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Finite Element Method with Applications in Engineering by T. L. Eldho, Y. M. Desai

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5.3 ONE-DIMENSIONAL ELEMENTS

Generally, line elements are used with different order of interpolation function for one-dimensional finite element modelling. Various properties of linear line elements and related interpolation functions are discussed in this section.

5.3.1 Line Element: Linear Interpolation Function

As discussed earlier, line element is used to discretize one-dimensional problems. Let the field variable ɸ be a function of x, i.e., ɸ = ɸ(x). Let B and D be the points on the x-axis with co-ordinates xi and xj, respectively and the field variable values be ɸi and ɸj. It is required to evaluate the value of ɸ at any point between B and D. Let the co-ordinate of point G be x, where the ɸ value is to be determined. From geometry in ...

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