FEA (Finite Element Analysis)

Finite Element Analysis (FEA) is a computer simulation technique used in engineering analysis. It uses a numerical technique called the finite element method (FEM). In this, the object or system is represented by a geometrically similar model consisting of multiple, linked, simplified representations of discrete regions — finite elements. Equations of equilibrium, in conjunction with applicable physical considerations such as compatibility and constitutive relations, are applied to each element, and a system of simultaneous equations is constructed. The system of equations is solved for unknown values using the techniques of linear algebra or nonlinear numerical schemes, as appropriate.

FEA has become a solution to the task of predicting failure due to unknown stresses by showing problem areas in a material and allowing designers to see all of the theoretical stresses within. This method of product design and testing is far superior to the manufacturing costs which would accrue if each sample was actually built and tested.

There are generally two types of analysis: 2-D modeling, and 3-D modeling. While 2-D modeling conserves simplicity and allows the analysis to be run on a relatively normal computer, it tends to yield less accurate results. 3-D modeling, produces more accurate results while it can only be run satisfacotrily on a faster computer effectively. Within each of these modeling schemes, the programmer can insert numerous algorithms (functions) which may make the system behave linearly or non-linearly. Linear systems are far less complex and generally do not take into account plastic deformation. Non-linear systems do account for plastic deformation, and many also are capable of testing a material all the way to fracture.

While being an approximate method, the accuracy of the FEA method can be improved by refining the mesh in the model using more elements and nodes, though this will retard the process of converging.

Uses

A common use of FEA is for the determination of stresses and displacements in mechanical objects and systems. It is used in new product design, and also in existing product refinement. A company is able to verify whether a proposed design will be able to perform to the client's specifications prior to manufacturing or construction. Modifying an existing product or structure is utilized to qualify the product or structure for a new service condition. In case of structural failure, FEA may be used to help determine the design modifications to meet the new condition. However, it is also routinely used in the analysis of many other types of problems, including those in heat transfer, fluid dynamics and electromagnetism. FEA is able to handle complex systems that defy closed-form analytical solutions.

Some FEA softwraes

• ANSYS
• MSC-NASTRAN
• FEMPRO
• OOFEM (Free)
• freeFEM (Free)
• FElt (Free)

Poissons Ratio

When an element is stretched in one direction, it tends to get thinner in the other two directions. Hence, the change in longitudinal and lateral strains are opposite in nature (generally). Poisson's ratio ν, named after Simeon Poisson, is a measure of this tendency. It is defined as the ratio of the contraction strain normal to the applied load divided by the extension strain in the direction of the applied load. Since most common materials become thinner in cross section when stretched, Poisson's ratio for them is positive.

For a perfectly incompressible material, the Poisson's ratio would be exactly 0.5. Most practical engineering materials have ν between 0.0 and 0.5. Cork is close to 0.0, most steels are around 0.3, and rubber is almost 0.5. A Poisson's ratio greater than 0.5 cannot be maintained for large amounts of strain because at a certain strain the material would reach zero volume, and any further strain would give the material negative volume.

Some materials, mostly polymer foams, have a negative Poisson's ratio; if these auxetic materials are stretched in one direction, they become thicker in perpendicular directions.Foams with negative Poisson's ratios were produced from conventional low density open-cell polymer foams by causing the ribs of each cell to permanently protrude inward, resulting in a re-entrant structure.

An example of the practical application of a particular value of Poisson's ratio is the cork of a wine bottle. The cork must be easily inserted and removed, yet it also must withstand the pressure from within the bottle. Rubber, with a Poisson's ratio of 0.5, could not be used for this purpose because it would expand when compressed into the neck of the bottle and would jam. Cork, by contrast, with a Poisson's ratio of nearly zero, is ideal in this application.

It is anticipated that re-entrant foams may be used in such applications as sponges, robust shock absorbing material, air filters and fasteners. Negative Poisson's ratio effects can result from non-affine deformation, from certain chiral microstructures, on an atomic scale, or from structural hierarchy. Negative Poisson's ratio materials can exhibit slow decay of stress according to Saint-Venant's principle. Later writers have called such materials anti-rubber, auxetic (auxetics), or dilatational. These materials are an example of extremal materials.

Factor of Safety

It is common practice to size the machine elements, so that the maximum design stress is below the UTS (Ultimate Tensile Stress) or yield stress by an appropriate factor - the Factor of Safety, based on UTS(Ultimate Tensile Stress) or Yield Strength. The factor of safety
also known as Safety Factor, is used to provide a design
margin over the theoretical design capacity to allow for uncertainty in the design process. Factor of safety is reccomended by the conditions over which the designer has no control, that is to account for the uncertatinities involved in the design process.

The uncertainities include (but not limited to),

1. Uncertainity regarding exact properties of material. For example, the yield strength can only be specified in between a range.


2. Uncertainity regarding the size. The designer has to use the test data to design parts which are much smaller or larger. It is well known that a small part has more strength than a large one of same material.


3. Unceratinity due to machining processes.


4. Uncertainity due to the effect of assembly operations like riveting, welding etc.
   
5. Uncertainity due to effect of time on strength. Operating environments may cause a gradual deterioration of strength, leading to premature and unpredictable failure of the part.


6. Uncertainity in the nature and type of load applied.


7. Assumptions and appoximations made in the nature of surface conditions of the machine element.

Selection of factor of safety

The selection of the appropriate factor of safety to be used in design of components is essentially a compromise between the associated additional cost and weight and the benefit of increased safety or/and reliability. Generally an increased factor of safety results from a heavier component or a component made from a more exotic material or/and improved component design. An appropriate factor of safety is chosen based on several considerations. Prime considerations are the accuracy of load and wear estimates, the consequences of failure, and the cost of over engineering the component to achieve that factor of safety. For example, components whose failure could result in substantial financial loss, serious injury or death usually use a safety factor of four or higher (often ten). Non-critical components generally have a safety factor of two. Extreme care must be used in dealing with vibration loads, more so if the vibrations approach resonant frequencies. The vibrations resulting from seismic disturbances are often important and need to be considered in detail. Where higher factors might appear desirable, a more thorough analysis of the problem should be undertaken before deciding on their use.

• 1.25 - 1.5 - Material properties known in detail. Operating conditions known in detail. Loads and resultant stresses and strains known with with high degree of certainty. Material test certificates, proof loading, regular inspection and maintenance. Low weight is important to design.


• 1.5 - 2 - Known materials with certification under reasonably constant
  environmental conditions, subjected to loads and stresses that can be determined using qualified design procedures. Proof tests, regular inspection and maintenance required.


• 2 - 2.5 - Materials obtained for reputable suppliers to relevant standards
  operated in normal environments and subjected to loads and stresses that can be determined using checked calculations.


• 2.5 - 3 - For less tried materials or for brittle materials under average
  conditions of environment, load and stress.


• 3 - 4 - For untried materials used under average conditions of environment, load and stress. Should also be used with better-known materials that are to be used in uncertain environments or subject to uncertain stresses.

Usually the factor of safety is kept larger, except in aerospace and automobile industries. Here safety factors are kept low (about 1.15 - 1.25) because the costs associated with structural weight are so high. This low safety factor is why aerospace parts and materials are subject to more stringent testing and quality control. Now computers are being used to provide more accurate simulation of stresses that occur in components, particularly in the case of high value products where safety and saving weight is essential.