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from the problems described earlier for embedded or attached sensors. In his study, he<br />

has found that the electrical resist<strong>an</strong>ce method is only particularly effective for detecting<br />

small <strong>an</strong>d subtle defects in composite materials <strong>an</strong>d in joints.<br />

Based on the above literature, SHM c<strong>an</strong> be summarised as the acquisition of<br />

information to enable the diagnosis <strong>an</strong>d prognosis of <strong>structural</strong> integrity <strong>an</strong>d the ultimate<br />

objective is to continuously monitor <strong>an</strong>d assess the status of the integrity of a structure<br />

or its components with a high level of confidence <strong>an</strong>d reliability. Each of the techniques<br />

has its own adv<strong>an</strong>tages <strong>an</strong>d disadv<strong>an</strong>tages. Therefore, selection of the right sensors to be<br />

used for the right application will ensure the success of the SHM. Having described the<br />

full definitions <strong>an</strong>d concepts of SHM, FEA <strong>an</strong>d experiments that have been used as <strong>an</strong><br />

<strong>integrated</strong> approach to the diagnosis <strong>an</strong>d prognosis of the composite based pipeline<br />

repair will be discussed in the following sections.<br />

2.7 Introduction to Finite Element Analysis (FEA)<br />

FEA (also known as the method) has been successfully used for m<strong>an</strong>y years in<br />

the <strong>an</strong>alysis of complex structures (Walz et al., 1968) <strong>an</strong>d historically, it was first<br />

developed in the 1940s by Alex<strong>an</strong>der Hrennikoff <strong>an</strong>d Richard Cour<strong>an</strong>t. During this<br />

period it was called the finite-element method. In 1965 the first finite-element software<br />

was created by NASA <strong>an</strong>d it was called NASTRAN. At present, there are m<strong>an</strong>y types of<br />

<strong>structural</strong> <strong>an</strong>alysis software on the market. Some of these br<strong>an</strong>ds include: ALGOR,<br />

ANSYS, ABAQUS <strong>an</strong>d MARC (Knoxville, 2009).<br />

The Finite Element is a numerical technique for finding approximate solutions<br />

for partial differential equations (PDEs) as well as for integral equations. The solution<br />

approach is based either on eliminating the differential equation completely (steady<br />

state problems), or rendering the PDE into <strong>an</strong> approximating system of ordinary<br />

differential equations, which are then numerically <strong>integrated</strong> using st<strong>an</strong>dard techniques<br />

such as Euler's method, Runge-Kutta, etc. (Gilbert <strong>an</strong>d Fix, 1973). The major sources of<br />

error resulting from the use of finite element methods are round-off error <strong>an</strong>d<br />

42

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