Finite Element Method For Solving Engineering Problems

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,…