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FINITE ELEMENT METHODINTRODUCTIONMethods of engineering analysisTo achieve the above objectives, the analyst has at his disposal three distinct approaches: Analytical methods; Experimental techniques and Numerical methods.Analytical methods provide quick closed form solutions. But, they treat only simple geometries and idealized support and loading conditions. Using experimental techniques, scaled models or prototypes can be tested. This approach is costly both in terms of the model, instrumentation, test facilities and the actual test itself. Numerical methods require very few restrictive assumptions; it can treat complex geometries and realistic support and loading conditions. They are far more cost effective than experimental techniques.

The current interest in the engineering community on the development and application of computational tools based on numerical methods is thereby justified. This in fact was the motivation to develop the most versatile numerical method, namely, the finite element method (FEM).The goal of analysis is to verify a design prior to manufacture. While there are several methods of engineering analysis, the most comprehensive is the finite element analysis (FEA).The finite element method is essentially dependent for its success on the skillful use of digital computers. The method is put in the hands of professional engineers in the form of general-purpose programs.It is in general possible to use the FEM to provide accurate numerical solutions to almost any mathematical problem or mathematically modelled physical problem in diverse fields like solid mechanics, mechanics of composites, fluid dynamics, heat transfer, etc. Many continuum mechanics problems arise in engineering and these are usually posed by appropriate differential equations and boundary conditions to be imposed on unknown functions. All such problems can also be dealt with by FEM.Engineering AnalysisObjectives of engineering analysisDuring the design and development of a product (as an assemblage of parts), the analyst is quite often required to: calculate the displacements at certain points;calculate the entire distribution or displacement field; determine the stress distribution and hence predict strength;determine the natural frequencies and associated modes of vibration;determine the critical buckling loads and the associated mode shapes; predict and plot forced vibration response;predict and plot transient response;predict temperature distribution and hence thermal stress distribution; predict crack growth, residual strength and fatigue life; predict velocity, pressure and temperature distribution in fluids; study fluid-structure interactions (hydro-elasticity, aero-elasticity, etc.); study nonlinear effects (geometric and material nonlinearities);determine electric and magnetic fields, and many more

The finite element method (FEM), sometimes referred to as finite element analysis(FEA), is a computational technique used to obtain approximate solutions of boundary value problems in engineeringINTRODUCTION TO FEMDefinitions of Mechanics in dictionaries usually state two flavors:The branch of Physics that studies the effect of forces and energy on physical bodies.The practical application of that science to the design, construction or operation of material systems or devices, such as machines, vehicles or structures.These flavors are science and engineering oriented, respectively. But dictionaries are notoriously archaic. For our objectives it will be convenient to distinguish four flavors:

FEM Variants

The FEM Analysis Process