FEM Basics

Finite Element AnalysisIt is a numerical method of solving engineering problems. May be applied in: structural (only this is discussed here - if you could write about heat and fluid - let me know) heat transfer fluid flow

Why FEA?

Analytical solutions not easily obtained in certain problems.Mathematical expressions required for solution may be complex due to following factors: shape/geometry loading material properties

Underlying Concept

Replace geometry with a set of objects with a finite number of DOF Divide the body into finite number of simpler units (elements). Elements connected at nodal points set of elements is called mesh

Difference between FEA and Analystical method

Analytical methods involve solving for entire system at one go.FEA involvies defining equations for each element and combining to obtain the system solution. It is therefore an approximation technique.In other words Analytics is accurate but FEA is at best a good approximation.

FEA Approach

Most common technique isDisplacement Method loads are known resistance to deformation of elements known displacements are unknown valuesSolve for displacementsWe obtain Stress from the displacements (derived).

Structural FEA

Structural problems defined in terms of: loads (forces) resistance to deformation (stiffness) displacements given by: [k]{d} = {F}k=stiffness, d=displacement, F=force

In FEA, the assumption is that variation of displacement across an element is a simple function.we combine the results of the displacement of each nodepoint as a single set. There problem is a large group of simple algebraic equation solved using Matrix method.

Role of Computers in FEASimplicity of each individual equation.Connectivity of nodes (means resultant of adjacent elements applied)Large number of equations.Three good reasons to say that FEA is suited for solving uy analysisrsing computers.

Methodology-Pre-process-Analysis-Post Process

Pre-Process -Meshing and related activitiesApplication of Boundary conditions and loads

AnalysisThis part is done by the computer using the necessary analysis software.

Post ProcessOutput of FEA analysis is data.One important thing to note : the results are only as good as the input during modelling. If you have applied BC wrongly, then result is sure going to suffer.We can safely say "Garbage in, Garbage out"