objects. 

Q3. How does FEM differ from finite difference models? 

FEM does not overlap finite elements in space, unlike finite difference models. FEM provides a more flexible approach to modeling complex shapes and solving mathematical models. 

Q4. What is Finite Element Analysis (FEA)? 

FEA refers to the application of FEM to specific areas of analysis. It is a numerical method that provides approximate solutions to complex mechanical engineering problems.