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First Step of Finite Element Method!!!

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 The first step to Finite Element Method (FEM) is " Problem Formulation. Three fundamental steps of   Finite Element Method (FEM) Divide the whole domain into parts i.e. subdomains or elements.                                                                   Over each element (part) , seek an approximation to the solution as a linear function or combination of nodal values and approximate function, and drive the algebraic relations among the nodal values of the solution over each element.                                                                                         Assemble the elements and obtain the solution to the whole. Basic Features of   Finite Element Method (FEM) FEM can handle any engineering science problem whose physical phenomenon can be described by equation of calculus basically in the form of normal differential equations with any irregular geometry, non-uniform loading & non-linear properties.            FEM based general purpose software can be deve

History of Finite Element Method

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 History of Finite Element Method In 1906 , first time a structural problem related to civil engineering application was solved using 1-D beam  by hand calculation.  In 1909, Ritz developed a  direct method  to find an approximate solution for  boundary value  problems. It converts the often insoluble differential equation into solution of a matrix equation.  This method is also known Ritz's variation principle and the Rayleigh-Ritz principle. In 1915,  Galerkin published an article in which he put forward an idea of an approximate method for  differential equations , in particular  boundary value problems .  A method for approximating the solution to a problem in  weak form .  In 1943, Courant used the piecewise approximation to an assemblage of triangular elements to study the St. Vanant torsion Problem.  (formed the basis of Mathematical model of FEA) In 1950 , Aerospace industry engineers formulated stiffness equations. In 1960 , Clough was the first used the term "Finite

Finite Element Method (FEM) or Finite Element Analysis (FEA) !!!

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Finite Element Method (FEM)  Or  Finite Element Analysis (FEA)