FINITE ELEMENT ANALYSIS
Assignment 01 INTRODUCTION TO FEA, PAST PRESENT AND FUTURE OF FEA
Introduction:
Literally finite element analysis (FEA) sometimes referred as finite element method (FEM) means; Finite
: limited in size or number.
Element: small part of something. Analysis: detailed examination of something in order to interpret or explain it. FEA is a suitable implement to analyze simple as well as complex structures. Generally the real world engineering domains are very complicated to solve by analytically, because of irregular as well as asymmetrical geometries and due to complex loading and the environmental condition. A basic theme of the FEA is to divide the domain into many smaller and geometrically simpler simpler form called elements. Dividing the domain into smaller regions called elements, which are predefined shapes. shapes. The elements are are connected at the nodes. Nodes are are the selected finite points at which basic unknowns are to be determined. FEA is numerical method to handle complex geometry, any boundary conditions and material properties. The basic concept is to assume an approximate solution that satisfies the governing differential equation and boundary conditions. The whole idea is to get this assumed or approximate solution as close to the exact solution as possible. Basic steps in FEA:
General steps in formulating a FEA of a physical problem are common to all such analysis, whether structural, heat transfer, fluid flow or some other. In this section, a concise account of general steps in FEA with reference to a structural problem is given given After defining the geometric domain of the problem R. V. Bammankatti [Asst. Prof. Mechanical Eng. Dept.]
SGMCOE Mahagaon
FINITE ELEMENT ANALYSIS
1] Discretization of the domain 2] Selection of a proper displacement model (or interpolation model) 3] Derive the elemental stiffness matrix 4] Assemblage of elemental stiffness matrix to form global stiffness matrix 5] Solve to obtain nodal displacement i.e. field variables 6] Computation of elemental strains and stresses For Software packages
The general process of FEA by using software is divided into three main phases i.e. preprocessor, processor or solution and postprocessor. These steps are incorporated in commercial finite element software packages. Preprocessor The preprocessor phase allows the user to create or input CAD geometry, and provides the tools for meshing the geometry, support conditions, applying loads and material properties. The most crucial step in the finite element modelling process is the choice of elements and the discretization of the domain. Understanding of the basic engineering principles is very vital at this stage. Processor or solver During the solution phase, it starts with initializing global stiffness matrix and load matrix. Then element loop is entered to assemble element stiffness matrix. When element loop is completed global stiffness matrix is available. The next step in processing is to impose the boundary conditions. Now, the stiffness equations are ready. Standard solution package is used to solve the equation to get nodal variables. Special solution techniques are used to reduce data storage requirements and computation time. For static, linear problems, a wave front solver, based on Gauss elimination, is commonly used. Postprocessor
R. V. Bammankatti [Asst. Prof. Mechanical Eng. Dept.]
SGMCOE Mahagaon
FINITE ELEMENT ANALYSIS
The post processor takes the data from the solver and presents it in a form that the user can understand i.e. numerical values and also the counter plots, graphs etc. Here, the analyst checks the validity of the solution
While solution data can be manipulated many ways in postprocessing, the most important objective is to apply sound engineering judgment in determining whether the solution results are physically reasonable. Applications of FEA:
The range of applications of finite elements is too large to list, but to provide an idea of its versatility we list the following: Structure analysis: bridge analysis, valves, pipes, pressure vessels, Solid mechanics: stress analysis of a gear, a automotive power train, automotive engines and aircraft Dynamics: vibration of Sears Tower, earthquake, bullet impact, seismic analysis of dams, power plants, cities and high-rise buildings, crash analysis of cars, trains and aircraft Thermal analysis: heat radiation of finned surface, thermal stress brake disc, fluid flow analysis of coolant ponds, pollutants and contaminants, and air in ventilation systems Electrical analysis: Piezo actuator, electrical signal propagation, electronic chips, electric devices, electromagnetic analysis of antennas, transistors and aircraft signatures Biomaterials: human organs and tissues, analysis of surgical procedures such as plastic surgery, jaw reconstruction, and many others
.Advantages and disadvantages of FEA Advantages
1] FEA can handle any complex geometry and loading conditions for analysis.
R. V. Bammankatti [Asst. Prof. Mechanical Eng. Dept.]
SGMCOE Mahagaon
FINITE ELEMENT ANALYSIS
2] The FEA and its generalizations are the most powerful computer oriented method ever devised to practical engineering problems. 3] FE formulation and development of codes are possible. Disadvantages
1] FEA cannot provide closed form solution. 2] Users are usually highly qualified (education wise) with high computer proficiency.
History of FEA: Past of FEA
The origin of the modern FEA may be traced back to the early 1900’s and has been developed and imposed since then. A few major milestones are as follows. 1906: Civil engineering applications, structures analyzed by 1D beams. 1909: Ritz- Variational method- used trial functions to approximate solutions of differential equations. 1915: Galerkin- Weighted residual- provides very strong basis for FEM. 1940’s: R. Courant: introduced the concept of piecewise continuous functions in a subdomain, did the mathematical foundation for present form of FEM. He obtained approximate solution to vibration problems. 1950’s: Argyris, Kelsey, Turner- Direct continuum elements, aerospace industry engineers formulated stiffness equations of 100 degree of freedom problem was supposed to be very large at that time. They also published paper on ‘’ stiffness and deflection of complex structures’’. The formal presentation of FEM is attributed to Turner, Clough, martin and Topp (1956), who during 1952- 1953 succeeded to directly derive the stiffness of a rectangular panel at Boeing. R. V. Bammankatti [Asst. Prof. Mechanical Eng. Dept.]
SGMCOE Mahagaon
FINITE ELEMENT ANALYSIS
1960’s: Clough: The term ‘Finite element’ was first used by Clough (1969) 1963: R. J. Melosh: who systematized the Variational derivation of stiffness matrices and recognized that FEA is Rayleigh- Ritz method applied on small size elements. 1964- 1980: Major contributions are due to Bruce M. Irons, the inventor of isoparametric models, shape functions, frontal solvers and the patch test. 1967: The first book devoted to FEA was written by O. C. Zienkiewicz. Present of FEA
FEA can be applied to almost any type of analysis. This generality and numerical efficiency is major consideration for programmers when they decided which method to use in commercial software. The FEA delivers that versatility and efficiency and for this reason, has dominated the market of commercial analysis software. CAE groups get job orders like design analysis, optimization, failure analysis, NVH analysis etc... Present day many universities introduced this programme in undergraduate and post graduate courses as part of curriculum. Future of FEA
Research related to solution techniques in future focus will be mainly towards reducing time, improving quality and flow pattern of mesh generated by auto meshing. For reducing meshing time apart from conventional types of elements, research is also going on about polyhedral meshing and mesh less or mesh free analysis. Advantage of the polyhedral meshing could be described as less meshing time with higher accuracy and that too at less number of degree of freedom. In short it combines advantage of tetra and hex elements, but at the moment it would be too early to answer whether polyhedral mesh would be a regular feature of structural as well other types of analysis also.
R. V. Bammankatti [Asst. Prof. Mechanical Eng. Dept.]
SGMCOE Mahagaon
