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Running head: FINITE ELEMENT ANALYSIS 1 Finite Element Analysis Student’s Name Institutional Affiliation
FINITE ELEMENT ANALYSIS 2 Finite Element Analysis Introduction Introduction and Background of Finite Element Analysis The Finite Element Analysis (FEA) or Finite Element Method (FEM) denotes a numerical technique for identifying solutions to problems in mathematical physics and engineering. Often, FEA is vital to findings solutions for complex material, loading, and geometric properties. Precisely, the complex nature of mathematical and engineering problems involves analytical alternatives that cannot be obtained. The finite element technique has served as one of the most convenient and well-established approaches for the computation of complex problems in diverse engineering fields. Today, the application of FEA or FEM has occurred in fields such as geo-mechanics, heat conduction, hydrodynamics, biomedical engineering, nuclear engineering, mechanical engineering, and civil engineering. Mathematically, FEA is a powerful technique for the approximation of differential equations associated with various physical processes. FEA relies on some principal concepts that have defined its success since its introduction over the years. Barkanov (2001) observes that the success of the finite element method is founded primarily on the common procedures for calculating finite elements. FEA success procedures include problem formulation in diverse forms, discretization of the finite element from the problem formulation, and the effective solution of the final equations modelled for the finite element. Historically, the development of FEM occurred in 1909 when Ritz created an effective technique to approximate the solution of problems linked to the mechanics of distorted solids. Ritz technique entailed an approximation of the functional energy by comparing the unknown functions with known functions. Developments to the Ritz method occurred in 1943
FINITE ELEMENT ANALYSIS 3 when Courant introduced the unique linear functions outlined over triangular areas. Courant applied the enhanced technique to find the solution to problems associated with torsion. Significant transformations to the Ritz and Courant’s methods have happened over time, with the diversification of FEA taking place in 1960 when potentials of computers emerged to handle massive volumes of calculations. Use of computer programmes in Finite Element Analysis and Civil Engineering Problems (for example, modelling of structures) Technological advancements in computers and the power of computing by the use of various software, have offered unique techniques to identify numerical solutions to previously technical problems in finite element analysis. Accordingly, specialized computer software for FEA has offered a way to perform structural design and analysis in the civil engineering sector (Shaikh, 2012). The FEA software outcomes provide the designer and engineer with comprehensive insights into the distributions of strain and stress associated with a specific
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