So far, we have discussed about smart beams with embedded sensing and actuation having simple boundary conditions. In order to model complex beam, with composite cross section and generalised boundary condition. We need to develop a smart beam element by using F.E. technique. In this lecture, we will develop the same.

The analysis and design of smart laminated beams and plates with general geometric shapes require the use of powerful approximate techniques and the FEM is highly attractive for this purpose, particularly when actuating and sensing patches are to be modeled. A number of finite elements in this direction are being introduced. In this lecture, a simple 6 DOF laminated beam element with embedded piezo / magnetostrictive layer has been presented for beam analysis. The proposed 6 DOF smart finite element model is shown in fig. 40.1.

Figure 40.1: 6 DOF smart finite element model

The beam is divided into a number of sub domains called elements, and in each sub domain, the displacement field is assumed as

	(40.1)
	(40.2)

 where  is the nodal displacement vector given by:

(40.3)

and the shape functions are given by;