# Introduction to the Finite Element Method

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### Additional excerpts

...Models can frequently be acquired through discretizations such as the common nite di erence and nite element approaches [1]....

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### Cites methods from "Introduction to the Finite Element ..."

...Accordingly, emphasis will be given to formulations and solution techniques which are well suited to general-purpose numerical methods for solving elasticity problems on complex configurations, in particular the finite element method [28, 125] and the boundary element method [23, 40]....

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### "Introduction to the Finite Element ..." refers background in this paper

...4 where integration points are numbered as (1)....

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...With shape functions, any field inside element is presented as: u(ξ) = ∑ Niui , i = 1, 2, 3 At nodes the approximated function should be equal to its nodal value: u(−1) = u1 u(0) = u2 u(1) = u3 Since the element has three nodes the shape functions can be quadratic polynomials (with three coefficients)....

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...The shape function N1 can be written as: N1 = α1 + α2ξ + α3ξ(2) Unknown coefficients αi are defined from the following system of equations: N1(−1) = α1 − α2 + α3 = 1 N1(0) = α1 = 0 N1(1) = α1 + α2 + α3 = 0 The solution is: α1 = 0, α2 = −1/2, α3 = 1/2....

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867 citations

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