##### 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 *x*_{i} and *x*_{j}, respectively and the field variable values be ɸ_{i} and ɸ_{j}. 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 ...