Finite Element Method with Applications in Engineering

6.2 LINEAR SPRING

The linear spring–the simplest kind of line element–is considered first because it provides a simple, yet generally instructive, tool to illustrate the basic concepts of the FEM. For the illustration, consider the two spring assemblage as shown in Figure 6.1.

It is required to calculate the displacements at points (nodes) B and C, force each spring and for the reaction at A by employing FEM.

This problem can be solved by following the steps outlined in Chapter 4.

Step 1: Discretize and select element types

The two spring assemblage shown in Figure 6.1 is discretized by employing two-node spring elements, as shown in Figure 6.2(a).

The discretized model has three nodes–two externally applied nodal forces F₂ = F_B and F₃= F_c, and ...