FINITE ELEMENT ANALYSIS

What is FEA ?

WHAT is FEA ?

A complex problem is divided into a smaller and simpler problems that can be solved by using the existing knowledge of mechanics of materials and mathematical tools .

Why FEA ?

Modern mechanical design involves complicated shapes, sometimes made of different materials that as a whole cannot be solved by existing mathematical tools. Engineers need the FEA to evaluate their designs.

Basics of Finite Element Analysis

The process of dividing the model into small pieces is called meshing. The behavior of each element is well-known under all possible support and load scenarios. The finite element method uses elements with different shapes. Elements share common points called nodes.

FEM SOLUTION PROCESS:

PROCEDURES:1. Divide structure into pieces (elements with nodes) (discretization/meshing)2. Connect (assemble) the elements at the nodes to form an approximate system of equations for the whole structure (forming element matrices).3. Solve the system of equations involving unknown quantities at the nodes (e.g., displacements).4. Calculate desired quantities (e.g., strains and stresses) at selected elements.

EXAMPLES:

MESH

ANANLYSIS RESULTS

FEM Notation:Elements are defined by the following properties:

1. Dimensionality2. Nodal Points3. Geometry4. Degrees of Freedom5. Nodal Forces

ELEMENT TYPES:

Types of Engineering Analysis :

1.Structural Analysis2.Vibrational Analysis3.Fatigue4.Heat transfer

It consists of linear and non-linear models. Linear models use simple parameters and assume that the material is not plastically deformed. Non-linear models consist of stressing the material past its elastic capabilities. The stresses in the material then vary with the amount of deformation.

STRUCTURAL ANALYSIS:

VIBRATIONAL ANALYSIS:

This analysis is used to test a material against random vibrations, shock, and impact.

Each of these incidences may act on the natural vibrational frequency of the material which, in turn, may cause resonance and subsequent failure.

FATIGUE ANALYSIS:

This analysis helps designers to predict the life of a material or structure by showing the effects of cyclic loading on the specimen.

Such analysis can show the areas where crack propagation is most likely to occur.

Failure due to fatigue may also show the damage tolerance of the material.

HEAT TRANSFER ANALYSIS:

This analysis models the conductivity or thermal fluid dynamics of the material or structure .

This may consist of a steady-state or transient transfer. Steady-state transfer refers to constant thermo properties in the material that yield linear heat diffusion.

APPLICATIONS:

Visualization of how a car deforms in an asymmetrical crash using finite element analysis.

FEM allows detailed visualization of where structures bend or twist, and indicates the distribution of stresses and displacements.

FEM allows entire designs to be constructed, refined, and optimized before the design is manufactured.

FEA has also been proposed to use in stochastic modelling, for numerically solving probability models.

Benefits of FEM include increased accuracy, enhanced design and better insight into critical design parameters, virtual prototyping, fewer hardware prototypes, a faster and less expensive design cycle, increased productivity, and increased revenue.

The introduction of FEM has substantially decreased the time to take products from concept to the production line.

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