## Remark

If there is an applied distributed moment m x per unit of beam length, the external energy 13.8 must be augmented with a fQ m x O x dx term. This is further elaborated in Exercises 13.4 and 13.5. Such kind of distributed loading is uncommon in practice although in framework analysis occassionally the need arises for treating a concentrated moment C between nodes. Figure 13.7. The two-node plane beam element with four degrees of freedom. Figure 13.7. The two-node plane beam element with four...

## Exercises

This Chapter begins the exposition of the Direct Stiffness Method DSM of structural analysis. The DSM is by far the most common implementation of the Finite Element Method FEM . In particular, all major commercial FEM codes are based on the DSM. The exposition is done by following the DSM steps applied to a simple plane truss structure. 2.1. WHY A PLANE TRUSS The simplest structural finite element is the bar also called linear spring element, which is illustrated in Figure 2.1 a . Perhaps the...

## Distributed Force On Nodes Finite Element

In many thin structures modeled as continuous bodies the appearance of skinny elements is inevitable on account of computational economy reasons. An example is provided by the three-dimensional modeling of layered composites in aerospace and mechanical engineering problems. A physical interface, resulting from example from a change in material, should also be an interelement boundary. That is, elements must not cross interfaces. See Figure 8.3. In two-dimensional FE modeling, if you have a...