The Basic Principle of Finite Element Analysis - Case Study Example

1. Describe, with images, the basic principle of finite element analysis to include Elements, Meshing and Results Finite element analysis is an approximate method that involves discretising the entire problem domain into finite elements and later combining the element properties to obtain a global solution. The global system is analyzed by incorporating the boundary conditions to get the required solution (Cooks et al, 1989). Finite element analysis uses a network of grids obtained from connecting several points called nodes specified on the problem body or surface. These grids are called as meshes. The characteristics about the materials and its properties are programmed in the meshes which will be used to determine the system behavior under externally imposed conditions. The distribution of meshes is based on the type of the problem. If a location requires very refined analysis this region could have very fine meshes (Widas, 1997). A typical finite element application is shown as below. Here, the finite element model of the problem is shown in figure 1. The material is divided into small triangle shaped elements and hence it can be said that the body is meshed using triangular elements. Figure 1 (http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/num/widas/history.html) The FEA software consists of different type of elements that could be used in the analysis. The element refers to the geometrical shapes that are used to mesh the system. Some of the types of elements used usually used are rod elements, beam elements, plate/shell/composite elements and Solid elements Elements ; the different type of elements used for the finite element analysis is (i) Linear bar element : These elements have only linear dimension and is used to represent with nodes representing one unknown. Quadratic bar element: These elements are used to represent more complex curvatures. (ii) Rectangular element / Bilinear element (iii) Triangular element Meshing The process of dividing the problem element into the fine grids is known as meshing. The mesh would consist of similar elements or combination of different elements. Like for a irregular body the using square or rectangular elements might be useful in proper division of the domain space into small elements. This disadvantage shall be overcome by different type of elements like triangular elements to wards the boundary or irregular side for proper geometrical matching between the finite element model and the actual physical body. Another important aspect that need to be considered is the size of meshes that are used for the process of discretisation. The size of meshes could be course , large and well spread, or fine , small size and closer placed. The choice of the size depends on variery of factors. The type of the element chosen for a particular problem, nature of the variation of the unknowns, computational efficiency etc. For example, the choice between linear bar element and quadratic bar element is based on the experience of the analyst. Problems might require few number of complex elements or larger number of simpler element no strict guideline exist in this aspect. The experience gained from analysis would be the prime factor that would help in the proper choice of elements for a particular type of problem (Chandrupatla and Belegundu, 2007) Results All finite element computations would result in the be The element stiffness matrix in all cases would be of the form The equation is used to construct the element level matrices for the particular problem. The size of the matrix would depend on the type of the element chosen. For linear bar element with one unknown at each node the size of the matrix is 2 2. While for a bilinear element like rectangle with two unknowns at each node the size of the matrix would be 8 8. The element matrices hence formed shall be combined to get the global equations with appropriate boundary conditions incorporated in it. The equations are hence solved using any standard solver. The results obtained as presented using any post processing software attached to the finite element packages for better appreciation of the results (Cooks et al, 1989). 2. Describe, with images, how FEA software might be used in industry. What type of companies use FEA and what components or systems are commonly modelled using FEA Finite elements are used in the every analysis of engineering industry. Though it started as a tool to analyze structural system the application of finite elements have been spread to almost every field of engineering. Most of the applications in design are handled by finite element softwares that are either proprietary or free ware. The major industrial applications that illustrate the use of FEA software are given below. Finite Element Analysis is a numerical tool that helps to analyze the engineering problems relevant to all the major streams in engineering. It is widely used in civil, mechanical, electrical, aerospace, pollution studies, heat and mass transport, chemical, biomechanics etc. The important specific applications where finite element is widely used as given as follows. Construction Industry: A major area that depends on FEA in construction industry is the design process. The design of structural elements in high rise buildings, bridges, towers , tunnels etc demands accurate determination of stresses and hence, their safety levels. In addition, the other areas like water and wastewater treatment, soil engineering solutions , design of dams, design of pavements etc are the other significant area in construction sector that require finite element analysis. Large number of Finite Element softwares are currently in use to address these issues that claim specific advantages. A few images related to soil stress variation (Figure 21) and stress variation in bridge deck (Figure 3) illustrates how FEM is used in the construction and related industries. Figure 2 - Results of soil analysis using midas software (http://eng.midasuser.com/gts/experience/feel_02.asp) Figure 3 Deign of Bridge Deck ((http://www.lusas.com/case/composite/bridgedeck.html) Aerospace Industries The aerospace engineering involves design of complex elements of aircrafts, space crafts and other systems. This involve considering different parameters like load factors, atmospheric factors etc simultaneously in the analysis. Thus these type of analysis demands the use of sophisticated computational tools like Finite Element analysis. Figure 4 shows the details of finite element analysis undertaken for the wing tail section of the aircraft. The colours indicated show the variation of stresses under certain operating conditions. Figure 4 Design of wing tail using FEM (http://www.lusas.com/case/composite/wingsail.html) Pollution Control industries Environmental sustainability is an important component in all the development initiatives. Among this design for pollution reduction is important factor in all the engineering designs. Finite element analysis is used for designing the nest configuration to meet the above objectives. Figure 5 gives the images of such exercises undertaken to design the emission control from the vehicles. Figure 5 : Design of emission reduction system http://www.lusas.com/case/analyst/arvin.html) Design of Machines The design of machines is an major segments that involves considering variety of factors ranging from selection proper material to reliability of operation. The application is spread across different industrial segments like Automobile, heavy engineering, agro-machinery and processing industries. The finite element technique applied to decide on the power of machines, evaluate its performance characteristics, wear and tear etc. One such situation, where Finite element analysis is used in the design process is used is shown in figure 6. Figure 6 Finite Elements in Machine Design (http://www.lusas.com/case/analyst/engine.html) Biomechanics Replacing the body parts with artificial materials has become a common practice in the medical arena. This was made possible because of advancement of both computational science and material science. The Finite element method is used to analyze the stress level, material compatibility and its ideal geometry. An application where the FEM is used is to design the hip joint 3. Identify strengths and weaknesses of CosmosWorks. Describe your experiences with the software. ComosWorks is the standard software kit available along with the solid works modeling software. The software is an excellent tool for students to appreciate the engineering behavior of the designs created by them. The Cosmosworks is capable to generate the results of stresses or heat distribution pattern from a mechanical system that is modelled using Solidworks (Soildworks, 2008). This has helped me to appreciate my intuitions significantly in the design of the system by creating preliminary 3 dimensional models in solid works. Also, The Cosmosworks have helped me to realize how the system would, perform under normal operating conditions and also assess its reliability under extreme conditions. Thus redesign could be undertaken to eliminate the design drawbacks and finally arrive at the most acceptable design of the unit. Strengths of Cosmos works Ability to undertake the design checks on the parts designed using the Solid works. It is capable to undertake the real time analysis of the designs and hence a better perception on the component or material design process is possible. The safety of the designed components is an important part in engineering. Using the Cosmos works the factor of safety could be appropriately computed and decisions to augment designs could be undertaken easily. Real time simulations of the designs helps to gain a deeper level of understanding on the working aspect and our intuitive sense on designs could be improved upon significantly. Weakness of Cosmos works It would not help us to understand the actual mechanics involved in the design process. The process of analysis carried out is not available and hence need to be satisfied with the final outputs. Is more suitable for a design professional rather than a reach based learning of finite elements. Reference Chandrupatla, T R and Belegundu, A D (2007) , Introduction to finite elements in engineering, Pearson Prentice hall, Cooks, R D, Malkus, D S and Plesha, M E, (1989) Concepts and applications of finite element analysis, John Wiley and Sons. Cosmosworks (n.d.), Engineering analysis with cosmosworks professional, Retrieved on 6 March 2009 from Lucas (n.d.a) Composite wing sail design, case study Retrieved on 5 March 2009from from < http://www.lusas.com/case/composite/wingsail.html> Lucas b (n.d.b) Faster vibration analysis of automotive exhaust systems Retrieved on 5 March 2009 from Lucasa (n.d.c) Engine design Retrieved on 5 March 2009 from < http://www.lusas.com/case/analyst/engine.html> Solidworks (2008), Real solutions, Retrieved on 6 march 2009 from < http://www.solidworks.com/sw/products/cad-software-mechanical-engineering.htm> Midas (n.d), Geotechnical and Tunnel Analysis system, Retrieved on 5 March 2009 from < http://eng.midasuser.com/gts/experience/feel_02.asp>. Widas, P (1997), Introduction to finite elements, Retrieved on 6 March 2009 from Read More