Finite element analysis

(Redirected from Finite element)
Image:FAE visualization.jpg
Visualization of how a car deforms in an asymmetrical crash using 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). There are many finite element software packages, both free and proprietary.

 History

The finite element analysis was first developed in 1943 by Richard Courant, who used the Ritz method of numerical analysis and minimization of variational calculus to obtain approximate solutions to vibration systems. Shortly thereafter, a paper published in 1956 by M. J. Turner, R. W. Clough, H. C. Martin, and L. J. Topp established a broader definition of numerical analysis. The paper centered on the "stiffness and deflection of complex structures". Development of the finite element method in structural mechanics is usually based on an energy principle such as the virtual work principle or the minimum total potential energy principle.

 Use

In its applications, the object or system is represented by a geometrically similar model consisting of multiple, linked, simplified representations of discrete regions—i.e., finite elements on an unstructured grid. 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. 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.

A common use of FEA is for the determination of stresses and displacements in mechanical objects and systems. 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.

 Literature review of finite element analysis

Computer-aided Engineering analysis (CAE) is the application of computer software in engineering to analyze the robustness and performance of components and assemblies. It encompasses simulation, validation and optimization of products and manufacturing tools (Technalysis, 2006). The primary structural application of CAE takes the form of 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 general, there are three phases in any computer-aided engineering task: • Pre-processing – defining the finite element model and environmental factors to be applied to it. • Analysis solver (solution of finite element model) • Post-processing of results (using visualization tools)

Preprocessing

The first step (pre-processing) in using FEA is constructing a finite element model of the structure to be analysed. The input of a topological description of the structures geometric features is required in most FEA packages (Hieronimus, Klaus 1977). This can be in either 1D, 2D or 3D form, modelled by lines, shapes or surfaces representation respectively. The primary objective of the model is to realistically replicate the important parameters and features of the real model (Hieronimus, Klaus 1977). The simplest mechanism to achieve modelling similarity in structural analysis is to utilise pre-existing digital blueprints, design files, CAD models and/or data by importing that into a FEA environment. Once the finite element geometric model has been created, a meshing procedure is used to define and break the model up into small elements. In general a finite element model is defined by a mesh network, which is made up of the geometric arrangement of elements and nodes. Nodes represent points at which features such as displacements are calculated. FEA packages such as ANSYS use node numbers to serve as an identification tool in viewing solutions in structures such as deflections. Elements are bounded by sets of nodes, and define localised mass and stiffness properties of the model. Elements are also defined by mesh numbers which allow reference to be made to corresponding deflections or stresses at specific model locations (Hieronimus, Klaus 1977).

Analysis (computation of solution)

The next stage of the FEA process is analysis. The FEM conducts a series of computational procedures involving applied forces, and the properties of the elements which produces a model solution. Such a structural analysis allows the determination of effects such as deformations, strains, and stresses which are caused by applied structural loads such as force, pressure and gravity.

Visualisation

These results can then be studied using visualisation tools within FEA environment to view and to fully identify the implications of the analysis. Numerical and Graphical tools allow the precise location of data such as stresses and deflections to be identified.

Applications of FEA to the mechanical engineering industry

A variety of specialisations under the umbrella of the mechanical engineering discipline such as aeronautical, biomechanical and automotive industries all commonly utilise the benefits of integrated FEA in the design and development of their products. Several modern FEA packages include specific components such as thermal, electromagnetic, fluid and structural working environments. In a structural simulation FEA helps tremendously in producing stiffness and strength visualisations and also in minimising weight, materials and costs. FEA allows detailed visualisation of where structures bend or twist, and indicate the distribution of stresses and displacements. FEA software provides a wide range of simulation options with regards to controlling the complexity of both the modelling and the analysis of a system. Similarly, the desired level of accuracy required and the associated computational time requirements can be managed simultaneously to cater for most engineering applications. FEA allows entire designs to be constructed, refined and optimised before the design is actually manufactured. This powerful design tool has significantly improved both the standard of engineering designs and the methodology of the design process in many industrial applications (Hastings 1985). The introduction of FEA has substantially decreased the time taken to get products from concept to the production line (Hastings 1985). It is primarily through improved initial prototype designs using FEA that the testing and development stages have been accelerated (McLaren-Mercedes – 2006). In summary, the benefits of FEA 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 (Hastings 1985).

Computer aided design and finite element analysis in industry

The ability to model a structural system in 3D can provide a powerful and accurate analysis of almost any structure. 3D models in general, can be produced using a range of common computer aided design (CAD) packages. Models have the tendency to range largely in both complexity and in file format depending on 3D model creation software, and the complexity of the model’s geometry. FEA is a growing industry in product design, analysis and development in engineering. The trend of utilising FEA as an engineering tool is growing rapidly. The advancement in computer processing power, FEA and modelling software has allowed the continued integration of FEA in the engineering fields of product design and development. In the past, there have been many issues restricting the performance and ultimately the acceptance and utilisation of using FEA in conjunction with CAD in the product design and development stages. The gaps in compatibility between CAD file formats and FEA software limited the extent to which companies could easily design and test their products using the CAD and FEA combination respectively. Typically engineers would use specialist CAD and modelling software in the design of the product and then wish to export that design into a FEA package to test. However, those engineers who depended on data exchange through custom translators or exchange standards such as IGES or STEP cite occasional reliability problems causing unsuccessful exchange of geometry (Marc Halpern 1997). Thus, the creation of many models external to FEA environments was considered to be problematic in the success of FEA.

The current trend in FEA software & industry in engineering has been the increasing demand for integration between solid modelling and FEA analysis. During product design and development engineers require automatic updating of their latest models between CAD and FEA environments. There is still a need to improve the link between CAD and FEA making them technically closer together. However the demand for unitary CAD-FEA integration coupled with the improved computer and software developments has introduced a more robust and collaborative trend where compatibility problems are beginning to be eliminated. Designers are now beginning to introduce computer simulations capable of using pre-existing CAD files, without the need to modify and re-create models to suite FEA environments. (Marc Halpern 1997).

Current FEA trends in industry

Dynamic modelling

There is increasing demand for dynamic FEA modelling in the heavy vehicle industry. Many heavy vehicle companies are moving away from traditional static analysis and are employing dynamic simulation software. Dynamic simulation involves applying FEA in a more realistic sense to take into account the complicated effects of analysing multiple components and assemblies with real properties. Typical dynamic FEA used on components and assemblies is named Multi-body simulation (MSS) or Mechanical event simulation (MES).

Modelling assemblies

Dynamic simulation, used in conjunction with assembly modelling, introduces the need to fasten together components of different materials and geometries. Therefore, CAE tools should have comprehensive capabilities to easily and reliably model connectors, including joints that allow relative motion between components, rivets, and welds. Typical MSS models are composed of rigid bodies (wheels, axles, frame, engine, cab and trailer) connected by idealised joints and force elements. Joints and links may be modelled as either rigid links, springs, or dampers in order to simulate the dynamic characteristics of real truck components (Chee Kong Teo 2002). Force transfer across assembly components through connectors, makes them susceptible to high stresses. It is simpler and easier to idealize connectors as rigid links in these systems. This idealization provides a basic study of assembly behaviour in terms of understanding system characteristics; engineers must model joining parameters like fasteners accurately when performing stress analysis to determine how failures might take place (Marc Halpern 1997). “Representing connectors as rigid links assumes that connectors transfer loads across components without deforming and undergoing stress themselves. This unrealistic idealization yields incorrect predicted stresses in the regions local to the connectors, the exact locations where part failures will most likely initiate” (Marc Halpern 1997). Understandably, the detailed inclusion of every connection point and/or mechanism in an assembly is impractical to model (Marc Halpern, 1997). Therefore, improved representations of fasteners that are simple to use yet reliable should be investigated for use on a case by case basis (Marc Halpern, 1997).

Current modelling techniques in industry

Engineers at Leyland Trucks currently model their trucks using specialist dynamic FEA software. Each model contains a flexible body and chassis, springs, roll bars, axles, cab and engine suspension, the steering mechanism, and any frequency-dependent components such as rubber mounts. Extra details such as brakes, and out of balance engine forces can be included on an as ‘needed basis’ (FEA Information 2005).

Dynamic FEA simulation enables a variety of manoeuvres to be accurately tested. Tests such as steady-state cornering, roll over testing, lane changing, J-turns, Vibration analysis, collisions and straight line braking can all be conducted accurately using Dynamic FEA. Non-linear and time varying loads allow engineers to perform advanced realistic FEA enabling them to locate critical operating conditions and determine performance characteristics.

As a result of the improved dynamic testing capabilities engineers are able to determine the ultimate performance characteristics of the vehicle’s design without having to take physical risks. As a result of dynamic FEA the need for expensive destructive testing has been lessened substantially. (FEA Information 2005).

FEA and the truck industry

The truck industry is becoming more like other industries such as the automotive industry with regard to FEA’s involvement in the design process (FEA Information 2005). However due to the unique need by truck manufacturers to provide a variety of different body configurations, it is unlikely that trucks will ever move to the unitary streamlined FEA integration process, as seen in the automotive industry (FEA Information 2005). The design process hasn’t reached the required level of maturity where it can be simulation-driven. Further more the traditional design philosophy of the tried and tested truck designing techniques taking precedence is still held strong across the truck industry (FEA Information 2005). Although the industry remains far from adopting a complete bottom-up FEA integrated design process, FEA is fast increasing its role in product design and development in the truck industry.

References

• (McLaren-Mercedes – 2006) - http://www.mclaren.com/features/technical/stress_to_impress.php, viewed 3 October 2006.
• Hastings, J. K., Juds, M. A., Brauer, J. R., “Accuracy and Economy of Finite Element Magnetic Analysis”, 33rd Annual National Relay Conference, April 1985.
• Marc Halpern, Industrial Requirements and Practices in Finite Element Meshing: A Survey of Trends 1997, http://www.imr.sandia.gov/papers/imr6/halpern97.ps.gz.
• (Chee Kong Teo, Masters Thesis, Sensitivity Study Of A Truck Chassis, Mississippi State University, Department of Mechanical Engineering, December 2002).
• Grube, Kris W., “A Process for Investigating Geometric Sensitivity and Optimization of a Vehicle Structure,” Ford Research Publication EM-89-1989.
• Hieronimus, Klaus, “A Few Aspects on the Development of Structural Models,” SAE Technical Paper 770598, 1977.
• FEA Information , August 2005 edition, www.FEAinformation.com, , viewed 3 September 2006