Finite Element Analysis of Structures - Essay Example

What is Finite Element Analysis' Finite element analysis is a tool used in engineering to determine the physical effects a given set of boundary conditions will have on a part. Boundary conditions can be forces, temperatures, hydrostatic pressures, centrifugal pressures, torques, and displacements. The basic theory of finite element analysis is the same regardless of the type of analysis being done. The geometry being modeled will always be divided up into smaller divisions known as elements and the elements are connected together to form the finite element mesh. Each element contains nodes which are points were the elements are mathematically connected to one another. The idea of dividing a domain up into subdomains is the basic principle of how FEA works' FEA consists of a computer model of a material or design that is stressed and analyzed for specific results. It is used in new product design, and existing product refinement. A company is able to verify 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. There are generally two types of analysis that are used in industry: 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, however, produces more accurate results while sacrificing the ability to run on all but the fastest computers 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. How Does Finite Element Analysis Work' FEA uses a complex system of points called nodes which make a grid called a mesh . This mesh is programmed to contain the material and structural properties which define how the structure will react to certain loading conditions. Nodes are assigned at a certain density throughout the material depending on the anticipated stress levels of a particular area. Regions which will receive large amounts of stress usually have a higher node density than those which experience little or no stress. Points of interest may consist of: fracture point of previously tested material, fillets, corners, complex detail, and high stress areas. The mesh acts like a spider web in that from each node, there extends a mesh element to each of the adjacent nodes. This web of vectors is what carries the material properties to the object, creating many elements. A wide range of objective functions (variables within the system) are available for minimization or maximization: Mass, volume, temperature Strain energy, stress strain Force, displacement, velocity, acceleration Synthetic (User defined) There are multiple loading conditions which may be applied to a system. Next to Figure 3, some examples are shown: Point, pressure (Figure 3), thermal, gravity, and centrifugal static loads Thermal loads from solution of heat transfer analysis Enforced displacements Heat flux and convection Point, pressure and gravity dynamic loads Each FEA program may come with an element library, or one is constructed over time. Some sample elements are: Rod elements Beam elements Plate/Shell/Composite elements Shear panel Solid elements Spring elements Mass elements Rigid elements Viscous damping elements Many FEA programs also are equipped with the capability to use multiple materials within the structure such as: Isotropic, identical throughout Orthotropic, identical at 90 degrees General anisotropic, different throughout Types of Engineering Analysis Structural analysis 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 as in Figure 4. Vibrational 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 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 (Figure 5). Heat Transfer 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 thermoproperties in the material that yield linear heat diffusion. Results of Finite Element Analysis 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. Stress ''=stress ="intensity of internal force at a point " Stress is calculated by dividing the load by the cross sectional area of the test specimen. Strain ''=strain ="percentage deformation of an infinitesimal element " Strain is calculated by dividing the change in length by the original length. Linear and Non-Linear FEA Analysis: A linear FEA analysis is undertaken when a structure is expected to behave linearly. The stress is proportional to the strain, and the structure will return to its original configuration once the load has been removed. A structure is a load bearing member and can normally be classified as a bar, beam, column, or shaft. Conversely, a non-linear FEA is used to predict the behavior of a structure that is loaded beyond the elastic limits of the material of interest. The structure experiences plastic deformation and will not return to its original configuration or shape. Always perform a linear FEA on any structure whose behavior is unknown. A comparison of the stress level in structure and the yield strength of the choice material will determine if a non-linear FEA is required. The results of a linear FEA will be accurate and acceptable if the proper boundary conditions and meshing have been applied. The stress level must be below that of the yield strength of the material. Remember, stress is a function of geometry only while non-linear behavior is a function of stress and material properties. In the event that the stress level is greater than the yield strength of the chosen material, you have three options. First, perform a non-linear analysis to determine the degree of the plastic behavior and its suitability for the application. Second, look for a better material. Third, change your geometry to better manage the stress. Changing boundary conditions and load stiffening may also dictate the use of a non-linear FEA. Contact Finite Element Analysis: Finite Element Analysis, or FEA, is often used in the initial design stages of a new contact. Figure 6 shows the C-209-05.0-X contact with the proper restraints applied. Figure 6. Contact restraint. The green arrows in Figure 6 represent an immovable restraint that is applied to the areas on the contact that will be restrained when inserted into a body. The immovable restraint should be used on every contact because it prevents movement in the X, Y, and Z directions while still allowing rotation in any direction. This is a more accurate restraint method versus using a fixed option. The blue arrows are slider/roller restraints which are used to ensure that the contact pad being used stays normal to the contact when the displacement is applied. The orange arrows are the displacement restraints that are applied to the back side of the contact pad to simulate the force that is applied to the contact beam. These restraints are very important and must resemble the real world application as closely as possible to obtain adequate results. Some other important items to set up prior to running the analysis are to ensure the material for both bodies are set. The contact material should be selected according to the desired choice, and the contact pad should be set to a different material that has a much harder surface to prevent the deflection of the pad's surface from having any effect on the results. Once the material is defined, the contacts/gaps should all be defined. The global contact set must be changed to no penetration to ensure that the pusher and contact are treated as separate entities. The next step is to define a contact set between the contact and contact pad surfaces to ensure there is no penetration and no gap between the two objects. Once the contact is fully restrained and defined, the FEA can be run. Both linear and non-linear studies may be conducted, but it is important to keep in mind that the linear FEA does not account for any permanent set (or yielding) of the material. However, the linear analysis may be performed much quicker and can be used as a tool to check for any setup mistakes. Figure 7 and 8 below show the results from both a linear and non-linear analysis. Figure 7. Linear FEA for C-209-05.0-X contact at 0.014" deflection. Figure 8. Non-Linear FEA for C-209-05.0-X contact at 0.014" deflection. Conclusion: Finite Element Analysis is a very effective tool in designing and analytically testing a contact in the initial stages of development. The correlations between a proper FEA study and finished product has proven to be similar; however, slight mistakes or changes in a FEA model can skew the results. The analysis type (linear and non-linear), restraints, loads, and material selections must be closely monitored to achieve desirable results. BIBLIOGRAPHY An Introduction to the Finite Element Method, J.N. Reddy. Read More