## ABSTRACT

Derivations of the BCM and HBCM, for 3-D linear elasticity, together with representative numerical results for selected problems, are presented in this chapter.

A regularized form of the standard boundary integral equation (Rizzo [141]), for 3-D linear elasticity (see equation (1.26) in Chapter 1), is:

0 = ∫ ∂B

[Uik(x,y)σij(y)− Σijk(x,y){ui(y)− ui(x)}] ej · dS(y)

≡ ∫ ∂B

Fk · dS(y) (4.1)

Here, as before, ∂B is the bounding surface of a body B (B is an open set) with inﬁnitesimal surface area dS = dSn, where n is the unit outward normal to ∂B at a point on it. The stress tensor is σ, the displacement vector is u and ej(j = 1, 2, 3) are global Cartesian unit vectors. The BEM Kelvin kernels are written in terms of (boundary) source and ﬁeld points. These are given in Chapter 1 as equations (1.22) and (1.18), respectively.